A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

PubMed

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Application of technology developed for flight simulation at NASA. Langley Research Center

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1991-01-01

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations including mathematical model computation and data input/output to the simulators must be deterministic and be completed in as short a time as possible. Personnel at NASA's Langley Research Center are currently developing the use of supercomputers for simulation mathematical model computation for real-time simulation. This, coupled with the use of an open systems software architecture, will advance the state-of-the-art in real-time flight simulation.

Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude.

PubMed

Zamora-Chimal, Criseida; Santillán, Moisés; Rodríguez-González, Jesús

2012-10-07

In this paper we introduce a mathematical model for the tryptophan operon regulatory pathway in Bacillus subtilis. This model considers the transcription-attenuation, and the enzyme-inhibition regulatory mechanisms. Special attention is paid to the estimation of all the model parameters from reported experimental data. With the aid of this model we investigate, from a mathematical-modeling point of view, whether the existing multiplicity of regulatory feedback loops is advantageous in some sense, regarding the dynamic response and the biochemical noise in the system. The tryptophan operon dynamic behavior is studied by means of deterministic numeric simulations, while the biochemical noise is analyzed with the aid of stochastic simulations. The model feasibility is tested comparing its stochastic and deterministic results with experimental reports. Our results for the wildtype and for a couple of mutant bacterial strains suggest that the enzyme-inhibition feedback loop, dynamically accelerates the operon response, and plays a major role in the reduction of biochemical noise. Also, the transcription-attenuation feedback loop makes the trp operon sensitive to changes in the endogenous tryptophan level, and increases the amplitude of the biochemical noise. Copyright © 2012 Elsevier Ltd. All rights reserved.

Thermostatted kinetic equations as models for complex systems in physics and life sciences.

PubMed

Bianca, Carlo

2012-12-01

Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics. Copyright © 2012 Elsevier B.V. All rights reserved.

Chaotic sources of noise in machine acoustics

NASA Astrophysics Data System (ADS)

Moon, F. C., Prof.; Broschart, Dipl.-Ing. T.

1994-05-01

In this paper a model is posited for deterministic, random-like noise in machines with sliding rigid parts impacting linear continuous machine structures. Such problems occur in gear transmission systems. A mathematical model is proposed to explain the random-like structure-borne and air-borne noise from such systems when the input is a periodic deterministic excitation of the quasi-rigid impacting parts. An experimental study is presented which supports the model. A thin circular plate is impacted by a chaotically vibrating mass excited by a sinusoidal moving base. The results suggest that the plate vibrations might be predicted by replacing the chaotic vibrating mass with a probabilistic forcing function. Prechaotic vibrations of the impacting mass show classical period doubling phenomena.

Sensitivity analysis in a Lassa fever deterministic mathematical model

NASA Astrophysics Data System (ADS)

Abdullahi, Mohammed Baba; Doko, Umar Chado; Mamuda, Mamman

2015-05-01

Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and education to reduced person to person contact.

Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study.

PubMed

Twycross, Jamie; Band, Leah R; Bennett, Malcolm J; King, John R; Krasnogor, Natalio

2010-03-26

Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks. In this case study, we solve an auxin-transport model using analytical methods, deterministic numerical simulations and stochastic numerical simulations. Although the three approaches in general predict the same behaviour, the approaches provide different information that we use to gain distinct insights into the modelled biological system. We show in particular that the analytical approach readily provides straightforward mathematical expressions for the concentrations and transport speeds, while the stochastic simulations naturally provide information on the variability of the system. Our study provides a constructive comparison which highlights the advantages and disadvantages of each of the considered modelling approaches. This will prove helpful to researchers when weighing up which modelling approach to select. In addition, the paper goes some way to bridging the gap between these approaches, which in the future we hope will lead to integrative hybrid models.

The Use of Mathematical Models of Chlamydia Transmission to Address Public Health Policy Questions: A Systematic Review.

PubMed

Rönn, Minttu M; Wolf, Emory E; Chesson, Harrell; Menzies, Nicolas A; Galer, Kara; Gorwitz, Rachel; Gift, Thomas; Hsu, Katherine; Salomon, Joshua A

2017-05-01

Mathematical models of chlamydia transmission can help inform disease control policy decisions when direct empirical evaluation of alternatives is impractical. We reviewed published chlamydia models to understand the range of approaches used for policy analyses and how the studies have responded to developments in the field. We performed a literature review by searching Medline and Google Scholar (up to October 2015) to identify publications describing dynamic chlamydia transmission models used to address public health policy questions. We extracted information on modeling methodology, interventions, and key findings. We identified 47 publications (including two model comparison studies), which reported collectively on 29 distinct mathematical models. Nine models were individual-based, and 20 were deterministic compartmental models. The earliest studies evaluated the benefits of national-level screening programs and predicted potentially large benefits from increased screening. Subsequent trials and further modeling analyses suggested the impact might have been overestimated. Partner notification has been increasingly evaluated in mathematical modeling, whereas behavioral interventions have received relatively limited attention. Our review provides an overview of chlamydia transmission models and gives a perspective on how mathematical modeling has responded to increasing empirical evidence and addressed policy questions related to prevention of chlamydia infection and sequelae.

Spatial modeling of cell signaling networks.

PubMed

Cowan, Ann E; Moraru, Ion I; Schaff, James C; Slepchenko, Boris M; Loew, Leslie M

2012-01-01

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling. Copyright © 2012 Elsevier Inc. All rights reserved.

Real-time flood forecasting

USGS Publications Warehouse

Lai, C.; Tsay, T.-K.; Chien, C.-H.; Wu, I.-L.

2009-01-01

Researchers at the Hydroinformatic Research and Development Team (HIRDT) of the National Taiwan University undertook a project to create a real time flood forecasting model, with an aim to predict the current in the Tamsui River Basin. The model was designed based on deterministic approach with mathematic modeling of complex phenomenon, and specific parameter values operated to produce a discrete result. The project also devised a rainfall-stage model that relates the rate of rainfall upland directly to the change of the state of river, and is further related to another typhoon-rainfall model. The geographic information system (GIS) data, based on precise contour model of the terrain, estimate the regions that were perilous to flooding. The HIRDT, in response to the project's progress, also devoted their application of a deterministic model to unsteady flow of thermodynamics to help predict river authorities issue timely warnings and take other emergency measures.

Fuzzy linear model for production optimization of mining systems with multiple entities

NASA Astrophysics Data System (ADS)

Vujic, Slobodan; Benovic, Tomo; Miljanovic, Igor; Hudej, Marjan; Milutinovic, Aleksandar; Pavlovic, Petar

2011-12-01

Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Optimal Control Inventory Stochastic With Production Deteriorating

NASA Astrophysics Data System (ADS)

Affandi, Pardi

2018-01-01

In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Exploration of cellular reaction systems.

PubMed

Kirkilionis, Markus

2010-01-01

We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal modelling of cellular regulatory networks (dynamic network theory) is compared with static network approaches in two first introductory sections on general network modelling. We concentrate next on deterministic rate-based dynamic regulatory networks and their derivation. In the derivation, we include methods from multiscale analysis and also look at structured large particles, here called macromolecular machines. It is clear that mass-action systems and their derivatives, i.e. networks based on enzyme kinetics, play the most dominant role in the literature. The tools to analyse cellular reaction networks are without doubt most complete for mass-action systems. We devote a long section at the end of the review to make a comprehensive review of related tools and mathematical methods. The emphasis is to show how cellular reaction networks can be analysed with the help of different associated graphs and the dissection into modules, i.e. sub-networks.

Hybrid deterministic/stochastic simulation of complex biochemical systems.

PubMed

Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina

2017-11-21

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.

A stochastic spatiotemporal model of a response-regulator network in the Caulobacter crescentus cell cycle

NASA Astrophysics Data System (ADS)

Li, Fei; Subramanian, Kartik; Chen, Minghan; Tyson, John J.; Cao, Yang

2016-06-01

The asymmetric cell division cycle in Caulobacter crescentus is controlled by an elaborate molecular mechanism governing the production, activation and spatial localization of a host of interacting proteins. In previous work, we proposed a deterministic mathematical model for the spatiotemporal dynamics of six major regulatory proteins. In this paper, we study a stochastic version of the model, which takes into account molecular fluctuations of these regulatory proteins in space and time during early stages of the cell cycle of wild-type Caulobacter cells. We test the stochastic model with regard to experimental observations of increased variability of cycle time in cells depleted of the divJ gene product. The deterministic model predicts that overexpression of the divK gene blocks cell cycle progression in the stalked stage; however, stochastic simulations suggest that a small fraction of the mutants cells do complete the cell cycle normally.

Distributed Time Synchronization Algorithms and Opinion Dynamics

NASA Astrophysics Data System (ADS)

Manita, Anatoly; Manita, Larisa

2018-01-01

We propose new deterministic and stochastic models for synchronization of clocks in nodes of distributed networks. An external accurate time server is used to ensure convergence of the node clocks to the exact time. These systems have much in common with mathematical models of opinion formation in multiagent systems. There is a direct analogy between the time server/node clocks pair in asynchronous networks and the leader/follower pair in the context of social network models.

Robust planning of dynamic wireless charging infrastructure for battery electric buses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Zhaocai; Song, Ziqi

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

Robust planning of dynamic wireless charging infrastructure for battery electric buses

DOE PAGES

Liu, Zhaocai; Song, Ziqi

2017-10-01

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

POD Model Reconstruction for Gray-Box Fault Detection

NASA Technical Reports Server (NTRS)

Park, Han; Zak, Michail

2007-01-01

Proper orthogonal decomposition (POD) is the mathematical basis of a method of constructing low-order mathematical models for the "gray-box" fault-detection algorithm that is a component of a diagnostic system known as beacon-based exception analysis for multi-missions (BEAM). POD has been successfully applied in reducing computational complexity by generating simple models that can be used for control and simulation for complex systems such as fluid flows. In the present application to BEAM, POD brings the same benefits to automated diagnosis. BEAM is a method of real-time or offline, automated diagnosis of a complex dynamic system.The gray-box approach makes it possible to utilize incomplete or approximate knowledge of the dynamics of the system that one seeks to diagnose. In the gray-box approach, a deterministic model of the system is used to filter a time series of system sensor data to remove the deterministic components of the time series from further examination. What is left after the filtering operation is a time series of residual quantities that represent the unknown (or at least unmodeled) aspects of the behavior of the system. Stochastic modeling techniques are then applied to the residual time series. The procedure for detecting abnormal behavior of the system then becomes one of looking for statistical differences between the residual time series and the predictions of the stochastic model.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

Demographic noise can reverse the direction of deterministic selection

PubMed Central

Constable, George W. A.; Rogers, Tim; McKane, Alan J.; Tarnita, Corina E.

2016-01-01

Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviors will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when demographic stochasticity is accounted for, selection can in fact act in the reverse direction to that predicted deterministically, instead favoring cooperative behaviors that appreciably increase the carrying capacity of the population. Populations that exist in larger numbers experience a selective advantage by being more stochastically robust to invasions than smaller populations, and this advantage can persist even in the presence of reproductive costs. We investigate this general effect in the specific context of public goods production and find conditions for stochastic selection reversal leading to the success of public good producers. This insight, developed here analytically, is missed by the deterministic analysis as well as by standard game theoretic models that enforce a fixed population size. The effect is found to be amplified by space; in this scenario we find that selection reversal occurs within biologically reasonable parameter regimes for microbial populations. Beyond the public good problem, we formulate a general mathematical framework for models that may exhibit stochastic selection reversal. In this context, we describe a stochastic analog to r−K theory, by which small populations can evolve to higher densities in the absence of disturbance. PMID:27450085

A Random Variable Approach to Nuclear Targeting and Survivability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Undem, Halvor A.

We demonstrate a common mathematical formalism for analyzing problems in nuclear survivability and targeting. This formalism, beginning with a random variable approach, can be used to interpret past efforts in nuclear-effects analysis, including targeting analysis. It can also be used to analyze new problems brought about by the post Cold War Era, such as the potential effects of yield degradation in a permanently untested nuclear stockpile. In particular, we illustrate the formalism through four natural case studies or illustrative problems, linking these to actual past data, modeling, and simulation, and suggesting future uses. In the first problem, we illustrate themore » case of a deterministically modeled weapon used against a deterministically responding target. Classic "Cookie Cutter" damage functions result. In the second problem, we illustrate, with actual target test data, the case of a deterministically modeled weapon used against a statistically responding target. This case matches many of the results of current nuclear targeting modeling and simulation tools, including the result of distance damage functions as complementary cumulative lognormal functions in the range variable. In the third problem, we illustrate the case of a statistically behaving weapon used against a deterministically responding target. In particular, we show the dependence of target damage on weapon yield for an untested nuclear stockpile experiencing yield degradation. Finally, and using actual unclassified weapon test data, we illustrate in the fourth problem the case of a statistically behaving weapon used against a statistically responding target.« less

Analytic uncertainty and sensitivity analysis of models with input correlations

NASA Astrophysics Data System (ADS)

Zhu, Yueying; Wang, Qiuping A.; Li, Wei; Cai, Xu

2018-03-01

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated parameters are often happened in practical applications. In the present paper, an analytic method is built for the uncertainty and sensitivity analysis of models in the presence of input correlations. With the method, it is straightforward to identify the importance of the independence and correlations of input variables in determining the model response. This allows one to decide whether or not the input correlations should be considered in practice. Numerical examples suggest the effectiveness and validation of our analytic method in the analysis of general models. A practical application of the method is also proposed to the uncertainty and sensitivity analysis of a deterministic HIV model.

Stochastic Modeling and Generation of Partially Polarized or Partially Coherent Electromagnetic Waves

NASA Technical Reports Server (NTRS)

Davis, Brynmor; Kim, Edward; Piepmeier, Jeffrey; Hildebrand, Peter H. (Technical Monitor)

2001-01-01

Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the non-deterministic nature of any real-world measurements while also providing a tractable mathematical framework. A stationary, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship the model is mathematically defined. The model is shown to be unique for any set of physical parameters. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given and computer simulation results are presented. The signals are constructed using the output of a multi-input multi-output linear filter system, driven with white noise.

Synchrony and entrainment properties of robust circadian oscillators

PubMed Central

Bagheri, Neda; Taylor, Stephanie R.; Meeker, Kirsten; Petzold, Linda R.; Doyle, Francis J.

2008-01-01

Systems theoretic tools (i.e. mathematical modelling, control, and feedback design) advance the understanding of robust performance in complex biological networks. We highlight phase entrainment as a key performance measure used to investigate dynamics of a single deterministic circadian oscillator for the purpose of generating insight into the behaviour of a population of (synchronized) oscillators. More specifically, the analysis of phase characteristics may facilitate the identification of appropriate coupling mechanisms for the ensemble of noisy (stochastic) circadian clocks. Phase also serves as a critical control objective to correct mismatch between the biological clock and its environment. Thus, we introduce methods of investigating synchrony and entrainment in both stochastic and deterministic frameworks, and as a property of a single oscillator or population of coupled oscillators. PMID:18426774

Chaotic Lagrangian models for turbulent relative dispersion.

PubMed

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Chaotic Lagrangian models for turbulent relative dispersion

NASA Astrophysics Data System (ADS)

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Human brain detects short-time nonlinear predictability in the temporal fine structure of deterministic chaotic sounds

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakada, Tsutomu

2013-04-01

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

A Mathematical Model for Alternation of Polygamy and Parthenogenesis: Stability Versus Efficiency and Analogy with Parasitism.

PubMed

Sanchez-Palencia, Evariste; Lherminier, Philippe; Françoise, Jean-Pierre

2016-12-01

The present work is a contribution to the understanding of the sempiternal problem of the "burden of factor two" implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually born males. This instability implies evolution of the system towards an attractor involving both (sexual and asexual) populations (which does not imply optimality of the population). We also exhibit the analogy with a parasite/host system.

Mathematical Modeling of the Origins of Life

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.

Using a mathematical model to evaluate the efficacy of TB control measures.

PubMed Central

Gammaitoni, L.; Nucci, M. C.

1997-01-01

We evaluated the efficacy of recommended tuberculosis (TB) infection control measures by using a deterministic mathematical model for airborne contagion. We examined the percentage of purified protein derivative conversions under various exposure conditions, environmental controlstrategies, and respiratory protective devices. We conclude that environmental control cannot eliminate the risk for TB transmission during high-risk procedures; respiratory protective devices, and particularly high-efficiency particulate air masks, may provide nearly complete protection if used with air filtration or ultraviolet irradiation. Nevertheless, the efficiency of these control measures decreases as the infectivity of the source case increases. Therefore, administrative control measures (e.g., indentifying and isolating patients with infectious TB) are the most effective because they substantially reduce the rate of infection. PMID:9284378

On higher order discrete phase-locked loops.

NASA Technical Reports Server (NTRS)

Gill, G. S.; Gupta, S. C.

1972-01-01

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Improving Deterministic Reserve Requirements for Security Constrained Unit Commitment and Scheduling Problems in Power Systems

NASA Astrophysics Data System (ADS)

Wang, Fengyu

Traditional deterministic reserve requirements rely on ad-hoc, rule of thumb methods to determine adequate reserve in order to ensure a reliable unit commitment. Since congestion and uncertainties exist in the system, both the quantity and the location of reserves are essential to ensure system reliability and market efficiency. The modeling of operating reserves in the existing deterministic reserve requirements acquire the operating reserves on a zonal basis and do not fully capture the impact of congestion. The purpose of a reserve zone is to ensure that operating reserves are spread across the network. Operating reserves are shared inside each reserve zone, but intra-zonal congestion may block the deliverability of operating reserves within a zone. Thus, improving reserve policies such as reserve zones may improve the location and deliverability of reserve. As more non-dispatchable renewable resources are integrated into the grid, it will become increasingly difficult to predict the transfer capabilities and the network congestion. At the same time, renewable resources require operators to acquire more operating reserves. With existing deterministic reserve requirements unable to ensure optimal reserve locations, the importance of reserve location and reserve deliverability will increase. While stochastic programming can be used to determine reserve by explicitly modelling uncertainties, there are still scalability as well as pricing issues. Therefore, new methods to improve existing deterministic reserve requirements are desired. One key barrier of improving existing deterministic reserve requirements is its potential market impacts. A metric, quality of service, is proposed in this thesis to evaluate the price signal and market impacts of proposed hourly reserve zones. Three main goals of this thesis are: 1) to develop a theoretical and mathematical model to better locate reserve while maintaining the deterministic unit commitment and economic dispatch structure, especially with the consideration of renewables, 2) to develop a market settlement scheme of proposed dynamic reserve policies such that the market efficiency is improved, 3) to evaluate the market impacts and price signal of the proposed dynamic reserve policies.

Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity

NASA Astrophysics Data System (ADS)

Hattaf, Khalid; Mahrouf, Marouane; Adnani, Jihad; Yousfi, Noura

2018-01-01

In this paper, we propose a stochastic delayed epidemic model with specific functional response. The time delay represents temporary immunity period, i.e., time from recovery to becoming susceptible again. We first show that the proposed model is mathematically and biologically well-posed. Moreover, the extinction of the disease and the persistence in the mean are established in the terms of a threshold value R0S which is smaller than the basic reproduction number R0 of the corresponding deterministic system.

Modelling and simulating reaction-diffusion systems using coloured Petri nets.

PubMed

Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming

2014-10-01

Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Network-level reproduction number and extinction threshold for vector-borne diseases.

PubMed

Xue, Ling; Scoglio, Caterina

2015-06-01

The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.

Predictive oncology: multidisciplinary, multi-scale in-silico modeling linking phenotype, morphology and growth

PubMed Central

Sanga, Sandeep; Frieboes, Hermann B.; Zheng, Xiaoming; Gatenby, Robert; Bearer, Elaine L.; Cristini, Vittorio

2007-01-01

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically review advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we propose and discuss a multi-scale, i.e., from the molecular to the gross tumor scale, mathematical and computational “first-principle” approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We demonstrate that this methodology, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as phenotype-diagnostic tool and thus to predict collective and individual tumor cell invasion of surrounding host. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior. PMID:17629503

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

Mathematical analysis of epidemiological models with heterogeneity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Ark, J.W.

1992-01-01

For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that eachmore » person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.« less

A model for Huanglongbing spread between citrus plants including delay times and human intervention

NASA Astrophysics Data System (ADS)

Vilamiu, Raphael G. d'A.; Ternes, Sonia; Braga, Guilherme A.; Laranjeira, Francisco F.

2012-09-01

The objective of this work was to present a compartmental deterministic mathematical model for representing the dynamics of HLB disease in a citrus orchard, including delay in the disease's incubation phase in the plants, and a delay period on the nymphal stage of Diaphorina citri, the most important HLB insect vector in Brazil. Numerical simulations were performed to assess the possible impacts of human detection efficiency of symptomatic plants, as well as the influence of a long incubation period of HLB in the plant.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plechac, Petr; Vlachos, Dionisios; Katsoulakis, Markos

2013-09-05

The overall objective of this project is to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals. Specific goals include: (i) Development of rigorous spatio-temporal coarse-grained kinetic Monte Carlo (KMC) mathematics and simulation for microscopic processes encountered in biomassmore » transformation. (ii) Development of hybrid multiscale simulation that links stochastic simulation to a deterministic partial differential equation (PDE) model for an entire reactor. (iii) Development of hybrid multiscale simulation that links KMC simulation with quantum density functional theory (DFT) calculations. (iv) Development of parallelization of models of (i)-(iii) to take advantage of Petaflop computing and enable real world applications of complex, multiscale models. In this NCE period, we continued addressing these objectives and completed the proposed work. Main initiatives, key results, and activities are outlined.« less

Rare events in finite and infinite dimensions

NASA Astrophysics Data System (ADS)

Reznikoff, Maria G.

Thermal noise introduces stochasticity into deterministic equations and makes possible events which are never seen in the zero temperature setting. The driving force behind the thesis work is a desire to bring analysis and probability to bear on a class of relevant and intriguing physical problems, and in so doing, to allow applications to drive the development of new mathematical theory. The unifying theme is the study of rare events under the influence of small, random perturbations, and the manifold mathematical problems which ensue. In the first part, we apply large deviation theory and prefactor estimates to a coherent rotation micromagnetic model in order to analyze thermally activated magnetic switching. We consider recent physical experiments and the mathematical questions "asked" by them. A stochastic resonance type phenomenon is discovered, leading to the definition of finite temperature astroids. Non-Arrhenius behavior is discussed. The analysis is extended to ramped astroids. In addition, we discover that for low damping and ultrashort pulses, deterministic effects can override thermal effects, in accord with very recent ultrashort pulse experiments. Even more interesting, perhaps, is the study of large deviations in the infinite dimensional context, i.e. in spatially extended systems. Inspired by recent numerical investigations, we study the stochastically perturbed Allen Cahn and Cahn Hilliard equations. For the Allen Cahn equation, we study the action minimization problem (a deterministic variational problem) and prove the action scaling in four parameter regimes, via upper and lower bounds. The sharp interface limit is studied. We formally derive a reduced action functional which lends insight into the connection between action minimization and curvature flow. For the Cahn Hilliard equation, we prove upper and lower bounds for the scaling of the energy barrier in the nucleation and growth regime. Finally, we consider rare events in large or infinite domains, in one spatial dimension. We introduce a natural reference measure through which to analyze the invariant measure of stochastically perturbed, nonlinear partial differential equations. Also, for noisy reaction diffusion equations with an asymmetric potential, we discover how to rescale space and time in order to map the dynamics in the zero temperature limit to the Poisson Model, a simple version of the Johnson-Mehl-Avrami-Kolmogorov model for nucleation and growth.

On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

Hpm of Estrogen Model on the Dynamics of Breast Cancer

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Balamuralitharan, S.; Sundaresan, T.

2018-04-01

We enhance a deterministic mathematical model involving universal dynamics on breast cancer with immune response. This is population model so includes Normal cells class, Tumor cells, Immune cells and Estrogen. The eects regarding Estrogen are below incorporated in the model. The effects show to that amount the arrival of greater Estrogen increases the danger over growing breast cancer. Furthermore, approximate solution regarding nonlinear differential equations is arrived by Homotopy Perturbation Method (HPM). Hes HPM is good and correct technique after solve nonlinear differential equation directly. Approximate solution learnt with the support of that method is suitable same as like the actual results in accordance with this models.

Deterministic analysis of processes at corroding metal surfaces and the study of electrochemical noise in these systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latanision, R.M.

1990-12-01

Electrochemical corrosion is pervasive in virtually all engineering systems and in virtually all industrial circumstances. Although engineers now understand how to design systems to minimize corrosion in many instances, many fundamental questions remain poorly understood and, therefore, the development of corrosion control strategies is based more on empiricism than on a deep understanding of the processes by which metals corrode in electrolytes. Fluctuations in potential, or current, in electrochemical systems have been observed for many years. To date, all investigations of this phenomenon have utilized non-deterministic analyses. In this work it is proposed to study electrochemical noise from a deterministicmore » viewpoint by comparison of experimental parameters, such as first and second order moments (non-deterministic), with computer simulation of corrosion at metal surfaces. In this way it is proposed to analyze the origins of these fluctuations and to elucidate the relationship between these fluctuations and kinetic parameters associated with metal dissolution and cathodic reduction reactions. This research program addresses in essence two areas of interest: (a) computer modeling of corrosion processes in order to study the electrochemical processes on an atomistic scale, and (b) experimental investigations of fluctuations in electrochemical systems and correlation of experimental results with computer modeling. In effect, the noise generated by mathematical modeling will be analyzed and compared to experimental noise in electrochemical systems. 1 fig.« less

Complexity in Soil Systems: What Does It Mean and How Should We Proceed?

NASA Astrophysics Data System (ADS)

Faybishenko, B.; Molz, F. J.; Brodie, E.; Hubbard, S. S.

2015-12-01

The complex soil systems approach is needed fundamentally for the development of integrated, interdisciplinary methods to measure and quantify the physical, chemical and biological processes taking place in soil, and to determine the role of fine-scale heterogeneities. This presentation is aimed at a review of the concepts and observations concerning complexity and complex systems theory, including terminology, emergent complexity and simplicity, self-organization and a general approach to the study of complex systems using the Weaver (1948) concept of "organized complexity." These concepts are used to provide understanding of complex soil systems, and to develop experimental and mathematical approaches to soil microbiological processes. The results of numerical simulations, observations and experiments are presented that indicate the presence of deterministic chaotic dynamics in soil microbial systems. So what are the implications for the scientists who wish to develop mathematical models in the area of organized complexity or to perform experiments to help clarify an aspect of an organized complex system? The modelers have to deal with coupled systems having at least three dependent variables, and they have to forgo making linear approximations to nonlinear phenomena. The analogous rule for experimentalists is that they need to perform experiments that involve measurement of at least three interacting entities (variables depending on time, space, and each other). These entities could be microbes in soil penetrated by roots. If a process being studied in a soil affects the soil properties, like biofilm formation, then this effect has to be measured and included. The mathematical implications of this viewpoint are examined, and results of numerical solutions to a system of equations demonstrating deterministic chaotic behavior are also discussed using time series and the 3D strange attractors.

"The Theory was Beautiful Indeed": Rise, Fall and Circulation of Maximizing Methods in Population Genetics (1930-1980).

PubMed

Grodwohl, Jean-Baptiste

2017-08-01

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: "our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection" (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this "obsession", by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura's and Richard Lewontin's works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

Computers in the Undergraduate Curriculum: An Aspect of the Many Section Problem.

ERIC Educational Resources Information Center

Churchill, Geoffrey

A brief case study of the resistance to technological change is presented using DOG, a small scale deterministic business game, as the example of technology. DOG, a decision mathematics game for the purpose of providing an environment for application of mathematical concepts, consists of assignments mostly utilizing matrix algebra but also some…

Continuum and discrete approach in modeling biofilm development and structure: a review.

PubMed

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Relation Between the Cell Volume and the Cell Cycle Dynamics in Mammalian cell

NASA Astrophysics Data System (ADS)

Magno, A. C. G.; Oliveira, I. L.; Hauck, J. V. S.

2016-08-01

The main goal of this work is to add and analyze an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Goldbeter (2011) [1]. The cell division occurs when the cyclinB/Cdkl complex is totally degraded (Tyson and Novak, 2011)[2] and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cytoplasmic content of the mother cell. The equations of our base model are only valid if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation principle for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were accomplished: deterministic and stochastic. In the stochastic simulation, the volume affects every model's parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation a stability analysis was performed. This elucidates how the growth factor impacts the stability of the model's limit cycles. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the cell volume variation

Mathematical model of gas plasma applied to chronic wounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, J. G.; Liu, X. Y.; Liu, D. W.

2013-11-15

Chronic wounds are a major burden for worldwide health care systems, and patients suffer pain and discomfort from this type of wound. Recently gas plasmas have been shown to safely speed chronic wounds healing. In this paper, we develop a deterministic mathematical model formulated by eight-species reaction-diffusion equations, and use it to analyze the plasma treatment process. The model follows spatial and temporal concentration within the wound of oxygen, chemoattractants, capillary sprouts, blood vessels, fibroblasts, extracellular matrix material, nitric oxide (NO), and inflammatory cell. Two effects of plasma, increasing NO concentration and reducing bacteria load, are considered in this model.more » The plasma treatment decreases the complete healing time from 25 days (normal wound healing) to 17 days, and the contributions of increasing NO concentration and reducing bacteria load are about 1/4 and 3/4, respectively. Increasing plasma treatment frequency from twice to three times per day accelerates healing process. Finally, the response of chronic wounds of different etiologies to treatment with gas plasmas is analyzed.« less

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

Laomettachit, Teeraphan; Chen, Katherine C; Baumann, William T; Tyson, John J

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a "standard component" modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with "standard components" can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

PubMed Central

Laomettachit, Teeraphan; Chen, Katherine C.; Baumann, William T.

2016-01-01

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast. PMID:27187804

A control theoretical approach to crowd management. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Borzí, Alfio; Caponigro, Marco

2016-09-01

The formulation of mathematical models for crowd dynamics is one current challenge in many fields of applied sciences. It involves the modelization of the complex behavior of a large number of individuals. In particular, the difficulty lays in describing emerging collective behaviors by means of a relatively small number of local interaction rules between individuals in a crowd. Clearly, the individual's free will involved in decision making processes and in the management of the social interactions cannot be described by a finite number of deterministic rules. On the other hand, in large crowds, this individual indeterminacy can be considered as a local fluctuation averaged to zero by the size of the crowd. While at the microscopic scale, using a system of coupled ODEs, the free will should be included in the mathematical description (e.g. with a stochastic term), the mesoscopic and macroscopic scales, modeled by PDEs, represent a powerful modelling tool that allows to neglect this feature and provide a reliable description. In this sense, the work by Bellomo, Clarke, Gibelli, Townsend, and Vreugdenhil [2] represents a mathematical-epistemological contribution towards the design of a reliable model of human behavior.

Stem cell transplantation as a dynamical system: are clinical outcomes deterministic?

PubMed

Toor, Amir A; Kobulnicky, Jared D; Salman, Salman; Roberts, Catherine H; Jameson-Lee, Max; Meier, Jeremy; Scalora, Allison; Sheth, Nihar; Koparde, Vishal; Serrano, Myrna; Buck, Gregory A; Clark, William B; McCarty, John M; Chung, Harold M; Manjili, Masoud H; Sabo, Roy T; Neale, Michael C

2014-01-01

Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However, the clinical course following SCT appears to demonstrate many characteristics of dynamical systems, especially when outcomes are considered in the context of immune reconstitution. Dynamical systems tend to evolve over time according to mathematically determined rules. Characteristically, the future states of the system are predicated on the states preceding them, and there is sensitivity to initial conditions. In SCT, the interaction between donor T cells and the recipient may be considered as such a system in which, graft source, conditioning, and early immunosuppression profoundly influence immune reconstitution over time. This eventually determines clinical outcomes, either the emergence of tolerance or the development of graft versus host disease. In this paper, parallels between SCT and dynamical systems are explored and a conceptual framework for developing mathematical models to understand disparate transplant outcomes is proposed.

Stem Cell Transplantation as a Dynamical System: Are Clinical Outcomes Deterministic?

PubMed Central

Toor, Amir A.; Kobulnicky, Jared D.; Salman, Salman; Roberts, Catherine H.; Jameson-Lee, Max; Meier, Jeremy; Scalora, Allison; Sheth, Nihar; Koparde, Vishal; Serrano, Myrna; Buck, Gregory A.; Clark, William B.; McCarty, John M.; Chung, Harold M.; Manjili, Masoud H.; Sabo, Roy T.; Neale, Michael C.

2014-01-01

Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However, the clinical course following SCT appears to demonstrate many characteristics of dynamical systems, especially when outcomes are considered in the context of immune reconstitution. Dynamical systems tend to evolve over time according to mathematically determined rules. Characteristically, the future states of the system are predicated on the states preceding them, and there is sensitivity to initial conditions. In SCT, the interaction between donor T cells and the recipient may be considered as such a system in which, graft source, conditioning, and early immunosuppression profoundly influence immune reconstitution over time. This eventually determines clinical outcomes, either the emergence of tolerance or the development of graft versus host disease. In this paper, parallels between SCT and dynamical systems are explored and a conceptual framework for developing mathematical models to understand disparate transplant outcomes is proposed. PMID:25520720

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Chaos-order transition in foraging behavior of ants.

PubMed

Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian; Schellnhuber, Hans Joachim

2014-06-10

The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants' physical abilities, and ants' knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal.

Chaos–order transition in foraging behavior of ants

PubMed Central

Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian; Schellnhuber, Hans Joachim

2014-01-01

The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants’ physical abilities, and ants’ knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal. PMID:24912159

The effects of hard water consumption on kidney function: Insights from mathematical modelling

NASA Astrophysics Data System (ADS)

Tambaru, David; Djahi, Bertha S.; Ndii, Meksianis Z.

2018-03-01

Most water sources in Nusa Tenggara Timur contain higher concentration of calcium and magnesium ions, which is known as hard water. Long-term consumption of hard water can cause kidney dysfunction, which may lead to the other diseases such as cerebrovascular disease, diabetes and others. Therefore, understanding the effects of hard water consumption on kidney function is of importance. This paper studies the transmission dynamics of kidney dysfunction due to the consumption of hard water using a mathematical model. We propose a new deterministic mathematical model comprising human and water compartments and conduct a global sensitivity analysis to determine the most influential parameters of the model. The Routh-Hurwitz criterion is used to examine the stability of the steady states. The results shows that the model has two steady states, which are locally stable. Moreover, we found that the most influential parameters are the maximum concentration of magnesium and calcium in the water, the increase rate of calcium and magnesium concentration in the water and the rate of effectiveness of water treatment. The results suggest that better water treatments are required to reduce the concentration of magnesium and calcium in the water. This aid in minimizing the probability of humans to attract kidney dysfunction. Furthermore, water-related data need to be collected for further investigation.

Short-term dynamics of intertidal microphytobenthic biomass. Mathematical modelling [La dynamique a court terme de la biomasse du microphytobenthos intertidal. Formalisation mathematique

USGS Publications Warehouse

Guarini, J.-M.; Gros, P.; Blanchard, G.F.; Bacher, C.

1999-01-01

We formulate a deterministic mathematical model to describe the dynamics of the microphytobenthos of intertidal mudflats. It is 'minimal' because it only takes into account the essential processes governing the functioning of the system: the autotrophic production, the active upward and downward migrations of epipelic microalgae, the saturation of the mud surface by a biofilm of diatoms and the global net loss rates of biomass. According to the photic environment of the benthic diatoms inhabiting intertidal mudflats, and to their migration rhythm, the model is composed of two sub-systems of ordinary differential equations; they describe the simultaneous evolution of the biomass 'S' concentrated in the mud surface biofilm - the photic layer - and of the biomass 'F' diluted in the topmost centimetre of the mud - the aphotic layer. Qualitatively, the model solutions agree fairly well with the in situ observed dynamics of the S + F biomass. The study of the mathematical properties of the model, under some simplifying assumptions, shows the convergence of solutions to a stable cyclic equilibrium, whatever the frequencies of the physical synchronizers of the production. The sensitivity analysis reveals the necessity of a better knowledge of the processes of biomass losses, which so far are uncertain, and may further vary in space and time.

Specialized Silicon Compilers for Language Recognition.

DTIC Science & Technology

1984-07-01

realizations of non-deterministic automata have been reported that solve these problems in diffierent ways. Floyd and Ullman [ 281 have presented a...in Applied Mathematics, pages 19-31. American Mathematical Society, 1967. [ 281 Floyd, R. W. and J. D. Ullman. The Compilation of Regular Expressions...Shannon (editor). Automata Studies, chapter 1, pages 3-41. Princeton University Press, Princeton. N. J., 1956. [44] Kohavi, Zwi . Switching and Finite

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

Some applications of mathematics in golf.

PubMed

Otto, S R

2017-08-01

At its core, like many other sports, golf is a game of integers. The minimization of the number of strokes played is generally what determines the winner, whether each of these are associated with the shortest of putts or the longest of drives. The outcomes of these shots are influenced by very slight changes, but hopefully in a deterministic sense. Understanding the mechanics of golf necessitates the development of models and this is coupled more often than not to the use of statistics. In essence, the individual aspects of the sport can be modelled adequately via fairly simplistic models, but the presence of a human at one end of the kinematic chain has a significant impact on the variability of the entire process. In this paper, we will review some of the ways that mathematics has been used to develop the understanding of the physical processes involved in the sport, including some of the analysis which is exploited within the Equipment Rules. We will also discuss some of the future challenges.

A mathematical study of a model for childhood diseases with non-permanent immunity

NASA Astrophysics Data System (ADS)

Moghadas, S. M.; Gumel, A. B.

2003-08-01

Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. Since vaccination is considered to be the most effective strategy against childhood diseases, the development of a framework that would predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. This paper provides this framework via qualitative and quantitative analysis of a deterministic mathematical model for the transmission dynamics of a childhood disease in the presence of a preventive vaccine that may wane over time. Using global stability analysis of the model, based on constructing a Lyapunov function, it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value. It is also shown that the disease will persist within the population if the coverage level is below this threshold. These results are verified numerically by constructing, and then simulating, a robust semi-explicit second-order finite-difference method.

Deterministic versus evidence-based attitude towards clinical diagnosis.

PubMed

Soltani, Akbar; Moayyeri, Alireza

2007-08-01

Generally, two basic classes have been proposed for scientific explanation of events. Deductive reasoning emphasizes on reaching conclusions about a hypothesis based on verification of universal laws pertinent to that hypothesis, while inductive or probabilistic reasoning explains an event by calculation of some probabilities for that event to be related to a given hypothesis. Although both types of reasoning are used in clinical practice, evidence-based medicine stresses on the advantages of the second approach for most instances in medical decision making. While 'probabilistic or evidence-based' reasoning seems to involve more mathematical formulas at the first look, this attitude is more dynamic and less imprisoned by the rigidity of mathematics comparing with 'deterministic or mathematical attitude'. In the field of medical diagnosis, appreciation of uncertainty in clinical encounters and utilization of likelihood ratio as measure of accuracy seem to be the most important characteristics of evidence-based doctors. Other characteristics include use of series of tests for refining probability, changing diagnostic thresholds considering external evidences and nature of the disease, and attention to confidence intervals to estimate uncertainty of research-derived parameters.

An introduction to chaotic and random time series analysis

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Understanding resistant effect of mosquito on fumigation strategy in dengue control program

NASA Astrophysics Data System (ADS)

Aldila, D.; Situngkir, N.; Nareswari, K.

2018-01-01

A mathematical model of dengue disease transmission will be introduced in this talk with involving fumigation intervention into mosquito population. Worsening effect of uncontrolled fumigation in the form of resistance of mosquito to fumigation chemicals will also be included into the model to capture the reality in the field. Deterministic approach in a 9 dimensional of ordinary differential equation will be used. Analytical result about the existence and local stability of the equilibrium points followed with the basic reproduction number will be discussed. Some numerical result will be performed for some scenario to give a better interpretation for the analytical results.

Multi-Strain Deterministic Chaos in Dengue Epidemiology, A Challenge for Computational Mathematics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Kooi, Bob W.; Stollenwerk, Nico

2009-09-01

Recently, we have analysed epidemiological models of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra has to be applied in comparison to get further insight into such dynamical structures. Especially, Lyapunov spectra, which quantify the predictability horizon in the epidemiological system, are computationally very demanding. We show ways to speed up computations of such Lyapunov spectra by a factor of more than ten by parallelizing previously used sequential C programs. Such fast computations of Lyapunov spectra will be especially of use in future investigations of seasonally forced versions of the present models, as they are needed for data analysis.

Vacuum effects over the closing of enterocutaneous fistulae: a mathematical modeling approach.

PubMed

Cattoni, D I; Chara, O

2008-01-01

Enterocutaneous fistulae are pathological communications between the intestinal lumen and the abdominal skin. Under surgery the mortality of this pathology is very high, therefore a vacuum applying system has been carried previously on attempting to close these fistulae. The objective of this article is the understanding of how these treatments might work through deterministic mathematical modelling. Four models are here proposed based on several assumptions involving: the conservation of the flow in the fistula, a low enough Reynolds number justifying a laminar flow, the use of Poiseuille law to model the movement of the fistulous liquid, as well as phenomenological equations including the fistula tissue and intermediate chamber compressibility. Interestingly, the four models show fistulae closing behaviour during experimental time (t<60 sec). To compare the models, both, simulations and pressure measurements, carried out on the vacuum connected to the patients, are performed. Time course of pressure are then simulated (from each model) and fitted to the experimental data. The model which best describes actual measurements shows exponential pumping flux kinetics. Applying this model, numerical relationship between the fistula compressibility and closure time is presented. The models here developed would contribute to clarify the treatment mechanism and, eventually, improve the fistulae treatment.

A cost-effectiveness model to personalize antiviral therapy in naive patients with genotype 1 chronic hepatitis C.

PubMed

Iannazzo, Sergio; Colombatto, Piero; Ricco, Gabriele; Oliveri, Filippo; Bonino, Ferruccio; Brunetto, Maurizia R

2015-03-01

Rapid virologic response is the best predictor of sustained virologic response with dual therapy in genotype-1 chronic hepatitis C, and its evaluation was proposed to tailor triple therapy in F0-F2 patients. Bio-mathematical modelling of viral dynamics during dual therapy has potentially higher accuracy than rapid virologic in the identification of patients who will eventually achieve sustained response. Study's objective was the cost-effectiveness analysis of a personalized therapy in naïve F0-F2 patients with chronic hepatitis C based on a bio-mathematical model (model-guided strategy) rather than on rapid virologic response (guideline-guided strategy). A deterministic bio-mathematical model of the infected cell dynamics was validated in a cohort of 135 patients treated with dual therapy. A decision-analytic economic model was then developed to compare model-guided and guideline-guided strategies in the Italian setting. The outcomes of the cost-effectiveness analysis with model-guided and guideline-guided strategy were 19.1-19.4 and 18.9-19.3 quality-adjusted-life-years. Total per-patient lifetime costs were €25,200-€26,000 with model-guided strategy and €28,800-€29,900 with guideline-guided strategy. When comparing model-guided with guideline-guided strategy the former resulted more effective and less costly. The adoption of the bio-mathematical predictive criterion has the potential to improve the cost-effectiveness of a personalized therapy for chronic hepatitis C, reserving triple therapy for those patients who really need it. Copyright © 2014 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved.

Multidisciplinary insight into clonal expansion of HTLV-1-infected cells in adult T-cell leukemia via modeling by deterministic finite automata coupled with high-throughput sequencing.

PubMed

Farmanbar, Amir; Firouzi, Sanaz; Park, Sung-Joon; Nakai, Kenta; Uchimaru, Kaoru; Watanabe, Toshiki

2017-01-31

Clonal expansion of leukemic cells leads to onset of adult T-cell leukemia (ATL), an aggressive lymphoid malignancy with a very poor prognosis. Infection with human T-cell leukemia virus type-1 (HTLV-1) is the direct cause of ATL onset, and integration of HTLV-1 into the human genome is essential for clonal expansion of leukemic cells. Therefore, monitoring clonal expansion of HTLV-1-infected cells via isolation of integration sites assists in analyzing infected individuals from early infection to the final stage of ATL development. However, because of the complex nature of clonal expansion, the underlying mechanisms have yet to be clarified. Combining computational/mathematical modeling with experimental and clinical data of integration site-based clonality analysis derived from next generation sequencing technologies provides an appropriate strategy to achieve a better understanding of ATL development. As a comprehensively interdisciplinary project, this study combined three main aspects: wet laboratory experiments, in silico analysis and empirical modeling. We analyzed clinical samples from HTLV-1-infected individuals with a broad range of proviral loads using a high-throughput methodology that enables isolation of HTLV-1 integration sites and accurate measurement of the size of infected clones. We categorized clones into four size groups, "very small", "small", "big", and "very big", based on the patterns of clonal growth and observed clone sizes. We propose an empirical formal model based on deterministic finite state automata (DFA) analysis of real clinical samples to illustrate patterns of clonal expansion. Through the developed model, we have translated biological data of clonal expansion into the formal language of mathematics and represented the observed clonality data with DFA. Our data suggest that combining experimental data (absolute size of clones) with DFA can describe the clonality status of patients. This kind of modeling provides a basic understanding as well as a unique perspective for clarifying the mechanisms of clonal expansion in ATL.

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

NASA Astrophysics Data System (ADS)

Ehrhardt, Matthias J.; Markiewicz, Pawel; Chambolle, Antonin; Richtárik, Peter; Schott, Jonathan; Schönlieb, Carola-Bibiane

2017-08-01

Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

PubMed

Sharma, Vijay

2009-09-10

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

PubMed Central

Sharma, Vijay

2009-01-01

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

Insights into the deterministic skill of air quality ensembles ...

EPA Pesticide Factsheets

Simulations from chemical weather models are subject to uncertainties in the input data (e.g. emission inventory, initial and boundary conditions) as well as those intrinsic to the model (e.g. physical parameterization, chemical mechanism). Multi-model ensembles can improve the forecast skill, provided that certain mathematical conditions are fulfilled. In this work, four ensemble methods were applied to two different datasets, and their performance was compared for ozone (O3), nitrogen dioxide (NO2) and particulate matter (PM10). Apart from the unconditional ensemble average, the approach behind the other three methods relies on adding optimum weights to members or constraining the ensemble to those members that meet certain conditions in time or frequency domain. The two different datasets were created for the first and second phase of the Air Quality Model Evaluation International Initiative (AQMEII). The methods are evaluated against ground level observations collected from the EMEP (European Monitoring and Evaluation Programme) and AirBase databases. The goal of the study is to quantify to what extent we can extract predictable signals from an ensemble with superior skill over the single models and the ensemble mean. Verification statistics show that the deterministic models simulate better O3 than NO2 and PM10, linked to different levels of complexity in the represented processes. The unconditional ensemble mean achieves higher skill compared to each stati

The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.

PubMed

Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin

2016-07-01

Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.

A white-box model of S-shaped and double S-shaped single-species population growth

PubMed Central

Kalmykov, Lev V.

2015-01-01

Complex systems may be mechanistically modelled by white-box modeling with using logical deterministic individual-based cellular automata. Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models). Most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka–Volterra models. In black-box models, the individual-based (mechanistic) mechanisms of population dynamics remain hidden. Here we mechanistically model the S-shaped and double S-shaped population growth of vegetatively propagated rhizomatous lawn grasses. Using purely logical deterministic individual-based cellular automata we create a white-box model. From a general physical standpoint, the vegetative propagation of plants is an analogue of excitation propagation in excitable media. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We have investigated mechanisms of the single-species population growth limited by habitat size, intraspecific competition, regeneration time and fecundity of individuals in two types of boundary conditions and at two types of fecundity. Besides that, we have compared the S-shaped and J-shaped population growth. We consider this white-box modeling approach as a method of artificial intelligence which works as automatic hyper-logical inference from the first principles of the studied subject. This approach is perspective for direct mechanistic insights into nature of any complex systems. PMID:26038717

Epidemic spreading on adaptively weighted scale-free networks.

PubMed

Sun, Mengfeng; Zhang, Haifeng; Kang, Huiyan; Zhu, Guanghu; Fu, Xinchu

2017-04-01

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces

NASA Astrophysics Data System (ADS)

Molz, F. J.; Murdoch, L. C.; Faybishenko, B.

2013-12-01

Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

User's manual for a parameter identification technique. [with options for model simulation for fixed input forcing functions and identification from wind tunnel and flight measurements

NASA Technical Reports Server (NTRS)

Kanning, G.

1975-01-01

A digital computer program written in FORTRAN is presented that implements the system identification theory for deterministic systems using input-output measurements. The user supplies programs simulating the mathematical model of the physical plant whose parameters are to be identified. The user may choose any one of three options. The first option allows for a complete model simulation for fixed input forcing functions. The second option identifies up to 36 parameters of the model from wind tunnel or flight measurements. The third option performs a sensitivity analysis for up to 36 parameters. The use of each option is illustrated with an example using input-output measurements for a helicopter rotor tested in a wind tunnel.

A hybrid CS-SA intelligent approach to solve uncertain dynamic facility layout problems considering dependency of demands

NASA Astrophysics Data System (ADS)

Moslemipour, Ghorbanali

2018-07-01

This paper aims at proposing a quadratic assignment-based mathematical model to deal with the stochastic dynamic facility layout problem. In this problem, product demands are assumed to be dependent normally distributed random variables with known probability density function and covariance that change from period to period at random. To solve the proposed model, a novel hybrid intelligent algorithm is proposed by combining the simulated annealing and clonal selection algorithms. The proposed model and the hybrid algorithm are verified and validated using design of experiment and benchmark methods. The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time points of view. Besides, the proposed model can be used in both of the stochastic and deterministic situations.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Phenotypic switching of populations of cells in a stochastic environment

NASA Astrophysics Data System (ADS)

Hufton, Peter G.; Lin, Yen Ting; Galla, Tobias

2018-02-01

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise-deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

The progression of the entropy of a five dimensional psychotherapeutic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badalamenti, A.F.; Langs, R.J.

This paper presents a study of the deterministic and stochastic behavior of the entropy of a 5-dimensional, 2400 state, system across each of six psychotherapeutic sessions. The growth of entropy was found to be logarithmic in each session. The stochastic behavior of a moving 600 second estimator of entropy revealed a Box-Jenkins model of type (1,1,0) - that is, the first difference of the entropy series was first order autoregressive or prior state sensitive. In addition, the patient and therapist entropy series exhibited no significant cross correlation across lags of -300 to +300 seconds. Yet all such pairs of seriesmore » exhibited high coherency past the frequency of .06 (on a full range of 0 to .5). Furthermore, all the patients and therapists were attracted to a geometric center of mass in 5-dimensional space which was different from the geometric center of the region where the system lived. The process significance of the findings and the relationship between the deterministic and stochastic results are discussed. The paper is then placed in the broader context of our efforts to provide new and meaningful quantitative dimensions and mathematical models to psychotherapy research. 59 refs.« less

Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

PubMed

Adamson, M W; Morozov, A Y; Kuzenkov, O A

2016-09-01

Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.

Hands-on-Entropy, Energy Balance with Biological Relevance

NASA Astrophysics Data System (ADS)

Reeves, Mark

2015-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is important contribution of the entropy in driving fundamental biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy). This has enabled students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce complex biological processes and structures in order model them mathematically to account for both deterministic and probabilistic processes. The students test these models in simulations and in laboratory experiments that are biologically relevant such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront random forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory. PMID:19816580

Expert system development for commonality analysis in space programs

NASA Technical Reports Server (NTRS)

Yeager, Dorian P.

1987-01-01

This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.

Exact PDF equations and closure approximations for advective-reactive transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Cognitive diagnosis modelling incorporating item response times.

PubMed

Zhan, Peida; Jiao, Hong; Liao, Dandan

2018-05-01

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters. © 2017 The British Psychological Society.

Grey fuzzy optimization model for water quality management of a river system

NASA Astrophysics Data System (ADS)

Karmakar, Subhankar; Mujumdar, P. P.

2006-07-01

A grey fuzzy optimization model is developed for water quality management of river system to address uncertainty involved in fixing the membership functions for different goals of Pollution Control Agency (PCA) and dischargers. The present model, Grey Fuzzy Waste Load Allocation Model (GFWLAM), has the capability to incorporate the conflicting goals of PCA and dischargers in a deterministic framework. The imprecision associated with specifying the water quality criteria and fractional removal levels are modeled in a fuzzy mathematical framework. To address the imprecision in fixing the lower and upper bounds of membership functions, the membership functions themselves are treated as fuzzy in the model and the membership parameters are expressed as interval grey numbers, a closed and bounded interval with known lower and upper bounds but unknown distribution information. The model provides flexibility for PCA and dischargers to specify their aspirations independently, as the membership parameters for different membership functions, specified for different imprecise goals are interval grey numbers in place of a deterministic real number. In the final solution optimal fractional removal levels of the pollutants are obtained in the form of interval grey numbers. This enhances the flexibility and applicability in decision-making, as the decision-maker gets a range of optimal solutions for fixing the final decision scheme considering technical and economic feasibility of the pollutant treatment levels. Application of the GFWLAM is illustrated with case study of the Tunga-Bhadra river system in India.

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

PRMS-IV, the precipitation-runoff modeling system, version 4

USGS Publications Warehouse

Markstrom, Steven L.; Regan, R. Steve; Hay, Lauren E.; Viger, Roland J.; Webb, Richard M.; Payn, Robert A.; LaFontaine, Jacob H.

2015-01-01

Computer models that simulate the hydrologic cycle at a watershed scale facilitate assessment of variability in climate, biota, geology, and human activities on water availability and flow. This report describes an updated version of the Precipitation-Runoff Modeling System. The Precipitation-Runoff Modeling System is a deterministic, distributed-parameter, physical-process-based modeling system developed to evaluate the response of various combinations of climate and land use on streamflow and general watershed hydrology. Several new model components were developed, and all existing components were updated, to enhance performance and supportability. This report describes the history, application, concepts, organization, and mathematical formulation of the Precipitation-Runoff Modeling System and its model components. This updated version provides improvements in (1) system flexibility for integrated science, (2) verification of conservation of water during simulation, (3) methods for spatial distribution of climate boundary conditions, and (4) methods for simulation of soil-water flow and storage.

A Joint Replenishment Inventory Model with Lost Sales

NASA Astrophysics Data System (ADS)

Devy, N. L.; Ai, T. J.; Astanti, R. D.

2018-04-01

This paper deals with two items joint replenishment inventory problem, in which the demand of each items are constant and deterministic. Inventory replenishment of items is conducted periodically every T time intervals. Among of these replenishments, joint replenishment of both items is possible. It is defined that item i is replenished every ZiT time intervals. Replenishment of items are instantaneous. All of shortages are considered as lost sales. The maximum allowance for lost sales of item i is Si. Mathematical model is formulated in order to determining the basic time cycle T, replenishment multiplier Zi , and maximum lost sales Si in order to minimize the total cost per unit time. A solution methodology is proposed for solve the model and a numerical example is provided for demonstrating the effectiveness of the proposed methodology.

Modelling the effect of an alternative host population on the spread of citrus Huanglongbing

NASA Astrophysics Data System (ADS)

d'A. Vilamiu, Raphael G.; Ternes, Sonia; Laranjeira, Francisco F.; de C. Santos, Tâmara T.

2013-10-01

The objective of this work was to model the spread of citrus Huanglongbing (HLB) considering the presence of a population of alternative hosts (Murraya paniculata). We developed a compartmental deterministic mathematical model for representing the dynamics of HLB disease in a citrus orchard, including delays in the latency and incubation phases of the disease in the plants and a delay period on the nymphal stage of Diaphorina citri, the insect vector of HLB in Brazil. The results of numerical simulations indicate that alternative hosts should not play a crucial role on HLB dynamics considering a typical scenario for the Recôncavo Baiano region in Brazil . Also, the current policy of removing symptomatic plants every three months should not be expected to significantly hinder HLB spread.

A mathematical model of Staphylococcus aureus control in dairy herds.

PubMed Central

Zadoks, R. N.; Allore, H. G.; Hagenaars, T. J.; Barkema, H. W.; Schukken, Y. H.

2002-01-01

An ordinary differential equation model was developed to simulate dynamics of Staphylococcus aureus mastitis. Data to estimate model parameters were obtained from an 18-month observational study in three commercial dairy herds. A deterministic simulation model was constructed to estimate values of the basic (R0) and effective (Rt) reproductive number in each herd, and to examine the effect of management on mastitis control. In all herds R0 was below the threshold value 1, indicating control of contagious transmission. Rt was higher than R0 because recovered individuals were more susceptible to infection than individuals without prior infection history. Disease dynamics in two herds were well described by the model. Treatment of subclinical mastitis and prevention of influx of infected individuals contributed to decrease of S. aureus prevalence. For one herd, the model failed to mimic field observations. Explanations for the discrepancy are given in a discussion of current knowledge and model assumptions. PMID:12403116

Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion

NASA Astrophysics Data System (ADS)

Majda, Andrew J.; Tong, Xin T.

2016-10-01

Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Xu; Tuo, Rui; Jeff Wu, C. F.

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE PAGES

He, Xu; Tuo, Rui; Jeff Wu, C. F.

2017-01-31

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Understanding the persistence of measles: reconciling theory, simulation and observation.

PubMed Central

Keeling, Matt J; Grenfell, Bryan T

2002-01-01

Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'. PMID:11886620

The past, present and future of cyber-physical systems: a focus on models.

PubMed

Lee, Edward A

2015-02-26

This paper is about better engineering of cyber-physical systems (CPSs) through better models. Deterministic models have historically proven extremely useful and arguably form the kingpin of the industrial revolution and the digital and information technology revolutions. Key deterministic models that have proven successful include differential equations, synchronous digital logic and single-threaded imperative programs. Cyber-physical systems, however, combine these models in such a way that determinism is not preserved. Two projects show that deterministic CPS models with faithful physical realizations are possible and practical. The first project is PRET, which shows that the timing precision of synchronous digital logic can be practically made available at the software level of abstraction. The second project is Ptides (programming temporally-integrated distributed embedded systems), which shows that deterministic models for distributed cyber-physical systems have practical faithful realizations. These projects are existence proofs that deterministic CPS models are possible and practical.

The Past, Present and Future of Cyber-Physical Systems: A Focus on Models

PubMed Central

Lee, Edward A.

2015-01-01

This paper is about better engineering of cyber-physical systems (CPSs) through better models. Deterministic models have historically proven extremely useful and arguably form the kingpin of the industrial revolution and the digital and information technology revolutions. Key deterministic models that have proven successful include differential equations, synchronous digital logic and single-threaded imperative programs. Cyber-physical systems, however, combine these models in such a way that determinism is not preserved. Two projects show that deterministic CPS models with faithful physical realizations are possible and practical. The first project is PRET, which shows that the timing precision of synchronous digital logic can be practically made available at the software level of abstraction. The second project is Ptides (programming temporally-integrated distributed embedded systems), which shows that deterministic models for distributed cyber-physical systems have practical faithful realizations. These projects are existence proofs that deterministic CPS models are possible and practical. PMID:25730486

Modeling heterogeneous responsiveness of intrinsic apoptosis pathway

PubMed Central

2013-01-01

Background Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism’s survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level. Results To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway. Conclusions Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness. PMID:23875784

Model of the material removal function and an experimental study on a magnetorheological finishing process using a small ball-end permanent-magnet polishing head.

PubMed

Chen, Mingjun; Liu, Henan; Cheng, Jian; Yu, Bo; Fang, Zhen

2017-07-01

In order to achieve the deterministic finishing of optical components with concave surfaces of a curvature radius less than 10 mm, a novel magnetorheological finishing (MRF) process using a small ball-end permanent-magnet polishing head with a diameter of 4 mm is introduced. The characteristics of material removal in the proposed MRF process are studied. The model of the material removal function for the proposed MRF process is established based on the three-dimensional hydrodynamics analysis and Preston's equation. The shear stress on the workpiece surface is calculated by means of resolving the presented mathematical model using a numerical solution method. The analysis result reveals that the material removal in the proposed MRF process shows a positive dependence on shear stress. Experimental research is conducted to investigate the effect of processing parameters on the material removal rate and improve the surface accuracy of a typical rotational symmetrical optical component. The experimental results show that the surface accuracy of the finished component of K9 glass material has been improved to 0.14 μm (PV) from the initial 0.8 μm (PV), and the finished surface roughness Ra is 0.0024 μm. It indicates that the proposed MRF process can be used to achieve the deterministic removal of surface material and perform the nanofinishing of small curvature radius concave surfaces.

Deterministic and stochastic CTMC models from Zika disease transmission

NASA Astrophysics Data System (ADS)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

Improving ground-penetrating radar data in sedimentary rocks using deterministic deconvolution

USGS Publications Warehouse

Xia, J.; Franseen, E.K.; Miller, R.D.; Weis, T.V.; Byrnes, A.P.

2003-01-01

Resolution is key to confidently identifying unique geologic features using ground-penetrating radar (GPR) data. Source wavelet "ringing" (related to bandwidth) in a GPR section limits resolution because of wavelet interference, and can smear reflections in time and/or space. The resultant potential for misinterpretation limits the usefulness of GPR. Deconvolution offers the ability to compress the source wavelet and improve temporal resolution. Unlike statistical deconvolution, deterministic deconvolution is mathematically simple and stable while providing the highest possible resolution because it uses the source wavelet unique to the specific radar equipment. Source wavelets generated in, transmitted through and acquired from air allow successful application of deterministic approaches to wavelet suppression. We demonstrate the validity of using a source wavelet acquired in air as the operator for deterministic deconvolution in a field application using "400-MHz" antennas at a quarry site characterized by interbedded carbonates with shale partings. We collected GPR data on a bench adjacent to cleanly exposed quarry faces in which we placed conductive rods to provide conclusive groundtruth for this approach to deconvolution. The best deconvolution results, which are confirmed by the conductive rods for the 400-MHz antenna tests, were observed for wavelets acquired when the transmitter and receiver were separated by 0.3 m. Applying deterministic deconvolution to GPR data collected in sedimentary strata at our study site resulted in an improvement in resolution (50%) and improved spatial location (0.10-0.15 m) of geologic features compared to the same data processed without deterministic deconvolution. The effectiveness of deterministic deconvolution for increased resolution and spatial accuracy of specific geologic features is further demonstrated by comparing results of deconvolved data with nondeconvolved data acquired along a 30-m transect immediately adjacent to a fresh quarry face. The results at this site support using deterministic deconvolution, which incorporates the GPR instrument's unique source wavelet, as a standard part of routine GPR data processing. ?? 2003 Elsevier B.V. All rights reserved.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

Modeling Day-to-day Flow Dynamics on Degradable Transport Network

PubMed Central

Gao, Bo; Zhang, Ronghui; Lou, Xiaoming

2016-01-01

Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties. PMID:27959903

Predicting reasoning from memory.

PubMed

Heit, Evan; Hayes, Brett K

2011-02-01

In an effort to assess the relations between reasoning and memory, in 8 experiments, the authors examined how well responses on an inductive reasoning task are predicted from responses on a recognition memory task for the same picture stimuli. Across several experimental manipulations, such as varying study time, presentation frequency, and the presence of stimuli from other categories, there was a high correlation between reasoning and memory responses (average r = .87), and these manipulations showed similar effects on the 2 tasks. The results point to common mechanisms underlying inductive reasoning and recognition memory abilities. A mathematical model, GEN-EX (generalization from examples), derived from exemplar models of categorization, is presented, which predicts both reasoning and memory responses from pairwise similarities among the stimuli, allowing for additional influences of subtyping and deterministic responding. (c) 2010 APA, all rights reserved.

A history of chaos theory.

PubMed

Oestreicher, Christian

2007-01-01

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.

A history of chaos theory

PubMed Central

Oestreicher, Christian

2007-01-01

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model

PubMed Central

Nené, Nuno R.; Dunham, Alistair S.; Illingworth, Christopher J. R.

2018-01-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. PMID:29500183

Optimal control problems of epidemic systems with parameter uncertainties: application to a malaria two-age-classes transmission model with asymptomatic carriers.

PubMed

Mwanga, Gasper G; Haario, Heikki; Capasso, Vicenzo

2015-03-01

The main scope of this paper is to study the optimal control practices of malaria, by discussing the implementation of a catalog of optimal control strategies in presence of parameter uncertainties, which is typical of infectious diseases data. In this study we focus on a deterministic mathematical model for the transmission of malaria, including in particular asymptomatic carriers and two age classes in the human population. A partial qualitative analysis of the relevant ODE system has been carried out, leading to a realistic threshold parameter. For the deterministic model under consideration, four possible control strategies have been analyzed: the use of Long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic and asymptomatic individuals. The numerical results show that using optimal control the disease can be brought to a stable disease free equilibrium when all four controls are used. The Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures is determined. The numerical simulations of the optimal control in the presence of parameter uncertainty demonstrate the robustness of the optimal control: the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the designing of cost-effective strategies for disease controls with multiple interventions, even under considerable uncertainty of model parameters. Copyright © 2014 Elsevier Inc. All rights reserved.

An efficient deterministic-probabilistic approach to modeling regional groundwater flow: 2. Application to Owens Valley, California

USGS Publications Warehouse

Guymon, Gary L.; Yen, Chung-Cheng

1990-01-01

The applicability of a deterministic-probabilistic model for predicting water tables in southern Owens Valley, California, is evaluated. The model is based on a two-layer deterministic model that is cascaded with a two-point probability model. To reduce the potentially large number of uncertain variables in the deterministic model, lumping of uncertain variables was evaluated by sensitivity analysis to reduce the total number of uncertain variables to three variables: hydraulic conductivity, storage coefficient or specific yield, and source-sink function. Results demonstrate that lumping of uncertain parameters reduces computational effort while providing sufficient precision for the case studied. Simulated spatial coefficients of variation for water table temporal position in most of the basin is small, which suggests that deterministic models can predict water tables in these areas with good precision. However, in several important areas where pumping occurs or the geology is complex, the simulated spatial coefficients of variation are over estimated by the two-point probability method.

An efficient deterministic-probabilistic approach to modeling regional groundwater flow: 2. Application to Owens Valley, California

NASA Astrophysics Data System (ADS)

Guymon, Gary L.; Yen, Chung-Cheng

1990-07-01

The applicability of a deterministic-probabilistic model for predicting water tables in southern Owens Valley, California, is evaluated. The model is based on a two-layer deterministic model that is cascaded with a two-point probability model. To reduce the potentially large number of uncertain variables in the deterministic model, lumping of uncertain variables was evaluated by sensitivity analysis to reduce the total number of uncertain variables to three variables: hydraulic conductivity, storage coefficient or specific yield, and source-sink function. Results demonstrate that lumping of uncertain parameters reduces computational effort while providing sufficient precision for the case studied. Simulated spatial coefficients of variation for water table temporal position in most of the basin is small, which suggests that deterministic models can predict water tables in these areas with good precision. However, in several important areas where pumping occurs or the geology is complex, the simulated spatial coefficients of variation are over estimated by the two-point probability method.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Optimal strategy for controlling the spread of Plasmodium Knowlesi malaria: Treatment and culling

NASA Astrophysics Data System (ADS)

Abdullahi, Mohammed Baba; Hasan, Yahya Abu; Abdullah, Farah Aini

2015-05-01

Plasmodium Knowlesi malaria is a parasitic mosquito-borne disease caused by a eukaryotic protist of genus Plasmodium Knowlesi transmitted by mosquito, Anopheles leucosphyrus to human and macaques. We developed and analyzed a deterministic Mathematical model for the transmission of Plasmodium Knowlesi malaria in human and macaques. The optimal control theory is applied to investigate optimal strategies for controlling the spread of Plasmodium Knowlesi malaria using treatment and culling as control strategies. The conditions for optimal control of the Plasmodium Knowlesi malaria are derived using Pontryagin's Maximum Principle. Finally, numerical simulations suggested that the combination of the control strategies is the best way to control the disease in any community.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Genetic algorithms using SISAL parallel programming language

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tejada, S.

1994-05-06

Genetic algorithms are a mathematical optimization technique developed by John Holland at the University of Michigan [1]. The SISAL programming language possesses many of the characteristics desired to implement genetic algorithms. SISAL is a deterministic, functional programming language which is inherently parallel. Because SISAL is functional and based on mathematical concepts, genetic algorithms can be efficiently translated into the language. Several of the steps involved in genetic algorithms, such as mutation, crossover, and fitness evaluation, can be parallelized using SISAL. In this paper I will l discuss the implementation and performance of parallel genetic algorithms in SISAL.

A systems approach to college drinking: development of a deterministic model for testing alcohol control policies.

PubMed

Scribner, Richard; Ackleh, Azmy S; Fitzpatrick, Ben G; Jacquez, Geoffrey; Thibodeaux, Jeremy J; Rommel, Robert; Simonsen, Neal

2009-09-01

The misuse and abuse of alcohol among college students remain persistent problems. Using a systems approach to understand the dynamics of student drinking behavior and thus forecasting the impact of campus policy to address the problem represents a novel approach. Toward this end, the successful development of a predictive mathematical model of college drinking would represent a significant advance for prevention efforts. A deterministic, compartmental model of college drinking was developed, incorporating three processes: (1) individual factors, (2) social interactions, and (3) social norms. The model quantifies these processes in terms of the movement of students between drinking compartments characterized by five styles of college drinking: abstainers, light drinkers, moderate drinkers, problem drinkers, and heavy episodic drinkers. Predictions from the model were first compared with actual campus-level data and then used to predict the effects of several simulated interventions to address heavy episodic drinking. First, the model provides a reasonable fit of actual drinking styles of students attending Social Norms Marketing Research Project campuses varying by "wetness" and by drinking styles of matriculating students. Second, the model predicts that a combination of simulated interventions targeting heavy episodic drinkers at a moderately "dry" campus would extinguish heavy episodic drinkers, replacing them with light and moderate drinkers. Instituting the same combination of simulated interventions at a moderately "wet" campus would result in only a moderate reduction in heavy episodic drinkers (i.e., 50% to 35%). A simple, five-state compartmental model adequately predicted the actual drinking patterns of students from a variety of campuses surveyed in the Social Norms Marketing Research Project study. The model predicted the impact on drinking patterns of several simulated interventions to address heavy episodic drinking on various types of campuses.

A Systems Approach to College Drinking: Development of a Deterministic Model for Testing Alcohol Control Policies*

PubMed Central

Scribner, Richard; Ackleh, Azmy S.; Fitzpatrick, Ben G.; Jacquez, Geoffrey; Thibodeaux, Jeremy J.; Rommel, Robert; Simonsen, Neal

2009-01-01

Objective: The misuse and abuse of alcohol among college students remain persistent problems. Using a systems approach to understand the dynamics of student drinking behavior and thus forecasting the impact of campus policy to address the problem represents a novel approach. Toward this end, the successful development of a predictive mathematical model of college drinking would represent a significant advance for prevention efforts. Method: A deterministic, compartmental model of college drinking was developed, incorporating three processes: (1) individual factors, (2) social interactions, and (3) social norms. The model quantifies these processes in terms of the movement of students between drinking compartments characterized by five styles of college drinking: abstainers, light drinkers, moderate drinkers, problem drinkers, and heavy episodic drinkers. Predictions from the model were first compared with actual campus-level data and then used to predict the effects of several simulated interventions to address heavy episodic drinking. Results: First, the model provides a reasonable fit of actual drinking styles of students attending Social Norms Marketing Research Project campuses varying by “wetness” and by drinking styles of matriculating students. Second, the model predicts that a combination of simulated interventions targeting heavy episodic drinkers at a moderately “dry” campus would extinguish heavy episodic drinkers, replacing them with light and moderate drinkers. Instituting the same combination of simulated interventions at a moderately “wet” campus would result in only a moderate reduction in heavy episodic drinkers (i.e., 50% to 35%). Conclusions: A simple, five-state compartmental model adequately predicted the actual drinking patterns of students from a variety of campuses surveyed in the Social Norms Marketing Research Project study. The model predicted the impact on drinking patterns of several simulated interventions to address heavy episodic drinking on various types of campuses. PMID:19737506

From qualitative data to quantitative models: analysis of the phage shock protein stress response in Escherichia coli

PubMed Central

2011-01-01

Background Bacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment. These are crucial for their survival, which requires them to react to extracellular stresses such as heat shock, ethanol treatment or phage infection. Here we focus on studying the phage shock protein (Psp) stress response in Escherichia coli induced by a phage infection or other damage to the bacterial membrane. This system has not yet been theoretically modelled or analysed in silico. Results We develop a model of the Psp response system, and illustrate how such models can be constructed and analyzed in light of available sparse and qualitative information in order to generate novel biological hypotheses about their dynamical behaviour. We analyze this model using tools from Petri-net theory and study its dynamical range that is consistent with currently available knowledge by conditioning model parameters on the available data in an approximate Bayesian computation (ABC) framework. Within this ABC approach we analyze stochastic and deterministic dynamics. This analysis allows us to identify different types of behaviour and these mechanistic insights can in turn be used to design new, more detailed and time-resolved experiments. Conclusions We have developed the first mechanistic model of the Psp response in E. coli. This model allows us to predict the possible qualitative stochastic and deterministic dynamic behaviours of key molecular players in the stress response. Our inferential approach can be applied to stress response and signalling systems more generally: in the ABC framework we can condition mathematical models on qualitative data in order to delimit e.g. parameter ranges or the qualitative system dynamics in light of available end-point or qualitative information. PMID:21569396

Stochastic modelling of human exposure to food chemicals and nutrients within the "Montecarlo" project: an exploration of the influence of brand loyalty and market share on intake estimates of intense sweeteners from sugar-free soft drinks.

PubMed

Leclercq, Catherine; Arcella, Davide; Le Donne, Cinzia; Piccinelli, Raffaela; Sette, Stefania; Soggiu, Maria Eleonora

2003-04-11

To get a more realistic view of exposure to food chemicals, risk managers are getting more interested in stochastic modelling as an alternative to deterministic approaches based on conservative assumptions. It allows to take into account all the available information in the concentration of the chemical present in foods and in food consumption patterns. Within the EC-funded "Montecarlo" project, a comprehensive set of mathematical algorithms was developed to take into account all the necessary components for stochastic modelling of a variety of food chemicals, nutrients and ingredients. An appropriate computer software is being developed. Since the concentration of food chemicals may vary among different brands of the same product, consumer behaviour with respect to brands may have an impact on exposure assessments. Numeric experiments were carried out on different ways of incorporating indicators of market share and brand loyalty in the mathematical algorithms developed within the stochastic model of exposure to intense sweeteners from sugar-free beverages. The 95th percentiles of intake were shown to vary according to the inclusion/exclusion of these indicators. The market share should be included in the model especially if the market is not equitably distributed between brands. If brand loyalty data are not available, the model may be run under theoretical scenarios.

Mathematical biomarkers for the autonomic regulation of cardiovascular system.

PubMed

Campos, Luciana A; Pereira, Valter L; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-10-07

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

Mathematical biomarkers for the autonomic regulation of cardiovascular system

PubMed Central

Campos, Luciana A.; Pereira, Valter L.; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-01-01

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance. PMID:24109456

Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries--Validation and Application to the 2014-2015 Ebola Virus Disease Epidemic.

PubMed

Ivorra, Benjamin; Ngom, Diène; Ramos, Ángel M

2015-09-01

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model.

PubMed

Nené, Nuno R; Dunham, Alistair S; Illingworth, Christopher J R

2018-05-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. Copyright © 2018 Nené et al.

Research on efficiency evaluation model of integrated energy system based on hybrid multi-attribute decision-making.

PubMed

Li, Yan

2017-05-25

The efficiency evaluation model of integrated energy system, involving many influencing factors, and the attribute values are heterogeneous and non-deterministic, usually cannot give specific numerical or accurate probability distribution characteristics, making the final evaluation result deviation. According to the characteristics of the integrated energy system, a hybrid multi-attribute decision-making model is constructed. The evaluation model considers the decision maker's risk preference. In the evaluation of the efficiency of the integrated energy system, the evaluation value of some evaluation indexes is linguistic value, or the evaluation value of the evaluation experts is not consistent. These reasons lead to ambiguity in the decision information, usually in the form of uncertain linguistic values and numerical interval values. In this paper, the risk preference of decision maker is considered when constructing the evaluation model. Interval-valued multiple-attribute decision-making method and fuzzy linguistic multiple-attribute decision-making model are proposed. Finally, the mathematical model of efficiency evaluation of integrated energy system is constructed.

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Discussion and revision of the mathematical modeling tool described in the previously published article "Modeling HIV Transmission risk among Mozambicans prior to their initiating highly active antiretroviral therapy".

PubMed

Cassels, Susan; Pearson, Cynthia R; Kurth, Ann E; Martin, Diane P; Simoni, Jane M; Matediana, Eduardo; Gloyd, Stephen

2009-07-01

Mathematical models are increasingly used in social and behavioral studies of HIV transmission; however, model structures must be chosen carefully to best answer the question at hand and conclusions must be interpreted cautiously. In Pearson et al. (2007), we presented a simple analytically tractable deterministic model to estimate the number of secondary HIV infections stemming from a population of HIV-positive Mozambicans and to evaluate how the estimate would change under different treatment and behavioral scenarios. In a subsequent application of the model with a different data set, we observed that the model produced an unduly conservative estimate of the number of new HIV-1 infections. In this brief report, our first aim is to describe a revision of the model to correct for this underestimation. Specifically, we recommend adjusting the population-level sexually transmitted infection (STI) parameters to be applicable to the individual-level model specification by accounting for the proportion of individuals uninfected with an STI. In applying the revised model to the original data, we noted an estimated 40 infections/1000 HIV-positive persons per year (versus the original 23 infections/1000 HIV-positive persons per year). In addition, the revised model estimated that highly active antiretroviral therapy (HAART) along with syphilis and herpes simplex virus type 2 (HSV-2) treatments combined could reduce HIV-1 transmission by 72% (versus 86% according to the original model). The second aim of this report is to discuss the advantages and disadvantages of mathematical models in the field and the implications of model interpretation. We caution that simple models should be used for heuristic purposes only. Since these models do not account for heterogeneity in the population and significantly simplify HIV transmission dynamics, they should be used to describe general characteristics of the epidemic and demonstrate the importance or sensitivity of parameters in the model.

Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition.

PubMed

Alemani, Davide; Pappalardo, Francesco; Pennisi, Marzio; Motta, Santo; Brusic, Vladimir

2012-02-28

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. Copyright © 2011 Elsevier B.V. All rights reserved.

Stochastic Petri Net extension of a yeast cell cycle model.

PubMed

Mura, Ivan; Csikász-Nagy, Attila

2008-10-21

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling

NASA Astrophysics Data System (ADS)

Pankratov, Oleg; Kuvshinov, Alexey

2016-01-01

Despite impressive progress in the development and application of electromagnetic (EM) deterministic inverse schemes to map the 3-D distribution of electrical conductivity within the Earth, there is one question which remains poorly addressed—uncertainty quantification of the recovered conductivity models. Apparently, only an inversion based on a statistical approach provides a systematic framework to quantify such uncertainties. The Metropolis-Hastings (M-H) algorithm is the most popular technique for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. However, all statistical inverse schemes require an enormous amount of forward simulations and thus appear to be extremely demanding computationally, if not prohibitive, if a 3-D set up is invoked. This urges development of fast and scalable 3-D modelling codes which can run large-scale 3-D models of practical interest for fractions of a second on high-performance multi-core platforms. But, even with these codes, the challenge for M-H methods is to construct proposal functions that simultaneously provide a good approximation of the target density function while being inexpensive to be sampled. In this paper we address both of these issues. First we introduce a variant of the M-H method which uses information about the local gradient and Hessian of the penalty function. This, in particular, allows us to exploit adjoint-based machinery that has been instrumental for the fast solution of deterministic inverse problems. We explain why this modification of M-H significantly accelerates sampling of the posterior probability distribution. In addition we show how Hessian handling (inverse, square root) can be made practicable by a low-rank approximation using the Lanczos algorithm. Ultimately we discuss uncertainty analysis based on stochastic inversion results. In addition, we demonstrate how this analysis can be performed within a deterministic approach. In the second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.

Disentangling Mechanisms That Mediate the Balance Between Stochastic and Deterministic Processes in Microbial Succession

DOE PAGES

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan D.; ...

2015-03-17

Despite growing recognition that deterministic and stochastic factors simultaneously influence bacterial communities, little is known about mechanisms shifting their relative importance. To better understand underlying mechanisms, we developed a conceptual model linking ecosystem development during primary succession to shifts in the stochastic/deterministic balance. To evaluate the conceptual model we coupled spatiotemporal data on soil bacterial communities with environmental conditions spanning 105 years of salt marsh development. At the local scale there was a progression from stochasticity to determinism due to Na accumulation with increasing ecosystem age, supporting a main element of the conceptual model. At the regional-scale, soil organic mattermore » (SOM) governed the relative influence of stochasticity and the type of deterministic ecological selection, suggesting scale-dependency in how deterministic ecological selection is imposed. Analysis of a new ecological simulation model supported these conceptual inferences. Looking forward, we propose an extended conceptual model that integrates primary and secondary succession in microbial systems.« less

How to reach linguistic consensus: a proof of convergence for the naming game.

PubMed

De Vylder, Bart; Tuyls, Karl

2006-10-21

In this paper we introduce a mathematical model of naming games. Naming games have been widely used within research on the origins and evolution of language. Despite the many interesting empirical results these studies have produced, most of this research lacks a formal elucidating theory. In this paper we show how a population of agents can reach linguistic consensus, i.e. learn to use one common language to communicate with one another. Our approach differs from existing formal work in two important ways: one, we relax the too strong assumption that an agent samples infinitely often during each time interval. This assumption is usually made to guarantee convergence of an empirical learning process to a deterministic dynamical system. Two, we provide a proof that under these new realistic conditions, our model converges to a common language for the entire population of agents. Finally the model is experimentally validated.

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE PAGES

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab; ...

2016-11-21

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

Effect of a preventive vaccine on the dynamics of HIV transmission

NASA Astrophysics Data System (ADS)

Gumel, A. B.; Moghadas, S. M.; Mickens, R. E.

2004-12-01

A deterministic mathematical model for the transmission dynamics of HIV infection in the presence of a preventive vaccine is considered. Although the equilibria of the model could not be expressed in closed form, their existence and threshold conditions for their stability are theoretically investigated. It is shown that the disease-free equilibrium is locally-asymptotically stable if the basic reproductive number R<1 (thus, HIV disease can be eradicated from the community) and unstable if R>1 (leading to the persistence of HIV within the community). A robust, positivity-preserving, non-standard finite-difference method is constructed and used to solve the model equations. In addition to showing that the anti-HIV vaccine coverage level and the vaccine-induced protection are critically important in reducing the threshold quantity R, our study predicts the minimum threshold values of vaccine coverage and efficacy levels needed to eradicate HIV from the community.

Shared and Unique Risk Factors Underlying Mathematical Disability and Reading and Spelling Disability.

PubMed

Slot, Esther M; van Viersen, Sietske; de Bree, Elise H; Kroesbergen, Evelyn H

2016-01-01

High comorbidity rates have been reported between mathematical learning disabilities (MD) and reading and spelling disabilities (RSD). Research has identified skills related to math, such as number sense (NS) and visuospatial working memory (visuospatial WM), as well as to literacy, such as phonological awareness (PA), rapid automatized naming (RAN) and verbal short-term memory (Verbal STM). In order to explain the high comorbidity rates between MD and RSD, 7-11-year-old children were assessed on a range of cognitive abilities related to literacy (PA, RAN, Verbal STM) and mathematical ability (visuospatial WM, NS). The group of children consisted of typically developing (TD) children (n = 32), children with MD (n = 26), children with RSD (n = 29), and combined MD and RSD (n = 43). It was hypothesized that, in line with the multiple deficit view on learning disorders, at least one unique predictor for both MD and RSD and a possible shared cognitive risk factor would be found to account for the comorbidity between the symptom dimensions literacy and math. Secondly, our hypotheses were that (a) a probabilistic multi-factorial risk factor model would provide a better fit to the data than a deterministic single risk factor model and (b) that a shared risk factor model would provide a better fit than the specific multi-factorial model. All our hypotheses were confirmed. NS and visuospatial WM were identified as unique cognitive predictors for MD, whereas PA and RAN were both associated with RSD. Also, a shared risk factor model with PA as a cognitive predictor for both RSD and MD fitted the data best, indicating that MD and RSD might co-occur due to a shared underlying deficit in phonological processing. Possible explanations are discussed in the context of sample selection and composition. This study shows that different cognitive factors play a role in mathematics and literacy, and that a phonological processing deficit might play a role in the occurrence of MD and RSD.

Vibration study of a vehicle suspension assembly with the finite element method

NASA Astrophysics Data System (ADS)

Cătălin Marinescu, Gabriel; Castravete, Ştefan-Cristian; Dumitru, Nicolae

2017-10-01

The main steps of the present work represent a methodology of analysing various vibration effects over suspension mechanical parts of a vehicle. A McPherson type suspension from an existing vehicle was created using CAD software. Using the CAD model as input, a finite element model of the suspension assembly was developed. Abaqus finite element analysis software was used to pre-process, solve, and post-process the results. Geometric nonlinearities are included in the model. Severe sources of nonlinearities such us friction and contact are also included in the model. The McPherson spring is modelled as linear spring. The analysis include several steps: preload, modal analysis, the reduction of the model to 200 generalized coordinates, a deterministic external excitation, a random excitation that comes from different types of roads. The vibration data used as an input for the simulation were previously obtained by experimental means. Mathematical expressions used for the simulation were also presented in the paper.

Sewer solids separation by sedimentation--the problem of modeling, validation and transferability.

PubMed

Kutzner, R; Brombach, H; Geiger, W F

2007-01-01

Sedimentation of sewer solids in tanks, ponds and similar devices is the most relevant process for the treatment of stormwater and combined sewer overflows in urban collecting systems. In the past a lot of research work was done to develop deterministic models for the description of this separation process. But these modern models are not commonly accepted in Germany until today. Water Authorities are sceptical with regard to model validation and transferability. Within this paper it is checked whether this scepticism is reasonable. A framework-proposal for the validation of mathematical models with zero or one dimensional spatial resolution for particle separation processes for stormwater and combined sewer overflow treatment is presented. This proposal was applied to publications of repute on sewer solids separation by sedimentation. The result was that none of the investigated models described in literature passed the validation entirely. There is an urgent need for future research in sewer solids sedimentation and remobilization!

Mathematical background of Parrondo's paradox

NASA Astrophysics Data System (ADS)

Behrends, Ehrhard

2004-05-01

Parrondo's paradox states that there are losing gambling games which, when being combined stochastically or in a suitable deterministic way, give rise to winning games. Here we investigate the probabilistic background. We show how the properties of the equilibrium distributions of the Markov chains under consideration give rise to the paradoxical behavior, and we provide methods how to find the best a priori strategies.

A New View of Radiation-Induced Cancer: Integrating Short-and Long-Term Processes. Part I: Approach

NASA Technical Reports Server (NTRS)

Shuryak, Igor; Hahnfeldt, Philip; Hlatky, Lynn; Sachs, Rainer K.; Brenner, David J.

2009-01-01

Mathematical models of radiation carcinogenesis are important for understanding mechanisms and for interpreting or extrapolating risk. There are two classes of such models: (1) long-term formalisms that track premalignant cell numbers throughout an entire lifetime but treat initial radiation dose-response simplistically and (2) short-term formalisms that provide a detailed initial dose-response even for complicated radiation protocols, but address its modulation during the subsequent cancer latency period only indirectly. We argue that integrating short- and long-term models is needed. As an example of this novel approach, we integrate a stochastic short-term initiation/ inactivation/repopulation model with a deterministic two-stage long-term model. Within this new formalism, the following assumptions are implemented: radiation initiates, promotes, or kills pre-malignant cells; a pre-malignant cell generates a clone, which, if it survives, quickly reaches a size limitation; the clone subsequently grows more slowly and can eventually generate a malignant cell; the carcinogenic potential of pre-malignant cells decreases with age.

The Deterministic Information Bottleneck

NASA Astrophysics Data System (ADS)

Strouse, D. J.; Schwab, David

2015-03-01

A fundamental and ubiquitous task that all organisms face is prediction of the future based on past sensory experience. Since an individual's memory resources are limited and costly, however, there is a tradeoff between memory cost and predictive payoff. The information bottleneck (IB) method (Tishby, Pereira, & Bialek 2000) formulates this tradeoff as a mathematical optimization problem using an information theoretic cost function. IB encourages storing as few bits of past sensory input as possible while selectively preserving the bits that are most predictive of the future. Here we introduce an alternative formulation of the IB method, which we call the deterministic information bottleneck (DIB). First, we argue for an alternative cost function, which better represents the biologically-motivated goal of minimizing required memory resources. Then, we show that this seemingly minor change has the dramatic effect of converting the optimal memory encoder from stochastic to deterministic. Next, we propose an iterative algorithm for solving the DIB problem. Additionally, we compare the IB and DIB methods on a variety of synthetic datasets, and examine the performance of retinal ganglion cell populations relative to the optimal encoding strategy for each problem.

Detailed gravity anomalies from GEOS-3 satellite altimetry data

NASA Technical Reports Server (NTRS)

Gopalapillai, G. S.; Mourad, A. G.

1978-01-01

A technique for deriving mean gravity anomalies from dense altimetry data was developed. A combination of both deterministic and statistical techniques was used. The basic mathematical model was based on the Stokes' equation which describes the analytical relationship between mean gravity anomalies and geoid undulations at a point; this undulation is a linear function of the altimetry data at that point. The overdetermined problem resulting from the excessive altimetry data available was solved using Least-Squares principles. These principles enable the simultaneous estimation of the associated standard deviations reflecting the internal consistency based on the accuracy estimates provided for the altimetry data as well as for the terrestrial anomaly data. Several test computations were made of the anomalies and their accuracy estimates using GOES-3 data.

Cognitive Diagnostic Analysis Using Hierarchically Structured Skills

ERIC Educational Resources Information Center

Su, Yu-Lan

2013-01-01

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…

Using cellular automata to simulate forest fire propagation in Portugal

NASA Astrophysics Data System (ADS)

Freire, Joana; daCamara, Carlos

2017-04-01

Wildfires in the Mediterranean region have severe damaging effects mainly due to large fire events [1, 2]. When restricting to Portugal, wildfires have burned over 1:4 million ha in the last decade. Considering the increasing tendency in the extent and severity of wildfires [1, 2], the availability of modeling tools of fire episodes is of crucial importance. Two main types of mathematical models are generally available, namely deterministic and stochastic models. Deterministic models attempt a description of fires, fuel and atmosphere as multiphase continua prescribing mass, momentum and energy conservation, which typically leads to systems of coupled PDEs to be solved numerically on a grid. Simpler descriptions, such as FARSITE, neglect the interaction with atmosphere and propagate the fire front using wave techniques. One of the most important stochastic models are Cellular Automata (CA), in which space is discretized into cells, and physical quantities take on a finite set of values at each cell. The cells evolve in discrete time according to a set of transition rules, and the states of the neighboring cells. In the present work, we implement and then improve a simple and fast CA model designed to operationally simulate wildfires in Portugal. The reference CA model chosen [3] has the advantage of having been applied successfully in other Mediterranean ecosystems, namely to historical fires in Greece. The model is defined on a square grid with propagation to 8 nearest and next-nearest neighbors, where each cell is characterized by 4 possible discrete states, corresponding to burning, not-yet burned, fuel-free and completely burned cells, with 4 possible rules of evolution which take into account fuel properties, meteorological conditions, and topography. As a CA model, it offers the possibility to run a very high number of simulations in order to verify and apply the model, and is easily modified by implementing additional variables and different rules for the evolution of the fire spread. We present and discuss the application of the CA model to the "Tavira wildfire" in which approximately 24,800ha were burned. The event took place in summer 2012, between July 18 and 21, and spread in the Tavira and São Brás de Alportel municipalities of Algarve, a province in the southern coast of Portugal. [1] DaCamara et. al. (2014), International Journal of Wildland Fire 23. [2] Amraoui et. al. (2013), Forest Ecology and Management 294. [3] Alexandridis et. al. (2008), Applied Mathematics and Computation 204.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

[Assessing the trend in the aging of the nursing staff at two hospitals of the Friuli Venezia Giulia region: application of a deterministic mathematical model].

PubMed

Guardini, Ilario; Deroma, Laura; Salmaso, Daniele; Palese, Alvisa

2011-01-01

The aging of the nursing workforce is a phenomenon that several industrialized countries has been facing for at least a decade. In Italy, for the period between 2011 and 2021, the issue associated with the nursing workforce will not be one of shortage but rather one of aging. The main objective of this study was to estimate the employed nurse population aging trends for the period 2009-2035 in two Teaching Hospitals (TH1 and TH2) located in the North of Italy. A deterministic mathematical model has been developed in order to obtain aging projections for the nursing workforce from 2009 until 2035. Within the next six years, the aging trend of nurse populations, with respect to 2008, at the TH 1 and 2 will show a steady increase of nurses aged over 45; specifically, a 29.4% vs. 34.1% increase and a 21.6% vs. 41.4% respectively. It is hypothesized that the TH 1 will have the highest proportion of nurses aged over 45 in 2014, whereas it is estimated that for the TH 2 this trend will continue until 2021 when the proportion of nurses aged over 45 will make up 48.8% out of the nurse population. The trend may lead to an increase in the number of experienced nurses; however, such a trend should be looked at with concern, with respect to the physical unsuitability. Nurses aged over 45 represent 20% of the workforce at both TH. Conclusions/implications for management and research. If the trend predicted by the model were to occur in the coming years, the problem of nursing workforce ageing will have to be addressed because it involves different expectations but also the perception of different work skills. The nursing direction is called to test new strategies for managing the staff and the career of nurses will also need to be redesigned, because contract law looks primarily at the initial stage of working life (specializations, university education, career opportunities) neglecting the final one (from the 50th year of age to retirement).

Numerical approaches to combustion modeling. Progress in Astronautics and Aeronautics. Vol. 135

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oran, E.S.; Boris, J.P.

1991-01-01

Various papers on numerical approaches to combustion modeling are presented. The topics addressed include; ab initio quantum chemistry for combustion; rate coefficient calculations for combustion modeling; numerical modeling of combustion of complex hydrocarbons; combustion kinetics and sensitivity analysis computations; reduction of chemical reaction models; length scales in laminar and turbulent flames; numerical modeling of laminar diffusion flames; laminar flames in premixed gases; spectral simulations of turbulent reacting flows; vortex simulation of reacting shear flow; combustion modeling using PDF methods. Also considered are: supersonic reacting internal flow fields; studies of detonation initiation, propagation, and quenching; numerical modeling of heterogeneous detonations, deflagration-to-detonationmore » transition to reactive granular materials; toward a microscopic theory of detonations in energetic crystals; overview of spray modeling; liquid drop behavior in dense and dilute clusters; spray combustion in idealized configurations: parallel drop streams; comparisons of deterministic and stochastic computations of drop collisions in dense sprays; ignition and flame spread across solid fuels; numerical study of pulse combustor dynamics; mathematical modeling of enclosure fires; nuclear systems.« less

Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

PubMed Central

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

DOE PAGES

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; ...

2013-10-15

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 2; Algebraic Approximation, Descriptive Parameters, and Normalized Universal Curve

NASA Technical Reports Server (NTRS)

Smialek, James L.

2002-01-01

A cyclic oxidation interfacial spalling model has been developed in Part 1. The governing equations have been simplified here by substituting a new algebraic expression for the series (Good-Smialek approximation). This produced a direct relationship between cyclic oxidation weight change and model input parameters. It also allowed for the mathematical derivation of various descriptive parameters as a function of the inputs. It is shown that the maximum in weight change varies directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the 1/2 power. The number of cycles to reach maximum and zero weight change vary inversely with the spall fraction, and the ratio of these cycles is exactly 1:3 for most oxides. By suitably normalizing the weight change and cycle number, it is shown that all cyclic oxidation weight change model curves can be represented by one universal expression for a given oxide scale.

Modeling Reality - How Computers Mirror Life

NASA Astrophysics Data System (ADS)

Bialynicki-Birula, Iwo; Bialynicka-Birula, Iwona

2005-01-01

The bookModeling Reality covers a wide range of fascinating subjects, accessible to anyone who wants to learn about the use of computer modeling to solve a diverse range of problems, but who does not possess a specialized training in mathematics or computer science. The material presented is pitched at the level of high-school graduates, even though it covers some advanced topics (cellular automata, Shannon's measure of information, deterministic chaos, fractals, game theory, neural networks, genetic algorithms, and Turing machines). These advanced topics are explained in terms of well known simple concepts: Cellular automata - Game of Life, Shannon's formula - Game of twenty questions, Game theory - Television quiz, etc. The book is unique in explaining in a straightforward, yet complete, fashion many important ideas, related to various models of reality and their applications. Twenty-five programs, written especially for this book, are provided on an accompanying CD. They greatly enhance its pedagogical value and make learning of even the more complex topics an enjoyable pleasure.

Noise induced phenomena in combustion

NASA Astrophysics Data System (ADS)

Liu, Hongliang

Quantitative models of combustion usually consist of systems of deterministic differential equations. However, there are reasons to suspect that noise may have a significant influence. In this thesis, our primary objective is to study the effect of noise on measurable quantities in the combustion process. Our first study involves combustion in a homogeneous gas. With a one step reaction model, we analytically estimate the requirements under which noise is important to create significant differences. Our simulation shows that a bi-modality phenomenon appears when appropriate parameters are applied, which agrees with our analytical result. Our second study involves steady planar flames. We use a relatively complete chemical model of the H2/air reaction system, which contains all eight reactive species (H2, O2, H, O, OH, H2O, HO2, H2O2) and N2. Our mathematical model for this system is a reacting flow model. We derive noise terms related to transport processes by a method advocated by Landau & Lifshitz, and we also derive noise terms related to chemical reactions. We develop a code to simulate this system. The numerical implementation relies on a good Riemann solver, suitable initial and boundary conditions, and so on. We also implement a code on a continuation method, which not only can be used to study approximate properties of laminar flames under deterministic governing equations, but also eliminates the difficulty of providing a suitable initial condition for governing equations with noise. With numerical experiments, we find the difference of flame speed exist when the noise is turned on or off although it is small when compared with the influence of other parameters, for example, the equivalence ratio. It will be a starting point for further studies to include noise in combustion.

Theory and applications survey of decentralized control methods

NASA Technical Reports Server (NTRS)

Athans, M.

1975-01-01

A nonmathematical overview is presented of trends in the general area of decentralized control strategies which are suitable for hierarchical systems. Advances in decentralized system theory are closely related to advances in the so-called stochastic control problem with nonclassical information pattern. The basic assumptions and mathematical tools pertaining to the classical stochastic control problem are outlined. Particular attention is devoted to pitfalls in the mathematical problem formulation for decentralized control. Major conclusions are that any purely deterministic approach to multilevel hierarchical dynamic systems is unlikely to lead to realistic theories or designs, that the flow of measurements and decisions in a decentralized system should not be instantaneous and error-free, and that delays in information exchange in a decentralized system lead to reasonable approaches to decentralized control. A mathematically precise notion of aggregating information is not yet available.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

PubMed Central

Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

2016-01-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell. PMID:27959915

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Mathematical modeling and pharmaceutical pricing: analyses used to inform in-licensing and developmental go/No-Go decisions.

PubMed

Vernon, John A; Hughen, W Keener; Johnson, Scott J

2005-05-01

In the face of significant real healthcare cost inflation, pressured budgets, and ongoing launches of myriad technology of uncertain value, payers have formalized new valuation techniques that represent a barrier to entry for drugs. Cost-effectiveness analysis predominates among these methods, which involves differencing a new technological intervention's marginal costs and benefits with a comparator's, and comparing the resulting ratio to a payer's willingness-to-pay threshold. In this paper we describe how firms are able to model the feasible range of future product prices when making in-licensing and developmental Go/No-Go decisions by considering payers' use of the cost-effectiveness method. We illustrate this analytic method with a simple deterministic example and then incorporate stochastic assumptions using both analytic and simulation methods. Using this strategic approach, firms may reduce product development and in-licensing risk.

Creating single-copy genetic circuits

PubMed Central

Lee, Jeong Wook; Gyorgy, Andras; Cameron, D. Ewen; Pyenson, Nora; Choi, Kyeong Rok; Way, Jeffrey C.; Silver, Pamela A.; Del Vecchio, Domitilla; Collins, James J.

2017-01-01

SUMMARY Synthetic biology is increasingly used to develop sophisticated living devices for basic and applied research. Many of these genetic devices are engineered using multi-copy plasmids, but as the field progresses from proof-of-principle demonstrations to practical applications, it is important to develop single-copy synthetic modules that minimize consumption of cellular resources and can be stably maintained as genomic integrants. Here we use empirical design, mathematical modeling and iterative construction and testing to build single-copy, bistable toggle switches with improved performance and reduced metabolic load that can be stably integrated into the host genome. Deterministic and stochastic models led us to focus on basal transcription to optimize circuit performance and helped to explain the resulting circuit robustness across a large range of component expression levels. The design parameters developed here provide important guidance for future efforts to convert functional multi-copy gene circuits into optimized single-copy circuits for practical, real-world use. PMID:27425413

Cell-Free Optogenetic Gene Expression System.

PubMed

Jayaraman, Premkumar; Yeoh, Jing Wui; Jayaraman, Sudhaghar; Teh, Ai Ying; Zhang, Jingyun; Poh, Chueh Loo

2018-04-20

Optogenetic tools provide a new and efficient way to dynamically program gene expression with unmatched spatiotemporal precision. To date, their vast potential remains untapped in the field of cell-free synthetic biology, largely due to the lack of simple and efficient light-switchable systems. Here, to bridge the gap between cell-free systems and optogenetics, we studied our previously engineered one component-based blue light-inducible Escherichia coli promoter in a cell-free environment through experimental characterization and mathematical modeling. We achieved >10-fold dynamic expression and demonstrated rapid and reversible activation of the target gene to generate oscillatory response. The deterministic model developed was able to recapitulate the system behavior and helped to provide quantitative insights to optimize dynamic response. This in vitro optogenetic approach could be a powerful new high-throughput screening technology for rapid prototyping of complex biological networks in both space and time without the need for chemical induction.

Rabies epidemic model with uncertainty in parameters: crisp and fuzzy approaches

NASA Astrophysics Data System (ADS)

Ndii, M. Z.; Amarti, Z.; Wiraningsih, E. D.; Supriatna, A. K.

2018-03-01

A deterministic mathematical model is formulated to investigate the transmission dynamics of rabies. In particular, we investigate the effects of vaccination, carrying capacity and the transmission rate on the rabies epidemics and allow for uncertainty in the parameters. We perform crisp and fuzzy approaches. We find that, in the case of crisp parameters, rabies epidemics may be interrupted when the carrying capacity and the transmission rate are not high. Our findings suggest that limiting the growth of dog population and reducing the potential contact between susceptible and infectious dogs may aid in interrupting rabies epidemics. We extend the work by considering a fuzzy carrying capacity and allow for low, medium, and high level of carrying capacity. The result confirms the results obtained by using crisp carrying capacity, that is, when the carrying capacity is not too high, the vaccination could confine the disease effectively.

Soliton driven angiogenesis

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Terragni, F.; Birnir, B.

2016-08-01

Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.

Deterministic models for traffic jams

NASA Astrophysics Data System (ADS)

Nagel, Kai; Herrmann, Hans J.

1993-10-01

We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the model shows self-organized critically driven by the slowest car.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Nonlinear Boltzmann equation for the homogeneous isotropic case: Some improvements to deterministic methods and applications to relaxation towards local equilibrium

NASA Astrophysics Data System (ADS)

Asinari, P.

2011-03-01

Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).

Elasto-limited plastic analysis of structures for probabilistic conditions

NASA Astrophysics Data System (ADS)

Movahedi Rad, M.

2018-06-01

With applying plastic analysis and design methods, significant saving in material can be obtained. However, as a result of this benefit excessive plastic deformations and large residual displacements might develop, which in turn might lead to unserviceability and collapse of the structure. In this study, for deterministic problem the residual deformation of structures is limited by considering a constraint on the complementary strain energy of the residual forces. For probabilistic problem the constraint for the complementary strain energy of the residual forces is given randomly and critical stresses updated during the iteration. Limit curves are presented for the plastic limit load factors. The results show that these constraints have significant effects on the load factors. The formulations of the deterministic and probabilistic problems lead to mathematical programming which are solved by the use of nonlinear algorithm.

Dynamic principle for ensemble control tools.

PubMed

Samoletov, A; Vasiev, B

2017-11-28

Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.

Modeling the role of environmental variables on the population dynamics of the malaria vector Anopheles gambiae sensu stricto

PubMed Central

2012-01-01

Background The impact of weather and climate on malaria transmission has attracted considerable attention in recent years, yet uncertainties around future disease trends under climate change remain. Mathematical models provide powerful tools for addressing such questions and understanding the implications for interventions and eradication strategies, but these require realistic modeling of the vector population dynamics and its response to environmental variables. Methods Published and unpublished field and experimental data are used to develop new formulations for modeling the relationships between key aspects of vector ecology and environmental variables. These relationships are integrated within a validated deterministic model of Anopheles gambiae s.s. population dynamics to provide a valuable tool for understanding vector response to biotic and abiotic variables. Results A novel, parsimonious framework for assessing the effects of rainfall, cloudiness, wind speed, desiccation, temperature, relative humidity and density-dependence on vector abundance is developed, allowing ease of construction, analysis, and integration into malaria transmission models. Model validation shows good agreement with longitudinal vector abundance data from Tanzania, suggesting that recent malaria reductions in certain areas of Africa could be due to changing environmental conditions affecting vector populations. Conclusions Mathematical models provide a powerful, explanatory means of understanding the role of environmental variables on mosquito populations and hence for predicting future malaria transmission under global change. The framework developed provides a valuable advance in this respect, but also highlights key research gaps that need to be resolved if we are to better understand future malaria risk in vulnerable communities. PMID:22877154

A deterministic computer simulation model of life-cycle lamb and wool production.

PubMed

Wang, C T; Dickerson, G E

1991-11-01

A deterministic mathematical computer model was developed to simulate effects on life-cycle efficiency of lamb and wool production from genetic improvement of performance traits under alternative management systems. Genetic input parameters can be varied for age at puberty, length of anestrus, fertility, precocity of fertility, number born, milk yield, mortality, growth rate, body fat, and wool growth. Management options include mating systems, lambing intervals, feeding levels, creep feeding, weaning age, marketing age or weight, and culling policy. Simulated growth of animals is linear from birth to inflection point, then slows asymptotically to specified mature empty BW and fat content when nutrition is not limiting. The ME intake requirement to maintain normal condition is calculated daily or weekly for maintenance, protein and fat deposition, wool growth, gestation, and lactation. Simulated feed intake is the minimum of availability, DM physical limit, or ME physiological limit. Tissue catabolism occurs when intake is below the requirement for essential functions. Mortality increases when BW is depressed. Equations developed for calculations of biological functions were validated with published and unpublished experimental data. Lifetime totals are accumulated for TDN, DM, and protein intake and for market lamb equivalent output values of empty body or carcass lean and wool from both lambs and ewes. These measures of efficiency for combinations of genetic, management, and marketing variables can provide the relative economic weighting of traits needed to derive optimal criteria for genetic selection among and within breeds under defined industry production systems.

Maternal smoking during pregnancy and failure of the georgia first grade criterion-referenced competency test.

PubMed

Feng, Jia; Kramer, Michael R; Dever, Bridget V; Dunlop, Anne L; Williams, Bryan; Jain, Lucky

2013-05-01

Maternal smoking during pregnancy (MSDP) has been reported to be associated with impaired measures of cognitive function, but it remains unclear whether exposure to MSDP has an impact upon offspring school performance. We examined the association between MSDP and failure of the Criterion-Referenced Competency Tests (CRCT) among Georgia first grade students. A retrospective cohort was created by deterministically linking 331 531 children born in Georgia from 1998 to 2002 (inclusive) to their individual CRCT education records from 2005 to 2009. We evaluated the association between MSDP (yes/no) and failure of the CRCT Reading, English/Language Arts (ELA), and Mathematics tests, with adjustment for maternal and child sociodemographic characteristics and birth outcomes. Log-binomial models estimated the risk ratios and 95% confidence intervals. Conditional models were fitted to paired sibling data. MSDP was associated with CRCT failure with an adjusted risk ratios for Reading: 1.16 [95% CI 1.12, 1.21]; ELA: 1.12 [95%CI 1.10, 1.15]; and Mathematics: 1.13 [95%CI 1.10, 1.16]. The association remained significant in paired sibling analyses. MSDP may have independent long-term effects on offspring school performance, which does not appear to be through smoking-related adverse birth outcomes. © 2013 Blackwell Publishing Ltd.

A Mathematical Model Of Dengue-Chikungunya Co-Infection In A Closed Population

NASA Astrophysics Data System (ADS)

Aldila, Dipo; Ria Agustin, Maya

2018-03-01

Dengue disease has been a major health problem in many tropical and sub-tropical countries since the early 1900s. On the other hand, according to a 2017 WHO fact sheet, Chikungunya was detected in the first outbreak in 1952 in Tanzania and has continued increasing until now in many tropical and sub-tropical countries. Both these diseases are vector-borne diseases which are spread by the same mosquito, i.e. the female Aedes aegypti. According to the WHO report, there is a great possibility that humans and mosquitos might be infected by dengue and chikungunya at the same time. Here in this article, a mathematical model approach will be used to understand the spread of dengue and chikungunya in a closed population. A model is developed as a nine-dimensional deterministic ordinary differential equation. Equilibrium points and their local stability are analyzed analytically and numerically. We find that the basic reproduction number, the endemic indicator, is given by the maximum of three different basic reproduction numbers of a complete system, i.e. basic reproduction numbers for dengue, chikungunya and for co-infection between dengue and chikungunya. We find that the basic reproduction number for the co-infection sub-system dominates other basic reproduction numbers whenever it is larger than one. Some numerical simulations are provided to confirm these analytical results.

Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update

NASA Technical Reports Server (NTRS)

1971-01-01

Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.

Realistic Simulation for Body Area and Body-To-Body Networks

PubMed Central

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D’Errico, Raffaele

2016-01-01

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices. PMID:27104537

Realistic Simulation for Body Area and Body-To-Body Networks.

PubMed

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D'Errico, Raffaele

2016-04-20

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices.

Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Madankan, R.; Pouget, S.; Singla, P., E-mail: psingla@buffalo.edu

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This papermore » presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.« less

Mathematical programming models for the economic design and assessment of wind energy conversion systems

NASA Astrophysics Data System (ADS)

Reinert, K. A.

The use of linear decision rules (LDR) and chance constrained programming (CCP) to optimize the performance of wind energy conversion clusters coupled to storage systems is described. Storage is modelled by LDR and output by CCP. The linear allocation rule and linear release rule prescribe the size and optimize a storage facility with a bypass. Chance constraints are introduced to explicitly treat reliability in terms of an appropriate value from an inverse cumulative distribution function. Details of deterministic programming structure and a sample problem involving a 500 kW and a 1.5 MW WECS are provided, considering an installed cost of $1/kW. Four demand patterns and three levels of reliability are analyzed for optimizing the generator choice and the storage configuration for base load and peak operating conditions. Deficiencies in ability to predict reliability and to account for serial correlations are noted in the model, which is concluded useful for narrowing WECS design options.

[Radiotherapy and chaos theory: the tit bird and the butterfly...].

PubMed

Denis, F; Letellier, C

2012-09-01

Although the same simple laws govern cancer outcome (cell division repeated again and again), each tumour has a different outcome before as well as after irradiation therapy. The linear-quadratic radiosensitivity model allows an assessment of tumor sensitivity to radiotherapy. This model presents some limitations in clinical practice because it does not take into account the interactions between tumour cells and non-tumoral bystander cells (such as endothelial cells, fibroblasts, immune cells...) that modulate radiosensitivity and tumor growth dynamics. These interactions can lead to non-linear and complex tumor growth which appears to be random but that is not since there is not so many tumors spontaneously regressing. In this paper we propose to develop a deterministic approach for tumour growth dynamics using chaos theory. Various characteristics of cancer dynamics and tumor radiosensitivity can be explained using mathematical models of competing cell species. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

INTEGRATED PROBABILISTIC AND DETERMINISTIC MODELING TECHNIQUES IN ESTIMATING EXPOSURE TO WATER-BORNE CONTAMINANTS: PART 2 PHARMACOKINETIC MODELING

EPA Science Inventory

The Total Exposure Model (TEM) uses deterministic and stochastic methods to estimate the exposure of a person performing daily activities of eating, drinking, showering, and bathing. There were 250 time histories generated, by subject with activities, for the three exposure ro...

Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures

PubMed Central

Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.

2014-01-01

Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295

Using stochastic models to incorporate spatial and temporal variability [Exercise 14

Treesearch

Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke

2003-01-01

To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...

Stochastic and deterministic models for agricultural production networks.

PubMed

Bai, P; Banks, H T; Dediu, S; Govan, A Y; Last, M; Lloyd, A L; Nguyen, H K; Olufsen, M S; Rempala, G; Slenning, B D

2007-07-01

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.

Measuring the Performance and Intelligence of Systems: Proceedings of the 2001 PerMIS Workshop

DTIC Science & Technology

2001-09-04

35 1.1 Interval Mathematics for Analysis of Multiresolutional Systems V. Kreinovich, Univ. of Texas, R. Alo, Univ. of Houston-Downtown...the possible combinations. In non-deterministic real- time systems , the problem is compounded by the uncertainty in the execution times of various...multiresolutional, multiscale ) in their essence because of multiresolutional character of the meaning of words [Rieger, 01]. In integrating systems , the presence of a

Toward quantum-like modeling of financial processes

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-05-01

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V(q) ("hard" market conditions, e.g., natural resources) and quantum-like U(q) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).

Managing a closed-loop supply chain inventory system with learning effects

NASA Astrophysics Data System (ADS)

Jauhari, Wakhid Ahmad; Dwicahyani, Anindya Rachma; Hendaryani, Oktiviandri; Kurdhi, Nughthoh Arfawi

2018-02-01

In this paper, we propose a closed-loop supply chain model consisting of a retailer and a manufacturer. We intend to investigate the impact of learning in regular production, remanufacturing and reworking. The customer demand is assumed deterministic and will be satisfied from both regular production and remanufacturing process. The return rate of used items depends on quality. We propose a mathematical model with the objective is to maximize the joint total profit by simultaneously determining the length of ordering cycle for the retailer and the number of regular production and remanufacturing cycle. The algorithm is suggested for finding the optimal solution. A numerical example is presented to illustrate the application of using a proposed model. The results show that the integrated model performs better in reducing total cost compared to the independent model. The total cost is most affected by the changes in the values of unit production cost and acceptable quality level. In addition, the changes in the defective items proportion and the fraction of holding costs significantly influence the retailer's ordering period.

A Bayesian network for modelling blood glucose concentration and exercise in type 1 diabetes.

PubMed

Ewings, Sean M; Sahu, Sujit K; Valletta, John J; Byrne, Christopher D; Chipperfield, Andrew J

2015-06-01

This article presents a new statistical approach to analysing the effects of everyday physical activity on blood glucose concentration in people with type 1 diabetes. A physiologically based model of blood glucose dynamics is developed to cope with frequently sampled data on food, insulin and habitual physical activity; the model is then converted to a Bayesian network to account for measurement error and variability in the physiological processes. A simulation study is conducted to determine the feasibility of using Markov chain Monte Carlo methods for simultaneous estimation of all model parameters and prediction of blood glucose concentration. Although there are problems with parameter identification in a minority of cases, most parameters can be estimated without bias. Predictive performance is unaffected by parameter misspecification and is insensitive to misleading prior distributions. This article highlights important practical and theoretical issues not previously addressed in the quest for an artificial pancreas as treatment for type 1 diabetes. The proposed methods represent a new paradigm for analysis of deterministic mathematical models of blood glucose concentration. © The Author(s) 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Characterizing Uncertainty and Variability in PBPK Models ...

EPA Pesticide Factsheets

Mode-of-action based risk and safety assessments can rely upon tissue dosimetry estimates in animals and humans obtained from physiologically-based pharmacokinetic (PBPK) modeling. However, risk assessment also increasingly requires characterization of uncertainty and variability; such characterization for PBPK model predictions represents a continuing challenge to both modelers and users. Current practices show significant progress in specifying deterministic biological models and the non-deterministic (often statistical) models, estimating their parameters using diverse data sets from multiple sources, and using them to make predictions and characterize uncertainty and variability. The International Workshop on Uncertainty and Variability in PBPK Models, held Oct 31-Nov 2, 2006, sought to identify the state-of-the-science in this area and recommend priorities for research and changes in practice and implementation. For the short term, these include: (1) multidisciplinary teams to integrate deterministic and non-deterministic/statistical models; (2) broader use of sensitivity analyses, including for structural and global (rather than local) parameter changes; and (3) enhanced transparency and reproducibility through more complete documentation of the model structure(s) and parameter values, the results of sensitivity and other analyses, and supporting, discrepant, or excluded data. Longer-term needs include: (1) theoretic and practical methodological impro

Estimating the epidemic threshold on networks by deterministic connections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Kezan, E-mail: lkzzr@sohu.com; Zhu, Guanghu; Fu, Xinchu

2014-12-15

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect thanmore » those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.« less

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops

NASA Astrophysics Data System (ADS)

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops.

PubMed

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Sihong, E-mail: sihong@math.pku.edu.cn; Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-11-01

Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution ofmore » a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.« less

The value of believing in free will: encouraging a belief in determinism increases cheating.

PubMed

Vohs, Kathleen D; Schooler, Jonathan W

2008-01-01

Does moral behavior draw on a belief in free will? Two experiments examined whether inducing participants to believe that human behavior is predetermined would encourage cheating. In Experiment 1, participants read either text that encouraged a belief in determinism (i.e., that portrayed behavior as the consequence of environmental and genetic factors) or neutral text. Exposure to the deterministic message increased cheating on a task in which participants could passively allow a flawed computer program to reveal answers to mathematical problems that they had been instructed to solve themselves. Moreover, increased cheating behavior was mediated by decreased belief in free will. In Experiment 2, participants who read deterministic statements cheated by overpaying themselves for performance on a cognitive task; participants who read statements endorsing free will did not. These findings suggest that the debate over free will has societal, as well as scientific and theoretical, implications.

A global parallel model based design of experiments method to minimize model output uncertainty.

PubMed

Bazil, Jason N; Buzzard, Gregory T; Rundell, Ann E

2012-03-01

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.

Effect of sample volume on metastable zone width and induction time

NASA Astrophysics Data System (ADS)

Kubota, Noriaki

2012-04-01

The metastable zone width (MSZW) and the induction time, measured for a large sample (say>0.1 L) are reproducible and deterministic, while, for a small sample (say<1 mL), these values are irreproducible and stochastic. Such behaviors of MSZW and induction time were theoretically discussed both with stochastic and deterministic models. Equations for the distribution of stochastic MSZW and induction time were derived. The average values of stochastic MSZW and induction time both decreased with an increase in sample volume, while, the deterministic MSZW and induction time remained unchanged. Such different behaviors with variation in sample volume were explained in terms of detection sensitivity of crystallization events. The average values of MSZW and induction time in the stochastic model were compared with the deterministic MSZW and induction time, respectively. Literature data reported for paracetamol aqueous solution were explained theoretically with the presented models.

Failed rib region prediction in a human body model during crash events with precrash braking.

PubMed

Guleyupoglu, B; Koya, B; Barnard, R; Gayzik, F S

2018-02-28

The objective of this study is 2-fold. We used a validated human body finite element model to study the predicted chest injury (focusing on rib fracture as a function of element strain) based on varying levels of simulated precrash braking. Furthermore, we compare deterministic and probabilistic methods of rib injury prediction in the computational model. The Global Human Body Models Consortium (GHBMC) M50-O model was gravity settled in the driver position of a generic interior equipped with an advanced 3-point belt and airbag. Twelve cases were investigated with permutations for failure, precrash braking system, and crash severity. The severities used were median (17 kph), severe (34 kph), and New Car Assessment Program (NCAP; 56.4 kph). Cases with failure enabled removed rib cortical bone elements once 1.8% effective plastic strain was exceeded. Alternatively, a probabilistic framework found in the literature was used to predict rib failure. Both the probabilistic and deterministic methods take into consideration location (anterior, lateral, and posterior). The deterministic method is based on a rubric that defines failed rib regions dependent on a threshold for contiguous failed elements. The probabilistic method depends on age-based strain and failure functions. Kinematics between both methods were similar (peak max deviation: ΔX head = 17 mm; ΔZ head = 4 mm; ΔX thorax = 5 mm; ΔZ thorax = 1 mm). Seat belt forces at the time of probabilistic failed region initiation were lower than those at deterministic failed region initiation. The probabilistic method for rib fracture predicted more failed regions in the rib (an analog for fracture) than the deterministic method in all but 1 case where they were equal. The failed region patterns between models are similar; however, there are differences that arise due to stress reduced from element elimination that cause probabilistic failed regions to continue to rise after no deterministic failed region would be predicted. Both the probabilistic and deterministic methods indicate similar trends with regards to the effect of precrash braking; however, there are tradeoffs. The deterministic failed region method is more spatially sensitive to failure and is more sensitive to belt loads. The probabilistic failed region method allows for increased capability in postprocessing with respect to age. The probabilistic failed region method predicted more failed regions than the deterministic failed region method due to force distribution differences.

Automatic mesh adaptivity for hybrid Monte Carlo/deterministic neutronics modeling of difficult shielding problems

DOE PAGES

Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; ...

2015-06-30

The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as muchmore » geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.« less

Aspen succession in the Intermountain West: A deterministic model

Treesearch

Dale L. Bartos; Frederick R. Ward; George S. Innis

1983-01-01

A deterministic model of succession in aspen forests was developed using existing data and intuition. The degree of uncertainty, which was determined by allowing the parameter values to vary at random within limits, was larger than desired. This report presents results of an analysis of model sensitivity to changes in parameter values. These results have indicated...

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

Preface to special issue in honor of Carlos Castillo-Chavez.

PubMed

Levin, Simon A

2013-01-01

A little more than a quarter-century ago, I received an inquiry from a young Assistant Professor of Applied Mathematics at the University of Tulsa, the honoree of this volume, Carlos Castillo-Chavez. Though he was well situated in a faculty job, he was not satisfied: He was interested in mathematical biology, having written an excellent thesis in population biology with Fred Brauer at Wisconsin entitled Linear and Nonlinear Deterministic Character-Dependent Models with Time Delay in Population Dynamics. But that success had only whetted his appetite to become more deeply embedded in biology, and he was prepared to give up his faculty job to start a postdoctoral fellowship in ecology. It is always difficult to read in such letters what potential exists in the author; but there was something about what Carlos wrote, the obvious sacrifice he was prepared to make, and my regard for Fred Brauer that convinced me that I must meet this fellow. We did meet, for lunch in an LA restaurant, and the qualities that have led to his remarkable career were immediately obvious. I resolved on the spot to make sure he joined our group. Carlos arrived at Cornell shortly thereafter, and did not leave for nearly twenty years.

Hybrid discrete-continuum modeling for transport, biofilm development and solid restructuring including electrostatic effects

NASA Astrophysics Data System (ADS)

Prechtel, Alexander; Ray, Nadja; Rupp, Andreas

2017-04-01

We want to present an approach for the mathematical, mechanistic modeling and numerical treatment of processes leading to the formation, stability, and turnover of soil micro-aggregates. This aims at deterministic aggregation models including detailed mechanistic pore-scale descriptions to account for the interplay of geochemistry and microbiology, and the link to soil functions as, e.g., the porosity. We therefore consider processes at the pore scale and the mesoscale (laboratory scale). At the pore scale transport by diffusion, advection, and drift emerging from electric forces can be taken into account, in addition to homogeneous and heterogeneous reactions of species. In the context of soil micro-aggregates the growth of biofilms or other glueing substances as EPS (extracellular polymeric substances) is important and affects the structure of the pore space in space and time. This model is upscaled mathematically in the framework of (periodic) homogenization to transfer it to the mesoscale resulting in effective coefficients/parameters there. This micro-macro model thus couples macroscopic equations that describe the transport and fluid flow at the scale of the porous medium (mesoscale) with averaged time- and space-dependent coefficient functions. These functions may be explicitly computed by means of auxiliary cell problems (microscale). Finally, the pore space in which the cell problems are defined is time and space dependent and its geometry inherits information from the transport equation's solutions. The microscale problems rely on versatile combinations of cellular automata and discontiuous Galerkin methods while on the mesoscale mixed finite elements are used. The numerical simulations allow to study the interplay between these processes.

Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies.

PubMed

Tilahun, Getachew Teshome; Makinde, Oluwole Daniel; Malonza, David

2017-01-01

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

Relevance of deterministic chaos theory to studies in functioning of dynamical systems

NASA Astrophysics Data System (ADS)

Glagolev, S. N.; Bukhonova, S. M.; Chikina, E. D.

2018-03-01

The paper considers chaotic behavior of dynamical systems typical for social and economic processes. Approaches to analysis and evaluation of system development processes are studies from the point of view of controllability and determinateness. Explanations are given for necessity to apply non-standard mathematical tools to explain states of dynamical social and economic systems on the basis of fractal theory. Features of fractal structures, such as non-regularity, self-similarity, dimensionality and fractionality are considered.

Dynamic responses of railroad car models to vertical and lateral rail inputs

NASA Technical Reports Server (NTRS)

Sewall, J. L.; Parrish, R. V.; Durling, B. J.

1971-01-01

Simplified dynamic models were applied in a study of vibration in a high-speed railroad car. The mathematical models used were a four-degree-of-freedom model for vertical responses to vertical rail inputs and a ten-degree-of-freedom model for lateral response to lateral or rolling (cross-level) inputs from the rails. Elastic properties of the passenger car body were represented by bending and torsion of a uniform beam. Rail-to-car (truck) suspensions were modeled as spring-mass-dashpot oscillators. Lateral spring nonlinearities approximating certain complicated truck mechanisms were introduced. The models were excited by displacement and, in some cases, velocity inputs from the rails by both deterministic (including sinusoidal) and random input functions. Results were obtained both in the frequency and time domains. Solutions in the time domain for the lateral model were obtained for a wide variety of transient and random inputs generated on-line by an analog computer. Variations in one of the damping properties of the lateral car suspension gave large fluctuations in response over a range of car speeds for a given input. This damping coefficient was significant in reducing lateral car responses that were higher for nonlinear springs for three different inputs.

Abstract quantum computing machines and quantum computational logics

NASA Astrophysics Data System (ADS)

Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

2016-06-01

Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

Flexibility evaluation of multiechelon supply chains.

PubMed

Almeida, João Flávio de Freitas; Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution.

Flexibility evaluation of multiechelon supply chains

PubMed Central

Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution. PMID:29584755

Systems biology of the modified branched Entner-Doudoroff pathway in Sulfolobus solfataricus

PubMed Central

Figueiredo, Ana Sofia; Esser, Dominik; Haferkamp, Patrick; Wieloch, Patricia; Schomburg, Dietmar; Siebers, Bettina; Schaber, Jörg

2017-01-01

Sulfolobus solfataricus is a thermoacidophilic Archaeon that thrives in terrestrial hot springs (solfatares) with optimal growth at 80°C and pH 2–4. It catabolizes specific carbon sources, such as D-glucose, to pyruvate via the modified Entner-Doudoroff (ED) pathway. This pathway has two parallel branches, the semi-phosphorylative and the non-phosphorylative. However, the strategy of S.solfataricus to endure in such an extreme environment in terms of robustness and adaptation is not yet completely understood. Here, we present the first dynamic mathematical model of the ED pathway parameterized with quantitative experimental data. These data consist of enzyme activities of the branched pathway at 70°C and 80°C and of metabolomics data at the same temperatures for the wild type and for a metabolic engineered knockout of the semi-phosphorylative branch. We use the validated model to address two questions: 1. Is this system more robust to perturbations at its optimal growth temperature? 2. Is the ED robust to deletion and perturbations? We employed a systems biology approach to answer these questions and to gain further knowledge on the emergent properties of this biological system. Specifically, we applied deterministic and stochastic approaches to study the sensitivity and robustness of the system, respectively. The mathematical model we present here, shows that: 1. Steady state metabolite concentrations of the ED pathway are consistently more robust to stochastic internal perturbations at 80°C than at 70°C; 2. These metabolite concentrations are highly robust when faced with the knockout of either branch. Connected with this observation, these two branches show different properties at the level of metabolite production and flux control. These new results reveal how enzyme kinetics and metabolomics synergizes with mathematical modelling to unveil new systemic properties of the ED pathway in S.solfataricus in terms of its adaptation and robustness. PMID:28692669

Tularosa Basin Play Fairway Analysis Data and Models

DOE Data Explorer

Nash, Greg

2017-07-11

This submission includes raster datasets for each layer of evidence used for weights of evidence analysis as well as the deterministic play fairway analysis (PFA). Data representative of heat, permeability and groundwater comprises some of the raster datasets. Additionally, the final deterministic PFA model is provided along with a certainty model. All of these datasets are best used with an ArcGIS software package, specifically Spatial Data Modeler.

Noise induced oscillations and coherence resonance in a generic model of the nonisothermal chemical oscillator

PubMed Central

Simakov, David S. A.; Pérez-Mercader, Juan

2013-01-01

Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance. PMID:23929212

Quantitative investigations of the epidemiology of phocine distemper virus (PDV) in European common seal populations.

PubMed

Grenfell, B T; Lonergan, M E; Harwood, J

1992-04-20

This paper uses simple mathematical models to examine the long-term dynamic consequences of the 1988 epizootic of phocine distemper virus (PDV) infection in Northern European common seal populations. In a preliminary analysis of single outbreaks of infection deterministic compartmental models are used to estimate feasible ranges for the transmission rate of the infection and the level of disease-induced mortality. These results also indicate that the level of transmission in 1988 was probably sufficient to eradicate the infection throughout the Northern European common seal populations by the end of the first outbreak. An analysis of longer-term infection dynamics, which takes account of the density-dependent recovery of seal population levels, corroborates this finding. It also indicates that a reintroduction of the virus would be unlikely to cause an outbreak on the scale of the 1988 epizootic until the seal population had recovered for at least 10 years. The general ecological implications of these results are discussed.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Effectiveness of the food recovery at the retailing stage under shelf life uncertainty: An application to Italian food chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muriana, Cinzia, E-mail: cinzia.muriana@unipa.it

Highlights: • The food recovery is seen as suitable way to manage food near to its expiry date. • The variability of the products shelf life must be taken into account. • The paper addresses the mathematic modeling of the profit related to food recovery. • The optimal time to withdraw the products is determinant for food recovery. - Abstract: Food losses represent a significant issue affecting food supply chains. The possibility of recovering such products can be seen as an effective way to reduce such a phenomenon, improve supply chain performances and ameliorate the conditions of undernourished people. Themore » topic has been already investigated by a previous paper enforcing the hypothesis of deterministic and constant Shelf Life (SL) of products. However, such a model cannot be properly extended to products affected by uncertainties of the SL as it does not take into account the deterioration costs and loss of profits due to the overcoming of the SL within the cycle time. Thus the present paper presents an extension of the previous one under stochastic conditions of the food quality. Differently from the previous publication, this work represents a general model applicable to all supply chains, especially to those managing fresh products characterized by uncertain SL such as fruits and vegetables. The deterioration costs and loss of profits are included in the model and the optimal time at which to withdraw the products from the shelves as well as the quantities to be shipped at each alternative destination have been determined. A comparison of the proposed model with that reported in the previous publication has been carried out in order to underline the impact of the SL variability on the optimality conditions. The results show that the food recovery strategy in the presence of uncertainty of the food quality is rewarding, even if the optimal profit is lower than that of the deterministic case.« less

Predicting coexistence of plants subject to a tolerance-competition trade-off.

PubMed

Haegeman, Bart; Sari, Tewfik; Etienne, Rampal S

2014-06-01

Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such a characterization. In the model plant species compete for sites where each site has a fixed stress condition. Species differ both in stress tolerance and competitive ability. Stress tolerance is quantified as the fraction of sites with stress conditions low enough to allow establishment. Competitive ability is quantified as the propensity to win the competition for empty sites. We derive the deterministic, discrete-time dynamical system for the species abundances. We prove the conditions under which plant species can coexist in a stable equilibrium. We show that the coexistence conditions can be characterized graphically, clearly illustrating the trade-off between stress tolerance and competitive ability. We compare our model with a recently proposed, continuous-time dynamical system for a tolerance-fecundity trade-off in plant communities, and we show that this model is a special case of the continuous-time version of our model.

Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2002-11-01

Neo-classical economic theory is based on the postulated, nonempiric notion of utility. Neo-classical economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics, however, a utility function generally does not exist mathematically due to nonintegrability. Price as a function of demand does not exist and all equilibria are unstable. Qualitatively, and empirically, the neo-classical prediction of price as a function of demand describes neither consumer nor trader demand. We also discuss five inconsistent definitions of equilibrium used in economics and finance, only one of which is correct, and then explain the fallacy in the economists’ notion of ‘temporary price equilibria’.

Combining Deterministic structures and stochastic heterogeneity for transport modeling

NASA Astrophysics Data System (ADS)

Zech, Alraune; Attinger, Sabine; Dietrich, Peter; Teutsch, Georg

2017-04-01

Contaminant transport in highly heterogeneous aquifers is extremely challenging and subject of current scientific debate. Tracer plumes often show non-symmetric but highly skewed plume shapes. Predicting such transport behavior using the classical advection-dispersion-equation (ADE) in combination with a stochastic description of aquifer properties requires a dense measurement network. This is in contrast to the available information for most aquifers. A new conceptual aquifer structure model is presented which combines large-scale deterministic information and the stochastic approach for incorporating sub-scale heterogeneity. The conceptual model is designed to allow for a goal-oriented, site specific transport analysis making use of as few data as possible. Thereby the basic idea is to reproduce highly skewed tracer plumes in heterogeneous media by incorporating deterministic contrasts and effects of connectivity instead of using unimodal heterogeneous models with high variances. The conceptual model consists of deterministic blocks of mean hydraulic conductivity which might be measured by pumping tests indicating values differing in orders of magnitudes. A sub-scale heterogeneity is introduced within every block. This heterogeneity can be modeled as bimodal or log-normal distributed. The impact of input parameters, structure and conductivity contrasts is investigated in a systematic manor. Furthermore, some first successful implementation of the model was achieved for the well known MADE site.

Modeling the within-host dynamics of cholera: bacterial-viral interaction.

PubMed

Wang, Xueying; Wang, Jin

2017-08-01

Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial-viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial-viral infection. Accordingly, a closed-form expression is derived for the disease extinction probability, and analytic estimates are validated with numerical simulations. The local and global dynamics of the bacterial-viral interaction are analysed using the deterministic model, and the result indicates that there is a sharp disease threshold characterized by the basic reproduction number [Formula: see text]: if [Formula: see text], vibrios ingested from the environment into human body will not cause cholera infection; if [Formula: see text], vibrios will grow with increased toxicity and persist within the host, leading to human cholera. In contrast, the stochastic model indicates, more realistically, that there is always a positive probability of disease extinction within the human host.

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

The influence of the free space environment on the superlight-weight thermal protection system: conception, methods, and risk analysis

NASA Astrophysics Data System (ADS)

Yatsenko, Vitaliy; Falchenko, Iurii; Fedorchuk, Viktor; Petrushynets, Lidiia

2016-07-01

This report focuses on the results of the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)". The bottom line is an analysis of influence of the free space environment on the superlight-weight thermal protection system (TPS). This report focuses on new methods that based on the following models: synergetic, physical, and computational. This report concentrates on four approaches. The first concerns the synergetic approach. The synergetic approach to the solution of problems of self-controlled synthesis of structures and creation of self-organizing technologies is considered in connection with the super-problem of creation of materials with new functional properties. Synergetics methods and mathematical design are considered according to actual problems of material science. The second approach describes how the optimization methods can be used to determine material microstructures with optimized or targeted properties. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The third approach concerns the dynamic probabilistic risk analysis of TPS l elements with complex characterizations for damages using a physical model of TPS system and a predictable level of ionizing radiation and space weather. Focusing is given mainly on the TPS model, mathematical models for dynamic probabilistic risk assessment and software for the modeling and prediction of the influence of the free space environment. The probabilistic risk assessment method for TPS is presented considering some deterministic and stochastic factors. The last approach concerns results of experimental research of the temperature distribution on the surface of the honeycomb sandwich panel size 150 x 150 x 20 mm at the diffusion welding in vacuum are considered. An equipment, which provides alignment of temperature fields in a product for the formation of equal strength of welded joints is considered. Many tasks in computational materials science can be posed as optimization problems. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The last approach is concerned with the generation of realizations of materials with specified but limited microstructural information: an intriguing inverse problem of both fundamental and practical importance. Computational models based upon the theories of molecular dynamics or quantum mechanics would enable the prediction and modification of fundamental materials properties. This problem is solved using deterministic and stochastic optimization techniques. The main optimization approaches in the frame of the EU project "Superlight-weight thermal protection system for space application" are discussed. Optimization approach to the alloys for obtaining materials with required properties using modeling techniques and experimental data will be also considered. This report is supported by the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)"

Estimation of Second Primary Cancer Risk After Treatment with Radioactive Iodine for Differentiated Thyroid Carcinoma.

PubMed

Corrêa, Nilton Lavatori; de Sá, Lidia Vasconcellos; de Mello, Rossana Corbo Ramalho

2017-02-01

An increase in the incidence of second primary cancers is the late effect of greatest concern that could occur in differentiated thyroid carcinoma (DTC) patients treated with radioactive iodine (RAI). The decision to treat a patient with RAI should therefore incorporate a careful risk-benefit analysis. The objective of this work was to adapt the risk-estimation models developed by the Biological Effects of Ionizing Radiation Committee to local epidemiological characteristics in order to assess the carcinogenesis risk from radiation in a population of Brazilian DTC patients treated with RAI. Absorbed radiation doses in critical organs were also estimated to determine whether they exceeded the thresholds for deterministic effects. A total of 416 DTC patients treated with RAI were retrospectively studied. Four organs were selected for absorbed dose estimation and subsequent calculation of carcinogenic risk: the kidney, stomach, salivary glands, and bone marrow. Absorbed doses were calculated by dose factors (absorbed dose per unit activity administered) previously established and based on standard human models. The lifetime attributable risk (LAR) of incidence of cancer as a function of age, sex, and organ-specific dose was estimated, relating it to the activity of RAI administered in the initial treatment. The salivary glands received the greatest absorbed doses of radiation, followed by the stomach, kidney, and bone marrow. None of these, however, surpassed the threshold for deterministic effects for a single administration of RAI. Younger patients received the same level of absorbed dose in the critical organs as older patients did. The lifetime attributable risk for stomach cancer incidence was by far the highest, followed in descending order by salivary-gland cancer, leukemia, and kidney cancer. RAI in a single administration is safe in terms of deterministic effects because even high-administered activities do not result in absorbed doses that exceed the thresholds for significant tissue reactions. The Biological Effects of Ionizing Radiation Committee mathematical models are a practical method of quantifying the risks of a second primary cancer, demonstrating a marked decrease in risk for younger patients with the administration of lower RAI activities and suggesting that only the smallest activities necessary to promote an effective ablation should be administered in low-risk DTC patients.

Modelling the transmission of healthcare associated infections: a systematic review

PubMed Central

2013-01-01

Background Dynamic transmission models are increasingly being used to improve our understanding of the epidemiology of healthcare-associated infections (HCAI). However, there has been no recent comprehensive review of this emerging field. This paper summarises how mathematical models have informed the field of HCAI and how methods have developed over time. Methods MEDLINE, EMBASE, Scopus, CINAHL plus and Global Health databases were systematically searched for dynamic mathematical models of HCAI transmission and/or the dynamics of antimicrobial resistance in healthcare settings. Results In total, 96 papers met the eligibility criteria. The main research themes considered were evaluation of infection control effectiveness (64%), variability in transmission routes (7%), the impact of movement patterns between healthcare institutes (5%), the development of antimicrobial resistance (3%), and strain competitiveness or co-colonisation with different strains (3%). Methicillin-resistant Staphylococcus aureus was the most commonly modelled HCAI (34%), followed by vancomycin resistant enterococci (16%). Other common HCAIs, e.g. Clostridum difficile, were rarely investigated (3%). Very few models have been published on HCAI from low or middle-income countries. The first HCAI model has looked at antimicrobial resistance in hospital settings using compartmental deterministic approaches. Stochastic models (which include the role of chance in the transmission process) are becoming increasingly common. Model calibration (inference of unknown parameters by fitting models to data) and sensitivity analysis are comparatively uncommon, occurring in 35% and 36% of studies respectively, but their application is increasing. Only 5% of models compared their predictions to external data. Conclusions Transmission models have been used to understand complex systems and to predict the impact of control policies. Methods have generally improved, with an increased use of stochastic models, and more advanced methods for formal model fitting and sensitivity analyses. Insights gained from these models could be broadened to a wider range of pathogens and settings. Improvements in the availability of data and statistical methods could enhance the predictive ability of models. PMID:23809195

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastién; Boto, João Pedro; Kooi, Bob W.; Mateus, Luís; Stollenwerk, Nico

2011-09-01

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Quantification of the microphytobenthic primary production in european intertidal mudflats - A modelling approach

USGS Publications Warehouse

Guarini, J.-M.; Blanchard, G.F.; Gros, P.

2000-01-01

A deterministic model quantifying the dynamics of the microphytobenthic biomass in the first centimeter of the mud was formulated as part of the MAST-III/INTRMUD project. The main modelled processes are production by photosynthesis, active vertical migration of the microphytobenthos and global biomass losses, encompassing grazing, mortality and resuspension during immersion periods. The model emphasizes the role of the interface between mud and air, which is crucial for the production. The microalgal biofilm present at the mud surface during day-time emersion periods induces most of the differences between microphytobenthos and phytoplankton communities dynamics. The study of the mathematical properties of the system, under some simplifying assumptions, shows the convergence of the solutions to a stable cyclic equilibrium, in the whole observed range of the frequencies of the physical synchronizers of the production. Resilience time estimates suggest that microphytobenthic biomass attains an equilibrium rapidly, even after a strong perturbation. Around the equilibrium, the local model solutions agree fairly with the in situ observed dynamics of the total biomass. The sensitivity analysis suggests investigating the processes governing biomass losses, which are so far uncertain, and may further vary in space and time. (C) 2000 Elsevier Science Ltd.

The Diffusion Model Is Not a Deterministic Growth Model: Comment on Jones and Dzhafarov (2014)

PubMed Central

Smith, Philip L.; Ratcliff, Roger; McKoon, Gail

2015-01-01

Jones and Dzhafarov (2014) claim that several current models of speeded decision making in cognitive tasks, including the diffusion model, can be viewed as special cases of other general models or model classes. The general models can be made to match any set of response time (RT) distribution and accuracy data exactly by a suitable choice of parameters and so are unfalsifiable. The implication of their claim is that models like the diffusion model are empirically testable only by artificially restricting them to exclude unfalsifiable instances of the general model. We show that Jones and Dzhafarov’s argument depends on enlarging the class of “diffusion” models to include models in which there is little or no diffusion. The unfalsifiable models are deterministic or near-deterministic growth models, from which the effects of within-trial variability have been removed or in which they are constrained to be negligible. These models attribute most or all of the variability in RT and accuracy to across-trial variability in the rate of evidence growth, which is permitted to be distributed arbitrarily and to vary freely across experimental conditions. In contrast, in the standard diffusion model, within-trial variability in evidence is the primary determinant of variability in RT. Across-trial variability, which determines the relative speed of correct responses and errors, is theoretically and empirically constrained. Jones and Dzhafarov’s attempt to include the diffusion model in a class of models that also includes deterministic growth models misrepresents and trivializes it and conveys a misleading picture of cognitive decision-making research. PMID:25347314

Self-organization of complex networks as a dynamical system

NASA Astrophysics Data System (ADS)

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

DOE PAGES

Tuo, Rui; Jeff Wu, C. F.

2016-07-19

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L 2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L 2-inconsistent calibration. This L 2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the Lmore » 2 calibration, is proposed and proven to be L 2-consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L 2-inconsistency problem.« less

Dynamics of non-holonomic systems with stochastic transport

NASA Astrophysics Data System (ADS)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

Random behaviour, amplification processes and number of participants: How they contribute to the foraging properties of ants

NASA Astrophysics Data System (ADS)

Deneubourg, J. L.; Aron, S.; Goss, S.; Pasteels, J. M.; Duerinck, G.

1986-10-01

Two major types of foraging organisation in ants are described and compared, being illustrated with experimental data and mathematical models. The first concerns large colonies of identical, unspecialised foragers. The communication and interaction between foragers and their randomness generates collective and efficient structures. The second concerns small societies of deterministic and specialised foragers, rarely communicating together. The first organisation is discussed in relation to the different recruitment mechanisms, trail-following error, quality and degree of aggregation of food-sources, and territorial marking, and is the key to many types of collective behaviour in social insects. The second is discussed in relation to spatial specialisation, foraging density, individual learning and genetic programming. The two organisations may be associated in the same colony. The choice of organisation is discussed in relation to colony size and size and predictability of food sources.

Self-organization of complex networks as a dynamical system.

PubMed

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

On the usage of ultrasound computational models for decision making under ambiguity

NASA Astrophysics Data System (ADS)

Dib, Gerges; Sexton, Samuel; Prowant, Matthew; Crawford, Susan; Diaz, Aaron

2018-04-01

Computer modeling and simulation is becoming pervasive within the non-destructive evaluation (NDE) industry as a convenient tool for designing and assessing inspection techniques. This raises a pressing need for developing quantitative techniques for demonstrating the validity and applicability of the computational models. Computational models provide deterministic results based on deterministic and well-defined input, or stochastic results based on inputs defined by probability distributions. However, computational models cannot account for the effects of personnel, procedures, and equipment, resulting in ambiguity about the efficacy of inspections based on guidance from computational models only. In addition, ambiguity arises when model inputs, such as the representation of realistic cracks, cannot be defined deterministically, probabilistically, or by intervals. In this work, Pacific Northwest National Laboratory demonstrates the ability of computational models to represent field measurements under known variabilities, and quantify the differences using maximum amplitude and power spectrum density metrics. Sensitivity studies are also conducted to quantify the effects of different input parameters on the simulation results.

Interrelation Between Safety Factors and Reliability

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac; Chamis, Christos C. (Technical Monitor)

2001-01-01

An evaluation was performed to establish relationships between safety factors and reliability relationships. Results obtained show that the use of the safety factor is not contradictory to the employment of the probabilistic methods. In many cases the safety factors can be directly expressed by the required reliability levels. However, there is a major difference that must be emphasized: whereas the safety factors are allocated in an ad hoc manner, the probabilistic approach offers a unified mathematical framework. The establishment of the interrelation between the concepts opens an avenue to specify safety factors based on reliability. In cases where there are several forms of failure, then the allocation of safety factors should he based on having the same reliability associated with each failure mode. This immediately suggests that by the probabilistic methods the existing over-design or under-design can be eliminated. The report includes three parts: Part 1-Random Actual Stress and Deterministic Yield Stress; Part 2-Deterministic Actual Stress and Random Yield Stress; Part 3-Both Actual Stress and Yield Stress Are Random.

({The) Solar System Large Planets influence on a new Maunder Miniμm}

NASA Astrophysics Data System (ADS)

Yndestad, Harald; Solheim, Jan-Erik

2016-04-01

In 1890´s G. Spörer and E. W. Maunder (1890) reported that the solar activity stopped in a period of 70 years from 1645 to 1715. Later a reconstruction of the solar activity confirms the grand minima Maunder (1640-1720), Spörer (1390-1550), Wolf (1270-1340), and the minima Oort (1010-1070) and Dalton (1785-1810) since the year 1000 A.D. (Usoskin et al. 2007). These minimum periods have been associated with less irradiation from the Sun and cold climate periods on Earth. An identification of a three grand Maunder type periods and two Dalton type periods in a period thousand years, indicates that sooner or later there will be a colder climate on Earth from a new Maunder- or Dalton- type period. The cause of these minimum periods, are not well understood. An expected new Maunder-type period is based on the properties of solar variability. If the solar variability has a deterministic element, we can estimate better a new Maunder grand minimum. A random solar variability can only explain the past. This investigation is based on the simple idea that if the solar variability has a deterministic property, it must have a deterministic source, as a first cause. If this deterministic source is known, we can compute better estimates the next expected Maunder grand minimum period. The study is based on a TSI ACRIM data series from 1700, a TSI ACRIM data series from 1000 A.D., sunspot data series from 1611 and a Solar Barycenter orbit data series from 1000. The analysis method is based on a wavelet spectrum analysis, to identify stationary periods, coincidence periods and their phase relations. The result shows that the TSI variability and the sunspots variability have deterministic oscillations, controlled by the large planets Jupiter, Uranus and Neptune, as the first cause. A deterministic model of TSI variability and sunspot variability confirms the known minimum and grand minimum periods since 1000. From this deterministic model we may expect a new Maunder type sunspot minimum period from about 2018 to 2055. The deterministic model of a TSI ACRIM data series from 1700 computes a new Maunder type grand minimum period from 2015 to 2071. A model of the longer TSI ACRIM data series from 1000 computes a new Dalton to Maunder type minimum irradiation period from 2047 to 2068.

Statistically qualified neuro-analytic failure detection method and system

DOEpatents

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

2002-03-02

An apparatus and method for monitoring a process involve development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two stages: deterministic model adaption and stochastic model modification of the deterministic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics, augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation error minimization technique. Stochastic model modification involves qualifying any remaining uncertainty in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system. Illustrative of the method and apparatus, the method is applied to a peristaltic pump system.

Study on individual stochastic model of GNSS observations for precise kinematic applications

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik; Szpunar, Ryszard

2015-04-01

The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.

Size-dependent piezoelectric energy-harvesting analysis of micro/nano bridges subjected to random ambient excitations

NASA Astrophysics Data System (ADS)

Radgolchin, Moeen; Moeenfard, Hamid

2018-02-01

The construction of self-powered micro-electro-mechanical units by converting the mechanical energy of the systems into electrical power has attracted much attention in recent years. While power harvesting from deterministic external excitations is state of the art, it has been much more difficult to derive mathematical models for scavenging electrical energy from ambient random vibrations, due to the stochastic nature of the excitations. The current research concerns analytical modeling of micro-bridge energy harvesters based on random vibration theory. Since classical elasticity fails to accurately predict the mechanical behavior of micro-structures, strain gradient theory is employed as a powerful tool to increase the accuracy of the random vibration modeling of the micro-harvester. Equations of motion of the system in the time domain are derived using the Lagrange approach. These are then utilized to determine the frequency and impulse responses of the structure. Assuming the energy harvester to be subjected to a combination of broadband and limited-band random support motion and transverse loading, closed-form expressions for mean, mean square, correlation and spectral density of the output power are derived. The suggested formulation is further exploited to investigate the effect of the different design parameters, including the geometric properties of the structure as well as the properties of the electrical circuit on the resulting power. Furthermore, the effect of length scale parameters on the harvested energy is investigated in detail. It is observed that the predictions of classical and even simple size-dependent theories (such as couple stress) appreciably differ from the findings of strain gradient theory on the basis of random vibration. This study presents a first-time modeling of micro-scale harvesters under stochastic excitations using a size-dependent approach and can be considered as a reliable foundation for future research in the field of micro/nano harvesters subjected to non-deterministic loads.

A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy

NASA Astrophysics Data System (ADS)

Liu, Xiangdong; Li, Qingze; Pan, Jianxin

2018-06-01

Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.

Impacts of Considering Climate Variability on Investment Decisions in Ethiopia

NASA Astrophysics Data System (ADS)

Strzepek, K.; Block, P.; Rosegrant, M.; Diao, X.

2005-12-01

In Ethiopia, climate extremes, inducing droughts or floods, are not unusual. Monitoring the effects of these extremes, and climate variability in general, is critical for economic prediction and assessment of the country's future welfare. The focus of this study involves adding climate variability to a deterministic, mean climate-driven agro-economic model, in an attempt to understand its effects and degree of influence on general economic prediction indicators for Ethiopia. Four simulations are examined, including a baseline simulation and three investment strategies: simulations of irrigation investment, roads investment, and a combination investment of both irrigation and roads. The deterministic model is transformed into a stochastic model by dynamically adding year-to-year climate variability through climate-yield factors. Nine sets of actual, historic, variable climate data are individually assembled and implemented into the 12-year stochastic model simulation, producing an ensemble of economic prediction indicators. This ensemble allows for a probabilistic approach to planning and policy making, allowing decision makers to consider risk. The economic indicators from the deterministic and stochastic approaches, including rates of return to investments, are significantly different. The predictions of the deterministic model appreciably overestimate the future welfare of Ethiopia; the predictions of the stochastic model, utilizing actual climate data, tend to give a better semblance of what may be expected. Inclusion of climate variability is vital for proper analysis of the predictor values from this agro-economic model.

Subspace algorithms for identifying separable-in-denominator 2D systems with deterministic-stochastic inputs

NASA Astrophysics Data System (ADS)

Ramos, José A.; Mercère, Guillaume

2016-12-01

In this paper, we present an algorithm for identifying two-dimensional (2D) causal, recursive and separable-in-denominator (CRSD) state-space models in the Roesser form with deterministic-stochastic inputs. The algorithm implements the N4SID, PO-MOESP and CCA methods, which are well known in the literature on 1D system identification, but here we do so for the 2D CRSD Roesser model. The algorithm solves the 2D system identification problem by maintaining the constraint structure imposed by the problem (i.e. Toeplitz and Hankel) and computes the horizontal and vertical system orders, system parameter matrices and covariance matrices of a 2D CRSD Roesser model. From a computational point of view, the algorithm has been presented in a unified framework, where the user can select which of the three methods to use. Furthermore, the identification task is divided into three main parts: (1) computing the deterministic horizontal model parameters, (2) computing the deterministic vertical model parameters and (3) computing the stochastic components. Specific attention has been paid to the computation of a stabilised Kalman gain matrix and a positive real solution when required. The efficiency and robustness of the unified algorithm have been demonstrated via a thorough simulation example.

Hydraulic tomography of discrete networks of conduits and fractures in a karstic aquifer by using a deterministic inversion algorithm

NASA Astrophysics Data System (ADS)

Fischer, P.; Jardani, A.; Lecoq, N.

2018-02-01

In this paper, we present a novel inverse modeling method called Discrete Network Deterministic Inversion (DNDI) for mapping the geometry and property of the discrete network of conduits and fractures in the karstified aquifers. The DNDI algorithm is based on a coupled discrete-continuum concept to simulate numerically water flows in a model and a deterministic optimization algorithm to invert a set of observed piezometric data recorded during multiple pumping tests. In this method, the model is partioned in subspaces piloted by a set of parameters (matrix transmissivity, and geometry and equivalent transmissivity of the conduits) that are considered as unknown. In this way, the deterministic optimization process can iteratively correct the geometry of the network and the values of the properties, until it converges to a global network geometry in a solution model able to reproduce the set of data. An uncertainty analysis of this result can be performed from the maps of posterior uncertainties on the network geometry or on the property values. This method has been successfully tested for three different theoretical and simplified study cases with hydraulic responses data generated from hypothetical karstic models with an increasing complexity of the network geometry, and of the matrix heterogeneity.

Learning Kriging by an instructive program.

NASA Astrophysics Data System (ADS)

Cuador, José

2016-04-01

There are three types of problem classification: the deterministic, the approximated and the stochastic problems. First, in the deterministic problems the law of the phenomenon and the data are known in the entire domain and for each instant of time. In the approximated problems, the law of the phenomenon behavior is unknown but the data can be known in the entire domain and for each instant of time. In the stochastic problems much of the law and the data are unknown in the domain, so in this case the spatial behavior of the data can only be explained with probabilistic laws. This is the most important reason why the students of geo-sciences careers and others related careers need to take courses in advance estimation methods. A good example of this situation is the estimation grades in ore mineral deposit for which the Geostatistics was formalized by G. Matheron in 1962 [6]. Geostatistics is defined as the application of the theory of Random Function to the recognition and estimation of natural phenomenon [4]. Nowadays, Geostatistics is widely used in several fields of earth sciences, for example: Mining, Oil exploration, Environment, Agricultural, Forest and others [3]. It provides a wide variety of tools for spatial data analysis and allows analysing models which are subjected to degrees of uncertainty with the rigor of mathematics and formal statistical analysis [9]. Adequate models for the Kriging interpolator has been developed according to the data behavior; however there are two key steps in applying this interpolator properly: the semivariogram determination and the Kriging neighborhood selection. The main objective of this paper is to present these two elements using an instructive program.

Combinatorial vector fields and the valley structure of fitness landscapes.

PubMed

Stadler, Bärbel M R; Stadler, Peter F

2010-12-01

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

Introduction to the focus issue: fifty years of chaos: applied and theoretical.

PubMed

Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

2012-12-01

The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

Stochastic simulations on a model of circadian rhythm generation.

PubMed

Miura, Shigehiro; Shimokawa, Tetsuya; Nomura, Taishin

2008-01-01

Biological phenomena are often modeled by differential equations, where states of a model system are described by continuous real values. When we consider concentrations of molecules as dynamical variables for a set of biochemical reactions, we implicitly assume that numbers of the molecules are large enough so that their changes can be regarded as continuous and they are described deterministically. However, for a system with small numbers of molecules, changes in their numbers are apparently discrete and molecular noises become significant. In such cases, models with deterministic differential equations may be inappropriate, and the reactions must be described by stochastic equations. In this study, we focus a clock gene expression for a circadian rhythm generation, which is known as a system involving small numbers of molecules. Thus it is appropriate for the system to be modeled by stochastic equations and analyzed by methodologies of stochastic simulations. The interlocked feedback model proposed by Ueda et al. as a set of deterministic ordinary differential equations provides a basis of our analyses. We apply two stochastic simulation methods, namely Gillespie's direct method and the stochastic differential equation method also by Gillespie, to the interlocked feedback model. To this end, we first reformulated the original differential equations back to elementary chemical reactions. With those reactions, we simulate and analyze the dynamics of the model using two methods in order to compare them with the dynamics obtained from the original deterministic model and to characterize dynamics how they depend on the simulation methodologies.

Understanding agent-based models of financial markets: A bottom-up approach based on order parameters and phase diagrams

NASA Astrophysics Data System (ADS)

Lye, Ribin; Tan, James Peng Lung; Cheong, Siew Ann

2012-11-01

We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N independent traders buy and sell M stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction fb of traders buy a random stock on offer, or a fraction fs of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.

Distinguishing between stochasticity and determinism: Examples from cell cycle duration variability.

PubMed

Pearl Mizrahi, Sivan; Sandler, Oded; Lande-Diner, Laura; Balaban, Nathalie Q; Simon, Itamar

2016-01-01

We describe a recent approach for distinguishing between stochastic and deterministic sources of variability, focusing on the mammalian cell cycle. Variability between cells is often attributed to stochastic noise, although it may be generated by deterministic components. Interestingly, lineage information can be used to distinguish between variability and determinism. Analysis of correlations within a lineage of the mammalian cell cycle duration revealed its deterministic nature. Here, we discuss the sources of such variability and the possibility that the underlying deterministic process is due to the circadian clock. Finally, we discuss the "kicked cell cycle" model and its implication on the study of the cell cycle in healthy and cancerous tissues. © 2015 WILEY Periodicals, Inc.

Estimation of internal organ motion-induced variance in radiation dose in non-gated radiotherapy

NASA Astrophysics Data System (ADS)

Zhou, Sumin; Zhu, Xiaofeng; Zhang, Mutian; Zheng, Dandan; Lei, Yu; Li, Sicong; Bennion, Nathan; Verma, Vivek; Zhen, Weining; Enke, Charles

2016-12-01

In the delivery of non-gated radiotherapy (RT), owing to intra-fraction organ motion, a certain degree of RT dose uncertainty is present. Herein, we propose a novel mathematical algorithm to estimate the mean and variance of RT dose that is delivered without gating. These parameters are specific to individual internal organ motion, dependent on individual treatment plans, and relevant to the RT delivery process. This algorithm uses images from a patient’s 4D simulation study to model the actual patient internal organ motion during RT delivery. All necessary dose rate calculations are performed in fixed patient internal organ motion states. The analytical and deterministic formulae of mean and variance in dose from non-gated RT were derived directly via statistical averaging of the calculated dose rate over possible random internal organ motion initial phases, and did not require constructing relevant histograms. All results are expressed in dose rate Fourier transform coefficients for computational efficiency. Exact solutions are provided to simplified, yet still clinically relevant, cases. Results from a volumetric-modulated arc therapy (VMAT) patient case are also presented. The results obtained from our mathematical algorithm can aid clinical decisions by providing information regarding both mean and variance of radiation dose to non-gated patients prior to RT delivery.

Forecasting seasonal influenza with a state-space SIR model.

PubMed

Osthus, Dave; Hickmann, Kyle S; Caragea, Petruţa C; Higdon, Dave; Del Valle, Sara Y

2017-03-01

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention's influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

Diffusion-Based Model for Synaptic Molecular Communication Channel.

PubMed

Khan, Tooba; Bilgin, Bilgesu A; Akan, Ozgur B

2017-06-01

Computational methods have been extensively used to understand the underlying dynamics of molecular communication methods employed by nature. One very effective and popular approach is to utilize a Monte Carlo simulation. Although it is very reliable, this method can have a very high computational cost, which in some cases renders the simulation impractical. Therefore, in this paper, for the special case of an excitatory synaptic molecular communication channel, we present a novel mathematical model for the diffusion and binding of neurotransmitters that takes into account the effects of synaptic geometry in 3-D space and re-absorption of neurotransmitters by the transmitting neuron. Based on this model we develop a fast deterministic algorithm, which calculates expected value of the output of this channel, namely, the amplitude of excitatory postsynaptic potential (EPSP), for given synaptic parameters. We validate our algorithm by a Monte Carlo simulation, which shows total agreement between the results of the two methods. Finally, we utilize our model to quantify the effects of variation in synaptic parameters, such as position of release site, receptor density, size of postsynaptic density, diffusion coefficient, uptake probability, and number of neurotransmitters in a vesicle, on maximum number of bound receptors that directly affect the peak amplitude of EPSP.

The threshold of a stochastic delayed SIR epidemic model with temporary immunity

NASA Astrophysics Data System (ADS)

Liu, Qun; Chen, Qingmei; Jiang, Daqing

2016-05-01

This paper is concerned with the asymptotic properties of a stochastic delayed SIR epidemic model with temporary immunity. Sufficient conditions for extinction and persistence in the mean of the epidemic are established. The threshold between persistence in the mean and extinction of the epidemic is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

A queuing model for road traffic simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerrouahane, N.; Aissani, D.; Bouallouche-Medjkoune, L.

We present in this article a stochastic queuing model for the raod traffic. The model is based on the M/G/c/c state dependent queuing model, and is inspired from the deterministic Godunov scheme for the road traffic simulation. We first propose a variant of M/G/c/c state dependent model that works with density-flow fundamental diagrams rather than density-speed relationships. We then extend this model in order to consider upstream traffic demand as well as downstream traffic supply. Finally, we show how to model a whole raod by concatenating raod sections as in the deterministic Godunov scheme.

Mathematical Modeling Of Production Of Bio-surfactant Through Bio-desulfurization Of Hydrotreated Diesel In A Fermenter

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Sujaya; Chowdhury, Ranjana; Bhattacharjee, Chiranjib

2010-10-01

The conventional deep desulfurization must be followed by a suitable desulfurization process to achieve ultra low sulfur diesel (ULSD) with 10-15 ppm sulfur level which satisfies the strict environmental regulations. Bio-desulfurization is one of the potential routes for the above mentioned purpose. In this present investigation our major concern is production of Ultra Low sulfur diesel (ULSD) and production of biosurfactant simultaneously using Rhodococcus sp. The substituted benzothiophenes (BTs) and dibenzothiophenes (DBTs) get converted to 2-hydroxy biphenyl, which is a potential bio-surfactant. Kinetics of biodesulfurisation of deep desulfurized diesel using Rhodococcus sp. has been studied with special reference to removal of organo-sulfur compounds in diesel and production of 2-hydroxy biphenyl. The sulfur concentration of feed diesel is in the range of 200-540 mg/L. Aqueous phase to diesel ratios have been varied in the range of 9:1 to 1:9. The optimum ratio has been found to be 1:4 and the maximum conversion of sulfur of 95% has been achieved. The values of Monod kinetic parameters, μmax, maximum specific growth rate and Ks, saturation constant of the microbial growth and Yield coefficient of surfactant have been measured to be 0.096 h-1, 71 mg/L, and 17 μmol/g dry cell weights respectively by conducting batch type experiments. A deterministic mathematical model has been developed using the kinetic parameters and the experimental data have been compared with simulated ones satisfactorily.

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ainsworth, Mark; Glusa, Christian

2016-06-30

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant.more » The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.« less

Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.

PubMed

Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M

2012-01-01

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

Effect of Nonlinearity in Hybrid Kinetic Monte Carlo-Continuum Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balter, Ariel I.; Lin, Guang; Tartakovsky, Alexandre M.

2012-04-23

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leadsmore » to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.« less

Mathematical modeling of malaria infection with innate and adaptive immunity in individuals and agent-based communities.

PubMed

Gurarie, David; Karl, Stephan; Zimmerman, Peter A; King, Charles H; St Pierre, Timothy G; Davis, Timothy M E

2012-01-01

Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns). We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. Our approach represents a novel, convenient and versatile method to model Plasmodium falciparum infection.

Nonclassical acoustics

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1976-01-01

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.

Universal map for cellular automata

NASA Astrophysics Data System (ADS)

García-Morales, V.

2012-08-01

A universal map is derived for all deterministic 1D cellular automata (CAs) containing no freely adjustable parameters and valid for any alphabet size and any neighborhood range (including non-symmetrical neighborhoods). The map can be extended to an arbitrary number of dimensions and topologies and to arbitrary order in time. Specific CA maps for the famous Conway's Game of Life and Wolfram's 256 elementary CAs are given. An induction method for CAs, based in the universal map, allows mathematical expressions for the orbits of a wide variety of elementary CAs to be systematically derived.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE PAGES

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

2016-05-03

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method.

PubMed

Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay

2017-11-01

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation

PubMed Central

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation. PMID:26761487

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

PubMed

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington's genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.

A hybrid model for predicting carbon monoxide from vehicular exhausts in urban environments

NASA Astrophysics Data System (ADS)

Gokhale, Sharad; Khare, Mukesh

Several deterministic-based air quality models evaluate and predict the frequently occurring pollutant concentration well but, in general, are incapable of predicting the 'extreme' concentrations. In contrast, the statistical distribution models overcome the above limitation of the deterministic models and predict the 'extreme' concentrations. However, the environmental damages are caused by both extremes as well as by the sustained average concentration of pollutants. Hence, the model should predict not only 'extreme' ranges but also the 'middle' ranges of pollutant concentrations, i.e. the entire range. Hybrid modelling is one of the techniques that estimates/predicts the 'entire range' of the distribution of pollutant concentrations by combining the deterministic based models with suitable statistical distribution models ( Jakeman, et al., 1988). In the present paper, a hybrid model has been developed to predict the carbon monoxide (CO) concentration distributions at one of the traffic intersections, Income Tax Office (ITO), in the Delhi city, where the traffic is heterogeneous in nature and meteorology is 'tropical'. The model combines the general finite line source model (GFLSM) as its deterministic, and log logistic distribution (LLD) model, as its statistical components. The hybrid (GFLSM-LLD) model is then applied at the ITO intersection. The results show that the hybrid model predictions match with that of the observed CO concentration data within the 5-99 percentiles range. The model is further validated at different street location, i.e. Sirifort roadway. The validation results show that the model predicts CO concentrations fairly well ( d=0.91) in 10-95 percentiles range. The regulatory compliance is also developed to estimate the probability of exceedance of hourly CO concentration beyond the National Ambient Air Quality Standards (NAAQS) of India. It consists of light vehicles, heavy vehicles, three- wheelers (auto rickshaws) and two-wheelers (scooters, motorcycles, etc).

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession.

PubMed

Dini-Andreote, Francisco; Stegen, James C; van Elsas, Jan Dirk; Salles, Joana Falcão

2015-03-17

Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages--which provide a larger spatiotemporal scale relative to within stage analyses--revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended--and experimentally testable--conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems.

Disentangling mechanisms that mediate the balance between stochastic and deterministic processes in microbial succession

PubMed Central

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan Dirk; Salles, Joana Falcão

2015-01-01

Ecological succession and the balance between stochastic and deterministic processes are two major themes within microbial ecology, but these conceptual domains have mostly developed independent of each other. Here we provide a framework that integrates shifts in community assembly processes with microbial primary succession to better understand mechanisms governing the stochastic/deterministic balance. Synthesizing previous work, we devised a conceptual model that links ecosystem development to alternative hypotheses related to shifts in ecological assembly processes. Conceptual model hypotheses were tested by coupling spatiotemporal data on soil bacterial communities with environmental conditions in a salt marsh chronosequence spanning 105 years of succession. Analyses within successional stages showed community composition to be initially governed by stochasticity, but as succession proceeded, there was a progressive increase in deterministic selection correlated with increasing sodium concentration. Analyses of community turnover among successional stages—which provide a larger spatiotemporal scale relative to within stage analyses—revealed that changes in the concentration of soil organic matter were the main predictor of the type and relative influence of determinism. Taken together, these results suggest scale-dependency in the mechanisms underlying selection. To better understand mechanisms governing these patterns, we developed an ecological simulation model that revealed how changes in selective environments cause shifts in the stochastic/deterministic balance. Finally, we propose an extended—and experimentally testable—conceptual model integrating ecological assembly processes with primary and secondary succession. This framework provides a priori hypotheses for future experiments, thereby facilitating a systematic approach to understand assembly and succession in microbial communities across ecosystems. PMID:25733885

Seven challenges for metapopulation models of epidemics, including households models.

PubMed

Ball, Frank; Britton, Tom; House, Thomas; Isham, Valerie; Mollison, Denis; Pellis, Lorenzo; Scalia Tomba, Gianpaolo

2015-03-01

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Stochastic Multi-Timescale Power System Operations With Variable Wind Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hongyu; Krad, Ibrahim; Florita, Anthony

This paper describes a novel set of stochastic unit commitment and economic dispatch models that consider stochastic loads and variable generation at multiple operational timescales. The stochastic model includes four distinct stages: stochastic day-ahead security-constrained unit commitment (SCUC), stochastic real-time SCUC, stochastic real-time security-constrained economic dispatch (SCED), and deterministic automatic generation control (AGC). These sub-models are integrated together such that they are continually updated with decisions passed from one to another. The progressive hedging algorithm (PHA) is applied to solve the stochastic models to maintain the computational tractability of the proposed models. Comparative case studies with deterministic approaches are conductedmore » in low wind and high wind penetration scenarios to highlight the advantages of the proposed methodology, one with perfect forecasts and the other with current state-of-the-art but imperfect deterministic forecasts. The effectiveness of the proposed method is evaluated with sensitivity tests using both economic and reliability metrics to provide a broader view of its impact.« less

Robust Sensitivity Analysis for Multi-Attribute Deterministic Hierarchical Value Models

DTIC Science & Technology

2002-03-01

such as weighted sum method, weighted 5 product method, and the Analytic Hierarchy Process ( AHP ). This research focuses on only weighted sum...different groups. They can be termed as deterministic, stochastic, or fuzzy multi-objective decision methods if they are classified according to the...weighted product model (WPM), and analytic hierarchy process ( AHP ). His method attempts to identify the most important criteria weight and the most

Dynamic analysis of a stochastic rumor propagation model

NASA Astrophysics Data System (ADS)

Jia, Fangju; Lv, Guangying

2018-01-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

A Perishable Inventory Model with Return

NASA Astrophysics Data System (ADS)

Setiawan, S. W.; Lesmono, D.; Limansyah, T.

2018-04-01

In this paper, we develop a mathematical model for a perishable inventory with return by assuming deterministic demand and inventory dependent demand. By inventory dependent demand, it means that demand at certain time depends on the available inventory at that time with certain rate. In dealing with perishable items, we should consider deteriorating rate factor that corresponds to the decreasing quality of goods. There are also costs involved in this model such as purchasing, ordering, holding, shortage (backordering) and returning costs. These costs compose the total costs in the model that we want to minimize. In the model we seek for the optimal return time and order quantity. We assume that after some period of time, called return time, perishable items can be returned to the supplier at some returning costs. The supplier will then replace them in the next delivery. Some numerical experiments are given to illustrate our model and sensitivity analysis is performed as well. We found that as the deteriorating rate increases, returning time becomes shorter, the optimal order quantity and total cost increases. When considering the inventory-dependent demand factor, we found that as this factor increases, assuming a certain deteriorating rate, returning time becomes shorter, optimal order quantity becomes larger and the total cost increases.

Queues with Choice via Delay Differential Equations

NASA Astrophysics Data System (ADS)

Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth

Delay or queue length information has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information. In the first fluid model, customers join each queue according to a Multinomial Logit Model, however, the queue length information the customer receives is delayed by a constant Δ. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of Δ. In the second model, customers receive information about the queue length through a moving average of the queue length. Although it has been shown empirically that giving patients moving average information causes oscillations and asynchronous behavior to occur in U.S. hospitals, we analytically and mathematically show for the first time that the moving average fluid model can exhibit oscillations and determine their dependence on the moving average window. Thus, our analysis provides new insight on how operators of service systems should report queue length information to customers and how delayed information can produce unwanted system dynamics.

Integrating urban recharge uncertainty into standard groundwater modeling practice: A case study on water main break predictions for the Barton Springs segment of the Edwards Aquifer, Austin, Texas

NASA Astrophysics Data System (ADS)

Sinner, K.; Teasley, R. L.

2016-12-01

Groundwater models serve as integral tools for understanding flow processes and informing stakeholders and policy makers in management decisions. Historically, these models tended towards a deterministic nature, relying on historical data to predict and inform future decisions based on model outputs. This research works towards developing a stochastic method of modeling recharge inputs from pipe main break predictions in an existing groundwater model, which subsequently generates desired outputs incorporating future uncertainty rather than deterministic data. The case study for this research is the Barton Springs segment of the Edwards Aquifer near Austin, Texas. Researchers and water resource professionals have modeled the Edwards Aquifer for decades due to its high water quality, fragile ecosystem, and stakeholder interest. The original case study and model that this research is built upon was developed as a co-design problem with regional stakeholders and the model outcomes are generated specifically for communication with policy makers and managers. Recently, research in the Barton Springs segment demonstrated a significant contribution of urban, or anthropogenic, recharge to the aquifer, particularly during dry period, using deterministic data sets. Due to social and ecological importance of urban water loss to recharge, this study develops an evaluation method to help predicted pipe breaks and their related recharge contribution within the Barton Springs segment of the Edwards Aquifer. To benefit groundwater management decision processes, the performance measures captured in the model results, such as springflow, head levels, storage, and others, were determined by previous work in elicitation of problem framing to determine stakeholder interests and concerns. The results of the previous deterministic model and the stochastic model are compared to determine gains to stakeholder knowledge through the additional modeling

Bayesian deterministic decision making: a normative account of the operant matching law and heavy-tailed reward history dependency of choices.

PubMed

Saito, Hiroshi; Katahira, Kentaro; Okanoya, Kazuo; Okada, Masato

2014-01-01

The decision making behaviors of humans and animals adapt and then satisfy an "operant matching law" in certain type of tasks. This was first pointed out by Herrnstein in his foraging experiments on pigeons. The matching law has been one landmark for elucidating the underlying processes of decision making and its learning in the brain. An interesting question is whether decisions are made deterministically or probabilistically. Conventional learning models of the matching law are based on the latter idea; they assume that subjects learn choice probabilities of respective alternatives and decide stochastically with the probabilities. However, it is unknown whether the matching law can be accounted for by a deterministic strategy or not. To answer this question, we propose several deterministic Bayesian decision making models that have certain incorrect beliefs about an environment. We claim that a simple model produces behavior satisfying the matching law in static settings of a foraging task but not in dynamic settings. We found that the model that has a belief that the environment is volatile works well in the dynamic foraging task and exhibits undermatching, which is a slight deviation from the matching law observed in many experiments. This model also demonstrates the double-exponential reward history dependency of a choice and a heavier-tailed run-length distribution, as has recently been reported in experiments on monkeys.

Resilience and vulnerability to a natural hazard: A mathematical framework based on viability theory

NASA Astrophysics Data System (ADS)

Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume

2013-04-01

This deals with the response of a coupled human and natural system (CHANS) to a natural hazard by using the concepts of resilience and vulnerability within the mathematical framework of viability theory. This theory applies to time-evolving systems such as CHANS and assumes that their desirable properties can be defined as a subset of their state space. Policies can also apply to influence the dynamics of such systems: viability theory aims at finding the policies which keep the properties of a controlled dynamical system for so long as no disturbance hits it. The states of the system such that the properties are guaranteed constitute what is called the viability kernel. This viability framework has been extended to describe the response to a perturbation such as a natural hazard. Resilience describes the capacity of the CHANS to recover by getting back in the viability kernel, where its properties are guaranteed until the onset of the next major event. Defined for a given controlled trajectory that the system may take after the event ends, resilience is (a) whether the system comes back to the viability kernel within a given budget such as a time constraint, but also (b) a decreasing function of vulnerability. Computed for a given trajectory as well, vulnerability is a measure of the consequence of violating a property. We propose a family of functions from which cost functions and other vulnerability indicators can be derived for a certain trajectory. There can be several vulnerability functions, representing for instance social, economic or ecological vulnerability, and each representing the violation of an associated property, but these functions need to be ultimately aggregated as a single indicator. Computing the resilience and vulnerability of a trajectory enables the viability framework to describe the response of both deterministic and stochastic systems to hazards. In the deterministic case, there is only one response trajectory for a given action policy, and methods exist to find the actions which yield the most resilient trajectory, namely the least vulnerable trajectory for which recovery is complete. In the stochastic case however, there is a range of possible trajectories. Statistics can be derived from the probability distribution of the resilience and vulnerability of the trajectories. Dynamic programming methods can then yield either the policies that maximize the probability of being resilient by achieving recovery within a given time horizon, or these which minimize a given vulnerability statistic. These objectives are different and can be in contradiction, so that trade-offs may have to be considered between them. The approach is illustrated in both the deterministic and stochastic cases through a simple model of lake eutrophication, for which the desirable ecological properties of the lake conflict with the economic interest of neighboring farmers.

Design Considerations of Polishing Lap for Computer-Controlled Cylindrical Polishing Process

NASA Technical Reports Server (NTRS)

Khan, Gufran S.; Gubarev, Mikhail; Speegle, Chet; Ramsey, Brian

2010-01-01

The future X-ray observatory missions, such as International X-ray Observatory, require grazing incidence replicated optics of extremely large collecting area (3 m2) in combination with angular resolution of less than 5 arcsec half-power diameter. The resolution of a mirror shell depends ultimately on the quality of the cylindrical mandrels from which they are being replicated. Mid-spatial-frequency axial figure error is a dominant contributor in the error budget of the mandrel. This paper presents our efforts to develop a deterministic cylindrical polishing process in order to keep the mid-spatial-frequency axial figure errors to a minimum. Simulation studies have been performed to optimize the operational parameters as well as the polishing lap configuration. Furthermore, depending upon the surface error profile, a model for localized polishing based on dwell time approach is developed. Using the inputs from the mathematical model, a mandrel, having conical approximated Wolter-1 geometry, has been polished on a newly developed computer-controlled cylindrical polishing machine. We report our first experimental results and discuss plans for further improvements in the polishing process.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data.

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way. PMID:25937674

Genetic information and ecosystem health: arguments for the application of chaos theory to identify boundary conditions for ecosystem management.

PubMed Central

Stomp, A M

1994-01-01

To meet the demands for goods and services of an exponentially growing human population, global ecosystems will come under increasing human management. The hallmark of successful ecosystem management will be long-term ecosystem stability. Ecosystems and the genetic information and processes which underlie interactions of organisms with the environment in populations and communities exhibit behaviors which have nonlinear characteristics. Nonlinear mathematical formulations describing deterministic chaos have been used successfully to model such systems in physics, chemistry, economics, physiology, and epidemiology. This approach can be extended to ecotoxicology and can be used to investigate how changes in genetic information determine the behavior of populations and communities. This article seeks to provide the arguments for such an approach and to give initial direction to the search for the boundary conditions within which lies ecosystem stability. The identification of a theoretical framework for ecotoxicology and the parameters which drive the underlying model is a critical component in the formulation of a prioritized research agenda and appropriate ecosystem management policy and regulation. PMID:7713038

Role of demographic stochasticity in a speciation model with sexual reproduction

NASA Astrophysics Data System (ADS)

Lafuerza, Luis F.; McKane, Alan J.

2016-03-01

Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localized clusters, suggesting a simple mechanism for sympatric speciation. Here we study the role of demographic stochasticity in a model of competing organisms subject to assortative mating. We find that in models with sexual reproduction, noise can also lead to the formation of phenotypic clusters in parameter ranges where deterministic models would lead to a homogeneous distribution. In some cases, noise can have a sizable effect, rendering the deterministic modeling insufficient to understand the phenotypic distribution.

Multi-parametric variational data assimilation for hydrological forecasting

NASA Astrophysics Data System (ADS)

Alvarado-Montero, R.; Schwanenberg, D.; Krahe, P.; Helmke, P.; Klein, B.

2017-12-01

Ensemble forecasting is increasingly applied in flow forecasting systems to provide users with a better understanding of forecast uncertainty and consequently to take better-informed decisions. A common practice in probabilistic streamflow forecasting is to force deterministic hydrological model with an ensemble of numerical weather predictions. This approach aims at the representation of meteorological uncertainty but neglects uncertainty of the hydrological model as well as its initial conditions. Complementary approaches use probabilistic data assimilation techniques to receive a variety of initial states or represent model uncertainty by model pools instead of single deterministic models. This paper introduces a novel approach that extends a variational data assimilation based on Moving Horizon Estimation to enable the assimilation of observations into multi-parametric model pools. It results in a probabilistic estimate of initial model states that takes into account the parametric model uncertainty in the data assimilation. The assimilation technique is applied to the uppermost area of River Main in Germany. We use different parametric pools, each of them with five parameter sets, to assimilate streamflow data, as well as remotely sensed data from the H-SAF project. We assess the impact of the assimilation in the lead time performance of perfect forecasts (i.e. observed data as forcing variables) as well as deterministic and probabilistic forecasts from ECMWF. The multi-parametric assimilation shows an improvement of up to 23% for CRPS performance and approximately 20% in Brier Skill Scores with respect to the deterministic approach. It also improves the skill of the forecast in terms of rank histogram and produces a narrower ensemble spread.

Aboveground and belowground arthropods experience different relative influences of stochastic versus deterministic community assembly processes following disturbance

PubMed Central

Martinez, Alexander S.; Faist, Akasha M.

2016-01-01

Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species) and belowground (species active in organic and mineral soil layers) arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community) and modified Winkler funnels (belowground community) and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity) among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the aboveground arthropod communities and vegetation and soil properties, but no significant association among belowground arthropod communities and environmental factors. Discussion Our results suggest context-dependent influences of stochastic and deterministic community assembly processes across different fractions of a spatially co-occurring ground-dwelling arthropod community following disturbance. This variation in assembly may be linked to contrasting ecological strategies and dispersal rates within above- and below-ground communities. Our findings add to a growing body of evidence indicating concurrent influences of stochastic and deterministic processes in community assembly, and highlight the need to consider potential variation across different fractions of biotic communities when testing community ecology theory and considering conservation strategies. PMID:27761333

Study on the evaluation method for fault displacement based on characterized source model

NASA Astrophysics Data System (ADS)

Tonagi, M.; Takahama, T.; Matsumoto, Y.; Inoue, N.; Irikura, K.; Dalguer, L. A.

2016-12-01

In IAEA Specific Safety Guide (SSG) 9 describes that probabilistic methods for evaluating fault displacement should be used if no sufficient basis is provided to decide conclusively that the fault is not capable by using the deterministic methodology. In addition, International Seismic Safety Centre compiles as ANNEX to realize seismic hazard for nuclear facilities described in SSG-9 and shows the utility of the deterministic and probabilistic evaluation methods for fault displacement. In Japan, it is required that important nuclear facilities should be established on ground where fault displacement will not arise when earthquakes occur in the future. Under these situations, based on requirements, we need develop evaluation methods for fault displacement to enhance safety in nuclear facilities. We are studying deterministic and probabilistic methods with tentative analyses using observed records such as surface fault displacement and near-fault strong ground motions of inland crustal earthquake which fault displacements arose. In this study, we introduce the concept of evaluation methods for fault displacement. After that, we show parts of tentative analysis results for deterministic method as follows: (1) For the 1999 Chi-Chi earthquake, referring slip distribution estimated by waveform inversion, we construct a characterized source model (Miyake et al., 2003, BSSA) which can explain observed near-fault broad band strong ground motions. (2) Referring a characterized source model constructed in (1), we study an evaluation method for surface fault displacement using hybrid method, which combines particle method and distinct element method. At last, we suggest one of the deterministic method to evaluate fault displacement based on characterized source model. This research was part of the 2015 research project `Development of evaluating method for fault displacement` by the Secretariat of Nuclear Regulation Authority (S/NRA), Japan.

Neuronal spike-train responses in the presence of threshold noise.

PubMed

Coombes, S; Thul, R; Laudanski, J; Palmer, A R; Sumner, C J

2011-03-01

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

Effect of Uncertainty on Deterministic Runway Scheduling

NASA Technical Reports Server (NTRS)

Gupta, Gautam; Malik, Waqar; Jung, Yoon C.

2012-01-01

Active runway scheduling involves scheduling departures for takeoffs and arrivals for runway crossing subject to numerous constraints. This paper evaluates the effect of uncertainty on a deterministic runway scheduler. The evaluation is done against a first-come- first-serve scheme. In particular, the sequence from a deterministic scheduler is frozen and the times adjusted to satisfy all separation criteria; this approach is tested against FCFS. The comparison is done for both system performance (throughput and system delay) and predictability, and varying levels of congestion are considered. The modeling of uncertainty is done in two ways: as equal uncertainty in availability at the runway as for all aircraft, and as increasing uncertainty for later aircraft. Results indicate that the deterministic approach consistently performs better than first-come-first-serve in both system performance and predictability.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations.

PubMed

Ngwa, Gideon A; Teboh-Ewungkem, Miranda I

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed.

Dimensionality of Motion and Binding Valency Govern Receptor-Ligand Kinetics As Revealed by Agent-Based Modeling.

PubMed

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor-ligand binding in the context of antibody-antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors-such as their dimensionality of motion, morphology, and binding valency-on the receptor-ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations

PubMed Central

Ngwa, Gideon A.

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed. PMID:27579053

Dimensionality of Motion and Binding Valency Govern Receptor–Ligand Kinetics As Revealed by Agent-Based Modeling

PubMed Central

Lehnert, Teresa; Figge, Marc Thilo

2017-01-01

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor–ligand binding in the context of antibody–antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors—such as their dimensionality of motion, morphology, and binding valency—on the receptor–ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors. PMID:29250071

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells.

PubMed

Cao, Pengxing; Tan, Xiahui; Donovan, Graham; Sanderson, Michael J; Sneyd, James

2014-08-01

The inositol trisphosphate receptor ([Formula: see text]) is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the [Formula: see text] have arisen. Firstly, how best should the [Formula: see text] be modeled? In other words, what fundamental properties of the [Formula: see text] allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of [Formula: see text], is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the [Formula: see text], and thus the behavior of the [Formula: see text] is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, [Formula: see text] stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic [Formula: see text] models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified [Formula: see text] models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

Fulai, Wang

2012-12-01

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1985-01-01

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastien; Stollenwerk, Nico

2010-09-01

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

Two Strain Dengue Model with Temporary Cross Immunity and Seasonality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguiar, Maira; Ballesteros, Sebastien; Stollenwerk, Nico

Models on dengue fever epidemiology have previously shown critical fluctuations with power law distributions and also deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. In our first model including well known biological features, we found a rich dynamical structure including limit cycles, symmetry breaking bifurcations, torus bifurcations, coexisting attractors including isola solutions and deterministic chaos (as indicated by positive Lyapunov exponents) in a much larger parameter region, which is also biologically more plausible than the previous results of other researches. Based on these findings we will investigate the model structures further including seasonality.

The threshold of a stochastic delayed SIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2016-11-01

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

Distributed modelling of hydrologic regime at three subcatchments of Kopaninský tok catchment

NASA Astrophysics Data System (ADS)

Žlábek, Pavel; Tachecí, Pavel; Kaplická, Markéta; Bystřický, Václav

2010-05-01

Kopaninský tok catchment is situated in crystalline area of Bohemo-Moravian highland hilly region, with cambisol cover and prevailing agricultural land use. It is a subject of long term (since 1980's) observation. Time series (discharge, precipitation, climatic parameters...) are nowadays available in 10 min. time step, water quality average daily composit samples plus samples during events are available. Soil survey resulting in reference soil hydraulic properties for horizons and vegetation cover survey incl. LAI measurement has been done. All parameters were analysed and used for establishing of distributed mathematical models of P6, P52 and P53 subcatchments, using MIKE SHE 2009 WM deterministic hydrologic modelling system. The aim is to simulate long-term hydrologic regime as well as rainfall-runoff events, serving the base for modelling of nitrate regime and agricultural management influence in the next step. Mentioned subcatchments differs in ratio of artificial drainage area, soil types, land use and slope angle. The models are set-up in a regular computational grid of 2 m size. Basic time step was set to 2 hrs, total simulated period covers 3 years. Runoff response and moisture regime is compared using spatially distributed simulation results. Sensitivity analysis revealed most important parameters influencing model response. Importance of spatial distribution of initial conditions was underlined. Further on, different runoff components in terms of their origin, flow paths and travel time were separated using a combination of two runoff separation techniques (a digital filter and a simple conceptual model GROUND) in 12 subcatchments of Kopaninský tok catchment. These two methods were chosen based on a number of methods testing. Ordinations diagrams performed with Canoco software were used to evaluate influence of different catchment parameters on different runoff components. A canonical ordination method analyses (RDA) was used to explain one data set (runoff components - either volumes of each runoff component or occurence of baseflow) with another data set (catchment parameters - proportion of arable land, proportion of forest, proportion of vulnerable zones with high infiltration capacity, average slope, topographic index and runoff coefficient). The influence was analysed both for long-term runoff balance and selected rainfall-runoff events. Keywords: small catchment, water balance modelling, rainfall-runoff modelling, distributed deterministic model, runoff separation, sensitivity analysis

On the deterministic and stochastic use of hydrologic models

USGS Publications Warehouse

Farmer, William H.; Vogel, Richard M.

2016-01-01

Environmental simulation models, such as precipitation-runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed-parameter precipitation-runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.

Theory and applications of a deterministic approximation to the coalescent model

PubMed Central

Jewett, Ethan M.; Rosenberg, Noah A.

2014-01-01

Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt ≈ E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt ≈ E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios. PMID:24412419

Ordinal optimization and its application to complex deterministic problems

NASA Astrophysics Data System (ADS)

Yang, Mike Shang-Yu

1998-10-01

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.

Dwell time algorithm based on the optimization theory for magnetorheological finishing

NASA Astrophysics Data System (ADS)

Zhang, Yunfei; Wang, Yang; Wang, Yajun; He, Jianguo; Ji, Fang; Huang, Wen

2010-10-01

Magnetorheological finishing (MRF) is an advanced polishing technique capable of rapidly converging to the required surface figure. This process can deterministically control the amount of the material removed by varying a time to dwell at each particular position on the workpiece surface. The dwell time algorithm is one of the most important key techniques of the MRF. A dwell time algorithm based on the1 matrix equation and optimization theory was presented in this paper. The conventional mathematical model of the dwell time was transferred to a matrix equation containing initial surface error, removal function and dwell time function. The dwell time to be calculated was just the solution to the large, sparse matrix equation. A new mathematical model of the dwell time based on the optimization theory was established, which aims to minimize the 2-norm or ∞-norm of the residual surface error. The solution meets almost all the requirements of precise computer numerical control (CNC) without any need for extra data processing, because this optimization model has taken some polishing condition as the constraints. Practical approaches to finding a minimal least-squares solution and a minimal maximum solution are also discussed in this paper. Simulations have shown that the proposed algorithm is numerically robust and reliable. With this algorithm an experiment has been performed on the MRF machine developed by ourselves. After 4.7 minutes' polishing, the figure error of a flat workpiece with a 50 mm diameter is improved by PV from 0.191λ(λ = 632.8 nm) to 0.087λ and RMS 0.041λ to 0.010λ. This algorithm can be constructed to polish workpieces of all shapes including flats, spheres, aspheres, and prisms, and it is capable of improving the polishing figures dramatically.

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

NASA Technical Reports Server (NTRS)

McClelland, Ryan S.; Bonafede, Joseph; Saha, Timo T.; Solly, Peter M.; Zhang, William W.

2016-01-01

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

Solving difficult problems creatively: a role for energy optimised deterministic/stochastic hybrid computing

PubMed Central

Palmer, Tim N.; O’Shea, Michael

2015-01-01

How is the brain configured for creativity? What is the computational substrate for ‘eureka’ moments of insight? Here we argue that creative thinking arises ultimately from a synergy between low-energy stochastic and energy-intensive deterministic processing, and is a by-product of a nervous system whose signal-processing capability per unit of available energy has become highly energy optimised. We suggest that the stochastic component has its origin in thermal (ultimately quantum decoherent) noise affecting the activity of neurons. Without this component, deterministic computational models of the brain are incomplete. PMID:26528173

Heart rate variability as determinism with jump stochastic parameters.

PubMed

Zheng, Jiongxuan; Skufca, Joseph D; Bollt, Erik M

2013-08-01

We use measured heart rate information (RR intervals) to develop a one-dimensional nonlinear map that describes short term deterministic behavior in the data. Our study suggests that there is a stochastic parameter with persistence which causes the heart rate and rhythm system to wander about a bifurcation point. We propose a modified circle map with a jump process noise term as a model which can qualitatively capture such this behavior of low dimensional transient determinism with occasional (stochastically defined) jumps from one deterministic system to another within a one parameter family of deterministic systems.

Tag-mediated cooperation with non-deterministic genotype-phenotype mapping

NASA Astrophysics Data System (ADS)

Zhang, Hong; Chen, Shu

2016-01-01

Tag-mediated cooperation provides a helpful framework for resolving evolutionary social dilemmas. However, most of the previous studies have not taken into account genotype-phenotype distinction in tags, which may play an important role in the process of evolution. To take this into consideration, we introduce non-deterministic genotype-phenotype mapping into a tag-based model with spatial prisoner's dilemma. By our definition, the similarity between genotypic tags does not directly imply the similarity between phenotypic tags. We find that the non-deterministic mapping from genotypic tag to phenotypic tag has non-trivial effects on tag-mediated cooperation. Although we observe that high levels of cooperation can be established under a wide variety of conditions especially when the decisiveness is moderate, the uncertainty in the determination of phenotypic tags may have a detrimental effect on the tag mechanism by disturbing the homophilic interaction structure which can explain the promotion of cooperation in tag systems. Furthermore, the non-deterministic mapping may undermine the robustness of the tag mechanism with respect to various factors such as the structure of the tag space and the tag flexibility. This observation warns us about the danger of applying the classical tag-based models to the analysis of empirical phenomena if genotype-phenotype distinction is significant in real world. Non-deterministic genotype-phenotype mapping thus provides a new perspective to the understanding of tag-mediated cooperation.

Physical Invariants of Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Time Domain and Frequency Domain Deterministic Channel Modeling for Tunnel/Mining Environments.

PubMed

Zhou, Chenming; Jacksha, Ronald; Yan, Lincan; Reyes, Miguel; Kovalchik, Peter

2017-01-01

Understanding wireless channels in complex mining environments is critical for designing optimized wireless systems operated in these environments. In this paper, we propose two physics-based, deterministic ultra-wideband (UWB) channel models for characterizing wireless channels in mining/tunnel environments - one in the time domain and the other in the frequency domain. For the time domain model, a general Channel Impulse Response (CIR) is derived and the result is expressed in the classic UWB tapped delay line model. The derived time domain channel model takes into account major propagation controlling factors including tunnel or entry dimensions, frequency, polarization, electrical properties of the four tunnel walls, and transmitter and receiver locations. For the frequency domain model, a complex channel transfer function is derived analytically. Based on the proposed physics-based deterministic channel models, channel parameters such as delay spread, multipath component number, and angular spread are analyzed. It is found that, despite the presence of heavy multipath, both channel delay spread and angular spread for tunnel environments are relatively smaller compared to that of typical indoor environments. The results and findings in this paper have application in the design and deployment of wireless systems in underground mining environments.

Time Domain and Frequency Domain Deterministic Channel Modeling for Tunnel/Mining Environments

PubMed Central

Zhou, Chenming; Jacksha, Ronald; Yan, Lincan; Reyes, Miguel; Kovalchik, Peter

2018-01-01

Understanding wireless channels in complex mining environments is critical for designing optimized wireless systems operated in these environments. In this paper, we propose two physics-based, deterministic ultra-wideband (UWB) channel models for characterizing wireless channels in mining/tunnel environments — one in the time domain and the other in the frequency domain. For the time domain model, a general Channel Impulse Response (CIR) is derived and the result is expressed in the classic UWB tapped delay line model. The derived time domain channel model takes into account major propagation controlling factors including tunnel or entry dimensions, frequency, polarization, electrical properties of the four tunnel walls, and transmitter and receiver locations. For the frequency domain model, a complex channel transfer function is derived analytically. Based on the proposed physics-based deterministic channel models, channel parameters such as delay spread, multipath component number, and angular spread are analyzed. It is found that, despite the presence of heavy multipath, both channel delay spread and angular spread for tunnel environments are relatively smaller compared to that of typical indoor environments. The results and findings in this paper have application in the design and deployment of wireless systems in underground mining environments.† PMID:29457801

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

PubMed

Rajeswari, M; Amudhavel, J; Pothula, Sujatha; Dhavachelvan, P

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

A new diode laser acupuncture therapy apparatus

NASA Astrophysics Data System (ADS)

Li, Chengwei; Huang, Zhen; Li, Dongyu; Zhang, Xiaoyuan

2006-06-01

Since the first laser-needles acupuncture apparatus was introduced in therapy, this kind of apparatus has been well used in laser biomedicine as its non-invasive, pain- free, non-bacterium, and safetool. The laser acupuncture apparatus in this paper is based on single-chip microcomputer and associated by semiconductor laser technology. The function like traditional moxibustion including reinforcing and reducing is implemented by applying chaos method to control the duty cycle of moxibustion signal, and the traditional lifting and thrusting of acupuncture is implemented by changing power output of the diode laser. The radiator element of diode laser is made and the drive circuit is designed. And chaos mathematic model is used to produce deterministic class stochastic signal to avoid the body adaptability. This function covers the shortages of continuous irradiation or that of simple disciplinary stimulate signal, which is controlled by some simple electronic circuit and become easily adjusted by human body. The realization of reinforcing and reducing of moxibustion is technological innovation in traditional acupuncture coming true in engineering.

Symbolic inversion of control relationships in model-based expert systems

NASA Technical Reports Server (NTRS)

Thomas, Stan

1988-01-01

Symbolic inversion is examined from several perspectives. First, a number of symbolic algebra and mathematical tool packages were studied in order to evaluate their capabilities and methods, specifically with respect to symbolic inversion. Second, the KATE system (without hardware interface) was ported to a Zenith Z-248 microcomputer running Golden Common Lisp. The interesting thing about the port is that it allows the user to have measurements vary and components fail in a non-deterministic manner based upon random value from probability distributions. Third, INVERT was studied as currently implemented in KATE, its operation documented, some of its weaknesses identified, and corrections made to it. The corrections and enhancements are primarily in the way that logical conditions involving AND's and OR's and inequalities are processed. In addition, the capability to handle equalities was also added. Suggestions were also made regarding the handling of ranges in INVERT. Last, other approaches to the inversion process were studied and recommendations were made as to how future versions of KATE should perform symbolic inversion.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

PubMed Central

Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849

Understanding the impact of Hib conjugate vaccine on transmission, immunity and disease in the United Kingdom

PubMed Central

McVERNON, J.; RAMSAY, M. E.; McLEAN, A. R.

2008-01-01

SUMMARY A rise in invasive Haemophilus influenzae type b (Hib) infections occurred 8 years after vaccine introduction in the United Kingdom. Aspects of Hib vaccine delivery unique to the United Kingdom have been implicated. The authors developed a fully age-structured deterministic susceptible–infected–resistant–susceptible mathematical model, expressed as a set of partial differential equations, to better understand the causes of declining vaccine effectiveness. We also investigated the consequences of the vaccine's impact on reducing Hib transmission for maintenance of immunity. Our findings emphasized the importance of maintaining high post-immunization antibody titres among age groups at greatest risk of invasive infections. In keeping with UK population-based estimates, low direct efficacy of immunological memory against disease was found, cautioning against over-reliance on evidence of priming alone as a correlate of population protection. The contribution of herd immunity to disease control was reinforced. Possible intervention strategies will be explored in subsequent work. PMID:17678559

Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems.

PubMed

Zhao, Xudong; Wang, Xinyong; Zong, Guangdeng; Zheng, Xiaolong

2017-10-01

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Risk assessment for furan contamination through the food chain in Belgian children.

PubMed

Scholl, Georges; Huybrechts, Inge; Humblet, Marie-France; Scippo, Marie-Louise; De Pauw, Edwin; Eppe, Gauthier; Saegerman, Claude

2012-08-01

Young, old, pregnant and immuno-compromised persons are of great concern for risk assessors as they represent the sub-populations most at risk. The present paper focuses on risk assessment linked to furan exposure in children. Only the Belgian population was considered because individual contamination and consumption data that are required for accurate risk assessment were available for Belgian children only. Two risk assessment approaches, the so-called deterministic and probabilistic, were applied and the results were compared for the estimation of daily intake. A significant difference between the average Estimated Daily Intake (EDI) was underlined between the deterministic (419 ng kg⁻¹ body weight (bw) day⁻¹) and the probabilistic (583 ng kg⁻¹ bw day⁻¹) approaches, which results from the mathematical treatment of the null consumption and contamination data. The risk was characterised by two ways: (1) the classical approach by comparison of the EDI to a reference dose (RfD(chronic-oral)) and (2) the most recent approach, namely the Margin of Exposure (MoE) approach. Both reached similar conclusions: the risk level is not of a major concern, but is neither negligible. In the first approach, only 2.7 or 6.6% (respectively in the deterministic and in the probabilistic way) of the studied population presented an EDI above the RfD(chronic-oral). In the second approach, the percentage of children displaying a MoE above 10,000 and below 100 is 3-0% and 20-0.01% in the deterministic and probabilistic modes, respectively. In addition, children were compared to adults and significant differences between the contamination patterns were highlighted. While major contamination was linked to coffee consumption in adults (55%), no item predominantly contributed to the contamination in children. The most important were soups (19%), dairy products (17%), pasta and rice (11%), fruit and potatoes (9% each).

Dual Roles for Spike Signaling in Cortical Neural Populations

PubMed Central

Ballard, Dana H.; Jehee, Janneke F. M.

2011-01-01

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding. PMID:21687798

High performance real-time flight simulation at NASA Langley

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1994-01-01

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations must be deterministic and be completed in as short a time as possible. This includes simulation mathematical model computational and data input/output to the simulators. In 1986, in response to increased demands for flight simulation performance, personnel at NASA's Langley Research Center (LaRC), working with the contractor, developed extensions to a standard input/output system to provide for high bandwidth, low latency data acquisition and distribution. The Computer Automated Measurement and Control technology (IEEE standard 595) was extended to meet the performance requirements for real-time simulation. This technology extension increased the effective bandwidth by a factor of ten and increased the performance of modules necessary for simulator communications. This technology is being used by more than 80 leading technological developers in the United States, Canada, and Europe. Included among the commercial applications of this technology are nuclear process control, power grid analysis, process monitoring, real-time simulation, and radar data acquisition. Personnel at LaRC have completed the development of the use of supercomputers for simulation mathematical model computational to support real-time flight simulation. This includes the development of a real-time operating system and the development of specialized software and hardware for the CAMAC simulator network. This work, coupled with the use of an open systems software architecture, has advanced the state of the art in real time flight simulation. The data acquisition technology innovation and experience with recent developments in this technology are described.

Stochastic switching in biology: from genotype to phenotype

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-03-01

There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a self-contained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels. However, applications to other examples of biological switching are also discussed, including stochastic ion channels, diffusion in randomly switching environments, bacterial chemotaxis, and stochastic neural networks.

Guidelines 13 and 14—Prediction uncertainty

USGS Publications Warehouse

Hill, Mary C.; Tiedeman, Claire

2005-01-01

An advantage of using optimization for model development and calibration is that optimization provides methods for evaluating and quantifying prediction uncertainty. Both deterministic and statistical methods can be used. Guideline 13 discusses using regression and post-audits, which we classify as deterministic methods. Guideline 14 discusses inferential statistics and Monte Carlo methods, which we classify as statistical methods.

Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations

DTIC Science & Technology

2015-02-17

of diminishing returns from vacci- nation will generally take place at smaller vaccine allocations V compared to the deterministic model. Optimal...take place and small r0 values where it does not is illustrat- ed in Fig. 4C. As r0 is decreased, the region between the two instances of switching...approximately distribute vaccine in proportion to population size. For large r0 (r0 ≳ 2.9), two switches take place . In the deterministic optimal solution, a

Hybrid Forecasting of Daily River Discharges Considering Autoregressive Heteroscedasticity

NASA Astrophysics Data System (ADS)

Szolgayová, Elena Peksová; Danačová, Michaela; Komorniková, Magda; Szolgay, Ján

2017-06-01

It is widely acknowledged that in the hydrological and meteorological communities, there is a continuing need to improve the quality of quantitative rainfall and river flow forecasts. A hybrid (combined deterministic-stochastic) modelling approach is proposed here that combines the advantages offered by modelling the system dynamics with a deterministic model and a deterministic forecasting error series with a data-driven model in parallel. Since the processes to be modelled are generally nonlinear and the model error series may exhibit nonstationarity and heteroscedasticity, GARCH-type nonlinear time series models are considered here. The fitting, forecasting and simulation performance of such models have to be explored on a case-by-case basis. The goal of this paper is to test and develop an appropriate methodology for model fitting and forecasting applicable for daily river discharge forecast error data from the GARCH family of time series models. We concentrated on verifying whether the use of a GARCH-type model is suitable for modelling and forecasting a hydrological model error time series on the Hron and Morava Rivers in Slovakia. For this purpose we verified the presence of heteroscedasticity in the simulation error series of the KLN multilinear flow routing model; then we fitted the GARCH-type models to the data and compared their fit with that of an ARMA - type model. We produced one-stepahead forecasts from the fitted models and again provided comparisons of the model's performance.

Forecasting seasonal influenza with a state-space SIR model

DOE PAGES

Osthus, Dave; Hickmann, Kyle S.; Caragea, Petruţa C.; ...

2017-04-08

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are onlymore » partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.« less

Forecasting seasonal influenza with a state-space SIR model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osthus, Dave; Hickmann, Kyle S.; Caragea, Petruţa C.

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are onlymore » partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.« less

On the Origin of Quantum Diffusion Coefficient and Quantum Potential

NASA Astrophysics Data System (ADS)

Gupta, Aseem

2016-03-01

Synchronizability of space and time experiences between different inhabitants of a spacetime is abstracted as a fundamental premise of Classical physics. Absence thereof i.e. desynchronization between space and time experiences of a system under study and the observer is then studied for a single dimension single particle system. Desynchronization fundamentally makes probability concepts enter physics ab-initio and not as secondary tools to deal with situations wherein incomplete information in situation following perfectly deterministic dynamics demands its introduction. Desynchronization model based on Poisson distribution of events vis-à-vis an observer, leads to expectation of particle's motion as a Brownian motion deriving Nelson's quantum diffusion coefficient naturally, without needing to postulate it. This model also incorporates physical effects akin to those of Bohm's Quantum Potential, again without needing any sub-quantum medium. Schrodinger's equation is shown to be derivable incorporating desynchronization only of space while Quantum Field Theory is shown to model desynchronization of time as well. Fundamental suggestion of the study is that it is desynchronization that is at the root of quantum phenomena rather than sub-micro scales of spacetime. Absence of possibility of synchronization between system's space and time and those of observer is studied. Mathematical modeling of desynchronized evolution explains some intriguing aspects of Quantum Mechanical theory.

The place of words and numbers in psychiatric research.

PubMed

Falissard, Bruno; Révah, Anne; Yang, Suzanne; Fagot-Largeault, Anne

2013-11-18

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean "quantitative/qualitative" dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide.

The place of words and numbers in psychiatric research

PubMed Central

2013-01-01

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean “quantitative/qualitative” dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide. PMID:24246064

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

PubMed

Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O

2006-03-01

The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.

Modeling disease transmission near eradication: An equation free approach

NASA Astrophysics Data System (ADS)

Williams, Matthew O.; Proctor, Joshua L.; Kutz, J. Nathan

2015-01-01

Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic "coarse" model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigns.

A deterministic model of electron transport for electron probe microanalysis

NASA Astrophysics Data System (ADS)

Bünger, J.; Richter, S.; Torrilhon, M.

2018-01-01

Within the last decades significant improvements in the spatial resolution of electron probe microanalysis (EPMA) were obtained by instrumental enhancements. In contrast, the quantification procedures essentially remained unchanged. As the classical procedures assume either homogeneity or a multi-layered structure of the material, they limit the spatial resolution of EPMA. The possibilities of improving the spatial resolution through more sophisticated quantification procedures are therefore almost untouched. We investigate a new analytical model (M 1-model) for the quantification procedure based on fast and accurate modelling of electron-X-ray-matter interactions in complex materials using a deterministic approach to solve the electron transport equations. We outline the derivation of the model from the Boltzmann equation for electron transport using the method of moments with a minimum entropy closure and present first numerical results for three different test cases (homogeneous, thin film and interface). Taking Monte Carlo as a reference, the results for the three test cases show that the M 1-model is able to reproduce the electron dynamics in EPMA applications very well. Compared to classical analytical models like XPP and PAP, the M 1-model is more accurate and far more flexible, which indicates the potential of deterministic models of electron transport to further increase the spatial resolution of EPMA.

Trend Estimation and Regression Analysis in Climatological Time Series: An Application of Structural Time Series Models and the Kalman Filter.

NASA Astrophysics Data System (ADS)

Visser, H.; Molenaar, J.

1995-05-01

The detection of trends in climatological data has become central to the discussion on climate change due to the enhanced greenhouse effect. To prove detection, a method is needed (i) to make inferences on significant rises or declines in trends, (ii) to take into account natural variability in climate series, and (iii) to compare output from GCMs with the trends in observed climate data. To meet these requirements, flexible mathematical tools are needed. A structural time series model is proposed with which a stochastic trend, a deterministic trend, and regression coefficients can be estimated simultaneously. The stochastic trend component is described using the class of ARIMA models. The regression component is assumed to be linear. However, the regression coefficients corresponding with the explanatory variables may be time dependent to validate this assumption. The mathematical technique used to estimate this trend-regression model is the Kaiman filter. The main features of the filter are discussed.Examples of trend estimation are given using annual mean temperatures at a single station in the Netherlands (1706-1990) and annual mean temperatures at Northern Hemisphere land stations (1851-1990). The inclusion of explanatory variables is shown by regressing the latter temperature series on four variables: Southern Oscillation index (SOI), volcanic dust index (VDI), sunspot numbers (SSN), and a simulated temperature signal, induced by increasing greenhouse gases (GHG). In all analyses, the influence of SSN on global temperatures is found to be negligible. The correlations between temperatures and SOI and VDI appear to be negative. For SOI, this correlation is significant, but for VDI it is not, probably because of a lack of volcanic eruptions during the sample period. The relation between temperatures and GHG is positive, which is in agreement with the hypothesis of a warming climate because of increasing levels of greenhouse gases. The prediction performance of the model is rather poor, and possible explanations are discussed.

Optimization,Modeling, and Control: Applications to Klystron Designing and Hepatitis C Virus Dynamics

NASA Astrophysics Data System (ADS)

Lankford, George Bernard

In this dissertation, we address applying mathematical and numerical techniques in the fields of high energy physics and biomedical sciences. The first portion of this thesis presents a method for optimizing the design of klystron circuits. A klystron is an electron beam tube lined with cavities that emit resonant frequencies to velocity modulate electrons that pass through the tube. Radio frequencies (RF) inserted in the klystron are amplified due to the velocity modulation of the electrons. The routine described in this work automates the selection of cavity positions, resonant frequencies, quality factors, and other circuit parameters to maximize the efficiency with required gain. The method is based on deterministic sampling methods. We will describe the procedure and give several examples for both narrow and wide band klystrons, using the klystron codes AJDISK (Java) and TESLA (Python). The rest of the dissertation is dedicated to developing, calibrating and using a mathematical model for hepatitis C dynamics with triple drug combination therapy. Groundbreaking new drugs, called direct acting antivirals, have been introduced recently to fight off chronic hepatitis C virus infection. The model we introduce is for hepatitis C dynamics treated with the direct acting antiviral drug, telaprevir, along with traditional interferon and ribavirin treatments to understand how this therapy affects the viral load of patients exhibiting different types of response. We use sensitivity and identifiability techniques to determine which parameters can be best estimated from viral load data. We use these estimations to give patient-specific fits of the model to partial viral response, end-of-treatment response, and breakthrough patients. We will then revise the model to incorporate an immune response dynamic to more accurately describe the dynamics. Finally, we will implement a suboptimal control to acquire a drug treatment regimen that will alleviate the systemic cost associated with constant drug treatment.

Using Bayesian Model Averaging (BMA) to calibrate probabilistic surface temperature forecasts over Iran

NASA Astrophysics Data System (ADS)

Soltanzadeh, I.; Azadi, M.; Vakili, G. A.

2011-07-01

Using Bayesian Model Averaging (BMA), an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM), with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and for HRM the initial and boundary conditions come from analysis of Global Model Europe (GME) of the German Weather Service. The resulting ensemble of seven members was run for a period of 6 months (from December 2008 to May 2009) over Iran. The 48-h raw ensemble outputs were calibrated using BMA technique for 120 days using a 40 days training sample of forecasts and relative verification data. The calibrated probabilistic forecasts were assessed using rank histogram and attribute diagrams. Results showed that application of BMA improved the reliability of the raw ensemble. Using the weighted ensemble mean forecast as a deterministic forecast it was found that the deterministic-style BMA forecasts performed usually better than the best member's deterministic forecast.

Ensemble assimilation of ARGO temperature profile, sea surface temperature, and altimetric satellite data into an eddy permitting primitive equation model of the North Atlantic Ocean

NASA Astrophysics Data System (ADS)

Yan, Y.; Barth, A.; Beckers, J. M.; Candille, G.; Brankart, J. M.; Brasseur, P.

2015-07-01

Sea surface height, sea surface temperature, and temperature profiles at depth collected between January and December 2005 are assimilated into a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. Sixty ensemble members are generated by adding realistic noise to the forcing parameters related to the temperature. The ensemble is diagnosed and validated by comparison between the ensemble spread and the model/observation difference, as well as by rank histogram before the assimilation experiments. An incremental analysis update scheme is applied in order to reduce spurious oscillations due to the model state correction. The results of the assimilation are assessed according to both deterministic and probabilistic metrics with independent/semiindependent observations. For deterministic validation, the ensemble means, together with the ensemble spreads are compared to the observations, in order to diagnose the ensemble distribution properties in a deterministic way. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centered random variable (RCRV) score in order to investigate the reliability properties of the ensemble forecast system. The improvement of the assimilation is demonstrated using these validation metrics. Finally, the deterministic validation and the probabilistic validation are analyzed jointly. The consistency and complementarity between both validations are highlighted.

Study of a tri-trophic prey-dependent food chain model of interacting populations.

PubMed

Haque, Mainul; Ali, Nijamuddin; Chakravarty, Santabrata

2013-11-01

The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. Biologically feasible equilibria of the system are observed and the behaviours of the system around each of them are described. In particular, persistence, stability (local and global) and bifurcation (saddle-node, transcritical, Hopf-Andronov) analysis of this model are obtained. Relevant results from previous well known food chain models are compared with the current findings. Global stability analysis is also carried out by constructing appropriate Lyapunov functions. Numerical simulations show that the present system is capable enough to produce chaotic dynamics when the rate of self-interaction is very low. On the other hand such chaotic behaviour disappears for a certain value of the rate of self interaction. In addition, numerical simulations with experimented parameters values confirm the analytical results and shows that intra-specific competitions bears a potential role in controlling the chaotic dynamics of the system; and thus the role of self interactions in food chain model is illustrated first time. Finally, a discussion of the ecological applications of the analytical and numerical findings concludes the paper. Copyright © 2013 Elsevier Inc. All rights reserved.

Discrete epidemic models with arbitrary stage distributions and applications to disease control.

PubMed

Hernandez-Ceron, Nancy; Feng, Zhilan; Castillo-Chavez, Carlos

2013-10-01

W.O. Kermack and A.G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack–McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of epidemics, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures.

LASSIE: simulating large-scale models of biochemical systems on GPUs.

PubMed

Tangherloni, Andrea; Nobile, Marco S; Besozzi, Daniela; Mauri, Giancarlo; Cazzaniga, Paolo

2017-05-10

Mathematical modeling and in silico analysis are widely acknowledged as complementary tools to biological laboratory methods, to achieve a thorough understanding of emergent behaviors of cellular processes in both physiological and perturbed conditions. Though, the simulation of large-scale models-consisting in hundreds or thousands of reactions and molecular species-can rapidly overtake the capabilities of Central Processing Units (CPUs). The purpose of this work is to exploit alternative high-performance computing solutions, such as Graphics Processing Units (GPUs), to allow the investigation of these models at reduced computational costs. LASSIE is a "black-box" GPU-accelerated deterministic simulator, specifically designed for large-scale models and not requiring any expertise in mathematical modeling, simulation algorithms or GPU programming. Given a reaction-based model of a cellular process, LASSIE automatically generates the corresponding system of Ordinary Differential Equations (ODEs), assuming mass-action kinetics. The numerical solution of the ODEs is obtained by automatically switching between the Runge-Kutta-Fehlberg method in the absence of stiffness, and the Backward Differentiation Formulae of first order in presence of stiffness. The computational performance of LASSIE are assessed using a set of randomly generated synthetic reaction-based models of increasing size, ranging from 64 to 8192 reactions and species, and compared to a CPU-implementation of the LSODA numerical integration algorithm. LASSIE adopts a novel fine-grained parallelization strategy to distribute on the GPU cores all the calculations required to solve the system of ODEs. By virtue of this implementation, LASSIE achieves up to 92× speed-up with respect to LSODA, therefore reducing the running time from approximately 1 month down to 8 h to simulate models consisting in, for instance, four thousands of reactions and species. Notably, thanks to its smaller memory footprint, LASSIE is able to perform fast simulations of even larger models, whereby the tested CPU-implementation of LSODA failed to reach termination. LASSIE is therefore expected to make an important breakthrough in Systems Biology applications, for the execution of faster and in-depth computational analyses of large-scale models of complex biological systems.

A stochastic model for correlated protein motions

NASA Astrophysics Data System (ADS)

Karain, Wael I.; Qaraeen, Nael I.; Ajarmah, Basem

2006-06-01

A one-dimensional Langevin-type stochastic difference equation is used to find the deterministic and Gaussian contributions of time series representing the projections of a Bovine Pancreatic Trypsin Inhibitor (BPTI) protein molecular dynamics simulation along different eigenvector directions determined using principal component analysis. The deterministic part shows a distinct nonlinear behavior only for eigenvectors contributing significantly to the collective protein motion.

Probabilistic Finite Element Analysis & Design Optimization for Structural Designs

NASA Astrophysics Data System (ADS)

Deivanayagam, Arumugam

This study focuses on implementing probabilistic nature of material properties (Kevlar® 49) to the existing deterministic finite element analysis (FEA) of fabric based engine containment system through Monte Carlo simulations (MCS) and implementation of probabilistic analysis in engineering designs through Reliability Based Design Optimization (RBDO). First, the emphasis is on experimental data analysis focusing on probabilistic distribution models which characterize the randomness associated with the experimental data. The material properties of Kevlar® 49 are modeled using experimental data analysis and implemented along with an existing spiral modeling scheme (SMS) and user defined constitutive model (UMAT) for fabric based engine containment simulations in LS-DYNA. MCS of the model are performed to observe the failure pattern and exit velocities of the models. Then the solutions are compared with NASA experimental tests and deterministic results. MCS with probabilistic material data give a good prospective on results rather than a single deterministic simulation results. The next part of research is to implement the probabilistic material properties in engineering designs. The main aim of structural design is to obtain optimal solutions. In any case, in a deterministic optimization problem even though the structures are cost effective, it becomes highly unreliable if the uncertainty that may be associated with the system (material properties, loading etc.) is not represented or considered in the solution process. Reliable and optimal solution can be obtained by performing reliability optimization along with the deterministic optimization, which is RBDO. In RBDO problem formulation, in addition to structural performance constraints, reliability constraints are also considered. This part of research starts with introduction to reliability analysis such as first order reliability analysis, second order reliability analysis followed by simulation technique that are performed to obtain probability of failure and reliability of structures. Next, decoupled RBDO procedure is proposed with a new reliability analysis formulation with sensitivity analysis, which is performed to remove the highly reliable constraints in the RBDO, thereby reducing the computational time and function evaluations. Followed by implementation of the reliability analysis concepts and RBDO in finite element 2D truss problems and a planar beam problem are presented and discussed.

Global Sensitivity Analysis for Process Identification under Model Uncertainty

NASA Astrophysics Data System (ADS)

Ye, M.; Dai, H.; Walker, A. P.; Shi, L.; Yang, J.

2015-12-01

The environmental system consists of various physical, chemical, and biological processes, and environmental models are always built to simulate these processes and their interactions. For model building, improvement, and validation, it is necessary to identify important processes so that limited resources can be used to better characterize the processes. While global sensitivity analysis has been widely used to identify important processes, the process identification is always based on deterministic process conceptualization that uses a single model for representing a process. However, environmental systems are complex, and it happens often that a single process may be simulated by multiple alternative models. Ignoring the model uncertainty in process identification may lead to biased identification in that identified important processes may not be so in the real world. This study addresses this problem by developing a new method of global sensitivity analysis for process identification. The new method is based on the concept of Sobol sensitivity analysis and model averaging. Similar to the Sobol sensitivity analysis to identify important parameters, our new method evaluates variance change when a process is fixed at its different conceptualizations. The variance considers both parametric and model uncertainty using the method of model averaging. The method is demonstrated using a synthetic study of groundwater modeling that considers recharge process and parameterization process. Each process has two alternative models. Important processes of groundwater flow and transport are evaluated using our new method. The method is mathematically general, and can be applied to a wide range of environmental problems.

Cross-frequency and band-averaged response variance prediction in the hybrid deterministic-statistical energy analysis method

NASA Astrophysics Data System (ADS)

Reynders, Edwin P. B.; Langley, Robin S.

2018-08-01

The hybrid deterministic-statistical energy analysis method has proven to be a versatile framework for modeling built-up vibro-acoustic systems. The stiff system components are modeled deterministically, e.g., using the finite element method, while the wave fields in the flexible components are modeled as diffuse. In the present paper, the hybrid method is extended such that not only the ensemble mean and variance of the harmonic system response can be computed, but also of the band-averaged system response. This variance represents the uncertainty that is due to the assumption of a diffuse field in the flexible components of the hybrid system. The developments start with a cross-frequency generalization of the reciprocity relationship between the total energy in a diffuse field and the cross spectrum of the blocked reverberant loading at the boundaries of that field. By making extensive use of this generalization in a first-order perturbation analysis, explicit expressions are derived for the cross-frequency and band-averaged variance of the vibrational energies in the diffuse components and for the cross-frequency and band-averaged variance of the cross spectrum of the vibro-acoustic field response of the deterministic components. These expressions are extensively validated against detailed Monte Carlo analyses of coupled plate systems in which diffuse fields are simulated by randomly distributing small point masses across the flexible components, and good agreement is found.

Hybrid stochastic and deterministic simulations of calcium blips.

PubMed

Rüdiger, S; Shuai, J W; Huisinga, W; Nagaiah, C; Warnecke, G; Parker, I; Falcke, M

2007-09-15

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Stochastic Analysis and Probabilistic Downscaling of Soil Moisture

NASA Astrophysics Data System (ADS)

Deshon, J. P.; Niemann, J. D.; Green, T. R.; Jones, A. S.

2017-12-01

Soil moisture is a key variable for rainfall-runoff response estimation, ecological and biogeochemical flux estimation, and biodiversity characterization, each of which is useful for watershed condition assessment. These applications require not only accurate, fine-resolution soil-moisture estimates but also confidence limits on those estimates and soil-moisture patterns that exhibit realistic statistical properties (e.g., variance and spatial correlation structure). The Equilibrium Moisture from Topography, Vegetation, and Soil (EMT+VS) model downscales coarse-resolution (9-40 km) soil moisture from satellite remote sensing or land-surface models to produce fine-resolution (10-30 m) estimates. The model was designed to produce accurate deterministic soil-moisture estimates at multiple points, but the resulting patterns do not reproduce the variance or spatial correlation of observed soil-moisture patterns. The primary objective of this research is to generalize the EMT+VS model to produce a probability density function (pdf) for soil moisture at each fine-resolution location and time. Each pdf has a mean that is equal to the deterministic soil-moisture estimate, and the pdf can be used to quantify the uncertainty in the soil-moisture estimates and to simulate soil-moisture patterns. Different versions of the generalized model are hypothesized based on how uncertainty enters the model, whether the uncertainty is additive or multiplicative, and which distributions describe the uncertainty. These versions are then tested by application to four catchments with detailed soil-moisture observations (Tarrawarra, Satellite Station, Cache la Poudre, and Nerrigundah). The performance of the generalized models is evaluated by comparing the statistical properties of the simulated soil-moisture patterns to those of the observations and the deterministic EMT+VS model. The versions of the generalized EMT+VS model with normally distributed stochastic components produce soil-moisture patterns with more realistic statistical properties than the deterministic model. Additionally, the results suggest that the variance and spatial correlation of the stochastic soil-moisture variations do not vary consistently with the spatial-average soil moisture.

Probabilistic Scenario-based Seismic Risk Analysis for Critical Infrastructures Method and Application for a Nuclear Power Plant

NASA Astrophysics Data System (ADS)

Klügel, J.

2006-12-01

Deterministic scenario-based seismic hazard analysis has a long tradition in earthquake engineering for developing the design basis of critical infrastructures like dams, transport infrastructures, chemical plants and nuclear power plants. For many applications besides of the design of infrastructures it is of interest to assess the efficiency of the design measures taken. These applications require a method allowing to perform a meaningful quantitative risk analysis. A new method for a probabilistic scenario-based seismic risk analysis has been developed based on a probabilistic extension of proven deterministic methods like the MCE- methodology. The input data required for the method are entirely based on the information which is necessary to perform any meaningful seismic hazard analysis. The method is based on the probabilistic risk analysis approach common for applications in nuclear technology developed originally by Kaplan & Garrick (1981). It is based (1) on a classification of earthquake events into different size classes (by magnitude), (2) the evaluation of the frequency of occurrence of events, assigned to the different classes (frequency of initiating events, (3) the development of bounding critical scenarios assigned to each class based on the solution of an optimization problem and (4) in the evaluation of the conditional probability of exceedance of critical design parameters (vulnerability analysis). The advantage of the method in comparison with traditional PSHA consists in (1) its flexibility, allowing to use different probabilistic models for earthquake occurrence as well as to incorporate advanced physical models into the analysis, (2) in the mathematically consistent treatment of uncertainties, and (3) in the explicit consideration of the lifetime of the critical structure as a criterion to formulate different risk goals. The method was applied for the evaluation of the risk of production interruption losses of a nuclear power plant during its residual lifetime.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Multi-Scale Modeling of the Gamma Radiolysis of Nitrate Solutions.

PubMed

Horne, Gregory P; Donoclift, Thomas A; Sims, Howard E; Orr, Robin M; Pimblott, Simon M

2016-11-17

A multiscale modeling approach has been developed for the extended time scale long-term radiolysis of aqueous systems. The approach uses a combination of stochastic track structure and track chemistry as well as deterministic homogeneous chemistry techniques and involves four key stages: radiation track structure simulation, the subsequent physicochemical processes, nonhomogeneous diffusion-reaction kinetic evolution, and homogeneous bulk chemistry modeling. The first three components model the physical and chemical evolution of an isolated radiation chemical track and provide radiolysis yields, within the extremely low dose isolated track paradigm, as the input parameters for a bulk deterministic chemistry model. This approach to radiation chemical modeling has been tested by comparison with the experimentally observed yield of nitrite from the gamma radiolysis of sodium nitrate solutions. This is a complex radiation chemical system which is strongly dependent on secondary reaction processes. The concentration of nitrite is not just dependent upon the evolution of radiation track chemistry and the scavenging of the hydrated electron and its precursors but also on the subsequent reactions of the products of these scavenging reactions with other water radiolysis products. Without the inclusion of intratrack chemistry, the deterministic component of the multiscale model is unable to correctly predict experimental data, highlighting the importance of intratrack radiation chemistry in the chemical evolution of the irradiated system.

A deterministic width function model

NASA Astrophysics Data System (ADS)

Puente, C. E.; Sivakumar, B.

Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions.

Probabilistic Modeling of the Renal Stone Formation Module

NASA Technical Reports Server (NTRS)

Best, Lauren M.; Myers, Jerry G.; Goodenow, Debra A.; McRae, Michael P.; Jackson, Travis C.

2013-01-01

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

A van der Waals-like Transition Between Normal and Cancerous Phases in Cell Populations Dynamics of Colorectal Cancer

NASA Astrophysics Data System (ADS)

Qiu, Kang; Wang, Li-Fang; Shen, Jian; Yousif, Alssadig A. M.; He, Peng; Shao, Dan-Dan; Zhang, Xiao-Min; Kirunda, John B.; Jia, Ya

2016-11-01

Based on a deterministic continuous model of cell populations dynamics in the colonic crypt and in colorectal cancer, we propose four combinations of feedback mechanisms in the differentiations from stem cells (SCs) to transit cells (TCs) and then to differentiated cells (DCs), the four combinations include the double linear (LL), the linear and saturating (LS), the saturating and linear (SL), and the double saturating (SS) feedbacks, respectively. The relative fluctuations of the population of SCs, TCs, and DCs around equilibrium states with four feedback mechanisms are studied by using the Langevin method. With the increasing of net growth rate of TCs, it is found that the Fano factors of TCs and DCs go to a peak in a transient phase, and then increase again to infinity in the cases of LS and SS feedbacks. The “up-down-up” characteristic on the Fano factor (like the van der Waals loop) demonstrates that there exists a transient phase between the normal and cancerous phases, our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics of a normal and abnormal (cancerous) phases.

Expansion Under Climate Change: The Genetic Consequences.

PubMed

Garnier, Jimmy; Lewis, Mark A

2016-11-01

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

NASA Astrophysics Data System (ADS)

Eugène, Sarah; Xue, Wei-Feng; Robert, Philippe; Doumic, Marie

2016-05-01

Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation.

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

PubMed Central

2013-01-01

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

Modeling DNA methylation by analyzing the individual configurations of single molecules

PubMed Central

Affinito, Ornella; Scala, Giovanni; Palumbo, Domenico; Florio, Ermanno; Monticelli, Antonella; Miele, Gennaro; Avvedimento, Vittorio Enrico; Usiello, Alessandro; Chiariotti, Lorenzo; Cocozza, Sergio

2016-01-01

ABSTRACT DNA methylation is often analyzed by reporting the average methylation degree of each cytosine. In this study, we used a single molecule methylation analysis in order to look at the methylation conformation of individual molecules. Using D-aspartate oxidase as a model gene, we performed an in-depth methylation analysis through the developmental stages of 3 different mouse tissues (brain, lung, and gut), where this gene undergoes opposite methylation destiny. This approach allowed us to track both methylation and demethylation processes at high resolution. The complexity of these dynamics was markedly simplified by introducing the concept of methylation classes (MCs), defined as the number of methylated cytosines per molecule, irrespective of their position. The MC concept smooths the stochasticity of the system, allowing a more deterministic description. In this framework, we also propose a mathematical model based on the Markov chain. This model aims to identify the transition probability of a molecule from one MC to another during methylation and demethylation processes. The results of our model suggest that: 1) both processes are ruled by a dominant class of phenomena, namely, the gain or loss of one methyl group at a time; and 2) the probability of a single CpG site becoming methylated or demethylated depends on the methylation status of the whole molecule at that time. PMID:27748645

Nascent RNA kinetics: Transient and steady state behavior of models of transcription

NASA Astrophysics Data System (ADS)

Choubey, Sandeep

2018-02-01

Regulation of transcription is a vital process in cells, but mechanistic details of this regulation still remain elusive. The dominant approach to unravel the dynamics of transcriptional regulation is to first develop mathematical models of transcription and then experimentally test the predictions these models make for the distribution of mRNA and protein molecules at the individual cell level. However, these measurements are affected by a multitude of downstream processes which make it difficult to interpret the measurements. Recent experimental advancements allow for counting the nascent mRNA number of a gene as a function of time at the single-inglr cell level. These measurements closely reflect the dynamics of transcription. In this paper, we consider a general mechanism of transcription with stochastic initiation and deterministic elongation and probe its impact on the temporal behavior of nascent RNA levels. Using techniques from queueing theory, we derive exact analytical expressions for the mean and variance of the nascent RNA distribution as functions of time. We apply these analytical results to obtain the mean and variance of nascent RNA distribution for specific models of transcription. These models of initiation exhibit qualitatively distinct transient behaviors for both the mean and variance which further allows us to discriminate between them. Stochastic simulations confirm these results. Overall the analytical results presented here provide the necessary tools to connect mechanisms of transcription initiation to single-cell measurements of nascent RNA.

Spatial delineation, fluid-lithology characterization, and petrophysical modeling of deepwater Gulf of Mexico reservoirs though joint AVA deterministic and stochastic inversion of three-dimensional partially-stacked seismic amplitude data and well logs

NASA Astrophysics Data System (ADS)

Contreras, Arturo Javier

This dissertation describes a novel Amplitude-versus-Angle (AVA) inversion methodology to quantitatively integrate pre-stack seismic data, well logs, geologic data, and geostatistical information. Deterministic and stochastic inversion algorithms are used to characterize flow units of deepwater reservoirs located in the central Gulf of Mexico. A detailed fluid/lithology sensitivity analysis was conducted to assess the nature of AVA effects in the study area. Standard AVA analysis indicates that the shale/sand interface represented by the top of the hydrocarbon-bearing turbidite deposits generate typical Class III AVA responses. Layer-dependent Biot-Gassmann analysis shows significant sensitivity of the P-wave velocity and density to fluid substitution, indicating that presence of light saturating fluids clearly affects the elastic response of sands. Accordingly, AVA deterministic and stochastic inversions, which combine the advantages of AVA analysis with those of inversion, have provided quantitative information about the lateral continuity of the turbidite reservoirs based on the interpretation of inverted acoustic properties and fluid-sensitive modulus attributes (P-Impedance, S-Impedance, density, and LambdaRho, in the case of deterministic inversion; and P-velocity, S-velocity, density, and lithotype (sand-shale) distributions, in the case of stochastic inversion). The quantitative use of rock/fluid information through AVA seismic data, coupled with the implementation of co-simulation via lithotype-dependent multidimensional joint probability distributions of acoustic/petrophysical properties, provides accurate 3D models of petrophysical properties such as porosity, permeability, and water saturation. Pre-stack stochastic inversion provides more realistic and higher-resolution results than those obtained from analogous deterministic techniques. Furthermore, 3D petrophysical models can be more accurately co-simulated from AVA stochastic inversion results. By combining AVA sensitivity analysis techniques with pre-stack stochastic inversion, geologic data, and awareness of inversion pitfalls, it is possible to substantially reduce the risk in exploration and development of conventional and non-conventional reservoirs. From the final integration of deterministic and stochastic inversion results with depositional models and analogous examples, the M-series reservoirs have been interpreted as stacked terminal turbidite lobes within an overall fan complex (the Miocene MCAVLU Submarine Fan System); this interpretation is consistent with previous core data interpretations and regional stratigraphic/depositional studies.

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

A Comparison of Two Mathematical Modeling Frameworks for Evaluating Sexually Transmitted Infection Epidemiology.

PubMed

Johnson, Leigh F; Geffen, Nathan

2016-03-01

Different models of sexually transmitted infections (STIs) can yield substantially different conclusions about STI epidemiology, and it is important to understand how and why models differ. Frequency-dependent models make the simplifying assumption that STI incidence is proportional to STI prevalence in the population, whereas network models calculate STI incidence more realistically by classifying individuals according to their partners' STI status. We assessed a deterministic frequency-dependent model approximation to a microsimulation network model of STIs in South Africa. Sexual behavior and demographic parameters were identical in the 2 models. Six STIs were simulated using each model: HIV, herpes, syphilis, gonorrhea, chlamydia, and trichomoniasis. For all 6 STIs, the frequency-dependent model estimated a higher STI prevalence than the network model, with the difference between the 2 models being relatively large for the curable STIs. When the 2 models were fitted to the same STI prevalence data, the best-fitting parameters differed substantially between models, with the frequency-dependent model suggesting more immunity and lower transmission probabilities. The fitted frequency-dependent model estimated that the effects of a hypothetical elimination of concurrent partnerships and a reduction in commercial sex were both smaller than estimated by the fitted network model, whereas the latter model estimated a smaller impact of a reduction in unprotected sex in spousal relationships. The frequency-dependent assumption is problematic when modeling short-term STIs. Frequency-dependent models tend to underestimate the importance of high-risk groups in sustaining STI epidemics, while overestimating the importance of long-term partnerships and low-risk groups.

The Stochastic Multi-strain Dengue Model: Analysis of the Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Stollenwerk, Nico; Kooi, Bob W.

2011-09-01

Dengue dynamics is well known to be particularly complex with large fluctuations of disease incidences. An epidemic multi-strain model motivated by dengue fever epidemiology shows deterministic chaos in wide parameter regions. The addition of seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of infectious diseases epidemics show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. The addition of noise can explain the fluctuations observed in the empirical data and for large enough population size, the stochastic system can be well described by the deterministic skeleton.

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

NASA Technical Reports Server (NTRS)

Jones, Robert L.; Goode, Plesent W. (Technical Monitor)

2000-01-01

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Stochastic Models for Precipitable Water in Convection

NASA Astrophysics Data System (ADS)

Leung, Kimberly

Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test-of-concept for eventual inclusion in a general circulation model. The stochastic scheme was designed to be coupled with the deterministic single-column simulation by modifying results of the existing convective scheme (Zhang-McFarlane) and was able to produce a 20-second resolution time series that effectively simulated observed PWV, as measured by correlation coefficient (0.5510), fractal dimension (1.9), statistics, and visual examination of temporal trends. Results indicate that simulation of a highly volatile time series of observed PWV is certainly achievable and has potential to improve prediction capabilities in climate modeling. Further, this study demonstrates the feasibility of adding a mathematics- and statistics-based stochastic scheme to an existing deterministic parameterization to simulate observed fractal behavior.

Identification of gene regulation models from single-cell data

NASA Astrophysics Data System (ADS)

Weber, Lisa; Raymond, William; Munsky, Brian

2018-09-01

In quantitative analyses of biological processes, one may use many different scales of models (e.g. spatial or non-spatial, deterministic or stochastic, time-varying or at steady-state) or many different approaches to match models to experimental data (e.g. model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ MATLAB and PYTHON software to consider a time-dependent input signal (e.g. a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g. deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast (Neuert et al 2013 Science 339 584–7) and human cells (Senecal et al 2014 Cell Rep. 8 75–83)5.

Estimate Tsunami Flow Conditions and Large-Debris Tracks for the Design of Coastal Infrastructures along Coastlines of the U.S. Pacific Northwest

NASA Astrophysics Data System (ADS)

Wei, Y.; Thomas, S.; Zhou, H.; Arcas, D.; Titov, V. V.

2017-12-01

The increasing potential tsunami hazards pose great challenges for infrastructures along the coastlines of the U.S. Pacific Northwest. Tsunami impact at a coastal site is usually assessed from deterministic scenarios based on 10,000 years of geological records in the Cascadia Subduction Zone (CSZ). Aside from these deterministic methods, the new ASCE 7-16 tsunami provisions provide engineering design criteria of tsunami loads on buildings based on a probabilistic approach. This work develops a site-specific model near Newport, OR using high-resolution grids, and compute tsunami inundation depth and velocities at the study site resulted from credible probabilistic and deterministic earthquake sources in the Cascadia Subduction Zone. Three Cascadia scenarios, two deterministic scenarios, XXL1 and L1, and a 2,500-yr probabilistic scenario compliant with the new ASCE 7-16 standard, are simulated using combination of a depth-averaged shallow water model for offshore propagation and a Boussinesq-type model for onshore inundation. We speculate on the methods and procedure to obtain the 2,500-year probabilistic scenario for Newport that is compliant with the ASCE 7-16 tsunami provisions. We provide details of model results, particularly the inundation depth and flow speed for a new building, which will also be designated as a tsunami vertical evacuation shelter, at Newport, Oregon. We show that the ASCE 7-16 consistent hazards are between those obtained from deterministic L1 and XXL1 scenarios, and the greatest impact on the building may come from later waves. As a further step, we utilize the inundation model results to numerically compute tracks of large vessels in the vicinity of the building site and estimate if these vessels will impact on the building site during the extreme XXL1 and ASCE 7-16 hazard-consistent scenarios. Two-step study is carried out first to study tracks of massless particles and then large vessels with assigned mass considering drag force, inertial force, ship grounding and mooring. The simulation results show that none of the large vessels will impact on the building site in all tested scenarios.

Mathematical assessment of Canada's pandemic influenza preparedness plan.

PubMed

Gumel, Abba B; Nuño, Miriam; Chowell, Gerardo

2008-03-01

The presence of the highly pathogenic avian H5N1 virus in wild bird populations in several regions of the world, together with recurrent cases of H5N1 influenza arising primarily from direct contact with poultry, have highlighted the urgent need for prepared-ness and coordinated global strategies to effectively combat a potential influenza pandemic. The purpose of the present study was to evaluate the Canadian pandemic influenza preparedness plan. A mathematical model of the transmission dynamics of influenza was used to keep track of the population according to risk of infection (low or high) and infection status (susceptible, exposed or infectious). The model was parametrized using available Canadian demographic data. The model was then used to evaluate the key components outlined in the Canadian plan. The results indicated that the number of cases, mortalities and hospitalizations estimated in the Canadian plan may have been underestimated; the use of antivirals, administered therapeutically, prophylactically or both, is the most effective single intervention followed by the use of a vaccine and basic public health measures; and the combined use of pharmaceutical interventions (antivirals and vaccine) can dramatically minimize the burden of the pending influenza pandemic in Canada. Based on increasing concerns of Oseltamivir resistance (wide-scale implementation), coupled with the expected unavailability of a suitable vaccine during the early stages of a pandemic, the present study evaluated the potential impact of non-pharmaceutical interventions (NPIs) which were not emphasized in the current Canadian plan. To this end, the findings suggest that the use of NPIs can drastically reduce the burden of a pandemic in Canada. A deterministic model was designed and used to assess Canada's pandemic preparedness plan. The study showed that the estimates of pandemic influenza burden given in the Canada pandemic preparedness plan may be an underestimate, and that Canada needs to adopt NPIs to complement its preparedness plan.

The Stochastic Modelling of Endemic Diseases

NASA Astrophysics Data System (ADS)

Susvitasari, Kurnia; Siswantining, Titin

2017-01-01

A study about epidemic has been conducted since a long time ago, but genuine progress was hardly forthcoming until the end of the 19th century (Bailey, 1975). Both deterministic and stochastic models were used to describe these. Then, from 1927 to 1939 Kermack and McKendrick introduced a generality of this model, including some variables to consider such as rate of infection and recovery. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, R0. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when R0 ≤ 1, minor epidemic occurs with probability one in both approaches, but when R0 > 1, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when R0 > 1 and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic’s equilibrium.

Economic analysis of interventions to improve village chicken production in Myanmar.

PubMed

Henning, J; Morton, J; Pym, R; Hla, T; Sunn, K; Meers, J

2013-07-01

A cost-benefit analysis using deterministic and stochastic modelling was conducted to identify the net benefits for households that adopt (1) vaccination of individual birds against Newcastle disease (ND) or (2) improved management of chick rearing by providing coops for the protection of chicks from predation and chick starter feed inside a creep feeder to support chicks' nutrition in village chicken flocks in Myanmar. Partial budgeting was used to assess the additional costs and benefits associated with each of the two interventions tested relative to neither strategy. In the deterministic model, over the first 3 years after the introduction of the interventions, the cumulative sum of the net differences from neither strategy was 13,189Kyat for ND vaccination and 77,645Kyat for improved chick management (effective exchange rate in 2005: 1000Kyat=1$US). Both interventions were also profitable after discounting over a 10-year period; Net Present Values for ND vaccination and improved chick management were 30,791 and 167,825Kyat, respectively. The Benefit-Cost Ratio for ND vaccination was very high (28.8). This was lower for improved chick management, due to greater costs of the intervention, but still favourable at 4.7. Using both interventions concurrently yielded a Net Present Value of 470,543Kyat and a Benefit-Cost Ratio of 11.2 over the 10-year period in the deterministic model. Using the stochastic model, for the first 3 years following the introduction of the interventions, the mean cumulative sums of the net difference were similar to those values obtained from the deterministic model. Sensitivity analysis indicated that the cumulative net differences were strongly influenced by grower bird sale income, particularly under improved chick management. The effects of the strategies on odds of households selling and consuming birds after 7 months, and numbers of birds being sold or consumed after this period also influenced profitability. Cost variations for equipment used under improved chick management were not markedly associated with profitability. Net Present Values and Benefit-Cost Ratios discounted over a 10-year period were also similar to the deterministic model when mean values obtained through stochastic modelling were used. In summary, the study showed that ND vaccination and improved chick management can improve the viability and profitability of village chicken production in Myanmar. Copyright © 2013 Elsevier B.V. All rights reserved.

Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stein, Michael

Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead tomore » predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the Pacific Ocean, and annual temperature extremes at a site in New York City. In each of these applications, our theoretical and computational innovations were directly motivated by the challenges posed by analyzing these and similar types of data.« less

Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines

DOE PAGES

Finney, Charles E.; Kaul, Brian C.; Daw, C. Stuart; ...

2015-02-18

Here we review developments in the understanding of cycle to cycle variability in internal combustion engines, with a focus on spark-ignited and premixed combustion conditions. Much of the research on cyclic variability has focused on stochastic aspects, that is, features that can be modeled as inherently random with no short term predictability. In some cases, models of this type appear to work very well at describing experimental observations, but the lack of predictability limits control options. Also, even when the statistical properties of the stochastic variations are known, it can be very difficult to discern their underlying physical causes andmore » thus mitigate them. Some recent studies have demonstrated that under some conditions, cyclic combustion variations can have a relatively high degree of low dimensional deterministic structure, which implies some degree of predictability and potential for real time control. These deterministic effects are typically more pronounced near critical stability limits (e.g. near tipping points associated with ignition or flame propagation) such during highly dilute fueling or near the onset of homogeneous charge compression ignition. We review recent progress in experimental and analytical characterization of cyclic variability where low dimensional, deterministic effects have been observed. We describe some theories about the sources of these dynamical features and discuss prospects for interactive control and improved engine designs. In conclusion, taken as a whole, the research summarized here implies that the deterministic component of cyclic variability will become a pivotal issue (and potential opportunity) as engine manufacturers strive to meet aggressive emissions and fuel economy regulations in the coming decades.« less

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Panel summary report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutjahr, A.L.; Kincaid, C.T.; Mercer, J.W.

1987-04-01

The objective of this report is to summarize the various modeling approaches that were used to simulate solute transport in a variably saturated emission. In particular, the technical strengths and weaknesses of each approach are discussed, and conclusions and recommendations for future studies are made. Five models are considered: (1) one-dimensional analytical and semianalytical solutions of the classical deterministic convection-dispersion equation (van Genuchten, Parker, and Kool, this report ); (2) one-dimensional simulation using a continuous-time Markov process (Knighton and Wagenet, this report); (3) one-dimensional simulation using the time domain method and the frequency domain method (Duffy and Al-Hassan, this report);more » (4) one-dimensional numerical approach that combines a solution of the classical deterministic convection-dispersion equation with a chemical equilibrium speciation model (Cederberg, this report); and (5) three-dimensional numerical solution of the classical deterministic convection-dispersion equation (Huyakorn, Jones, Parker, Wadsworth, and White, this report). As part of the discussion, the input data and modeling results are summarized. The models were used in a data analysis mode, as opposed to a predictive mode. Thus, the following discussion will concentrate on the data analysis aspects of model use. Also, all the approaches were similar in that they were based on a convection-dispersion model of solute transport. Each discussion addresses the modeling approaches in the order listed above.« less

Signal dependence of inter-pixel capacitance in hybridized HgCdTe H2RG arrays for use in James Webb space telescope's NIRcam

NASA Astrophysics Data System (ADS)

Donlon, Kevan; Ninkov, Zoran; Baum, Stefi

2016-08-01

Interpixel capacitance (IPC) is a deterministic electronic coupling by which signal generated in one pixel is measured in neighboring pixels. Examination of dark frames from test NIRcam arrays corroborates earlier results and simulations illustrating a signal dependent coupling. When the signal on an individual pixel is larger, the fractional coupling to nearest neighbors is lesser than when the signal is lower. Frames from test arrays indicate a drop in average coupling from approximately 1.0% at low signals down to approximately 0.65% at high signals depending on the particular array in question. The photometric ramifications for this non-uniformity are not fully understood. This non-uniformity intro-duces a non-linearity in the current mathematical model for IPC coupling. IPC coupling has been mathematically formalized as convolution by a blur kernel. Signal dependence requires that the blur kernel be locally defined as a function of signal intensity. Through application of a signal dependent coupling kernel, the IPC coupling can be modeled computationally. This method allows for simultaneous knowledge of the intrinsic parameters of the image scene, the result of applying a constant IPC, and the result of a signal dependent IPC. In the age of sub-pixel precision in astronomy these effects must be properly understood and accounted for in order for the data to accurately represent the object of observation. Implementation of this method is done through python scripted processing of images. The introduction of IPC into simulated frames is accomplished through convolution of the image with a blur kernel whose parameters are themselves locally defined functions of the image. These techniques can be used to enhance the data processing pipeline for NIRcam.

Stochastic oscillations in models of epidemics on a network of cities

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.; McKane, A. J.

2011-11-01

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction fjk of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities

NASA Astrophysics Data System (ADS)

Kunjwal, Ravi; Spekkens, Robert W.

2018-05-01

The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental measurements because these are never free of noise and thus never truly projective. For nonprojective measurements, therefore, one must drop the requirement that an outcome be assigned deterministically in the model and merely require that it be assigned a distribution over outcomes in a manner that is context-independent. By demanding context independence in the representation of preparations as well, one obtains a generalized principle of noncontextuality that also supports a quantum no-go theorem. Several recent works have shown how to derive inequalities on experimental data which, if violated, demonstrate the impossibility of finding a generalized-noncontextual model of this data. That is, these inequalities do not presume quantum theory and, in particular, they make sense without requiring an operational analog of the quantum notion of projectiveness. We here describe a technique for deriving such inequalities starting from arbitrary proofs of the Kochen-Specker theorem. It extends significantly previous techniques that worked only for logical proofs, which are based on sets of projective measurements that fail to admit of any deterministic noncontextual assignment, to the case of statistical proofs, which are based on sets of projective measurements that d o admit of some deterministic noncontextual assignments, but not enough to explain the quantum statistics.

Convergence studies of deterministic methods for LWR explicit reflector methodology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canepa, S.; Hursin, M.; Ferroukhi, H.

2013-07-01

The standard approach in modem 3-D core simulators, employed either for steady-state or transient simulations, is to use Albedo coefficients or explicit reflectors at the core axial and radial boundaries. In the latter approach, few-group homogenized nuclear data are a priori produced with lattice transport codes using 2-D reflector models. Recently, the explicit reflector methodology of the deterministic CASMO-4/SIMULATE-3 code system was identified to potentially constitute one of the main sources of errors for core analyses of the Swiss operating LWRs, which are all belonging to GII design. Considering that some of the new GIII designs will rely on verymore » different reflector concepts, a review and assessment of the reflector methodology for various LWR designs appeared as relevant. Therefore, the purpose of this paper is to first recall the concepts of the explicit reflector modelling approach as employed by CASMO/SIMULATE. Then, for selected reflector configurations representative of both GII and GUI designs, a benchmarking of the few-group nuclear data produced with the deterministic lattice code CASMO-4 and its successor CASMO-5, is conducted. On this basis, a convergence study with regards to geometrical requirements when using deterministic methods with 2-D homogenous models is conducted and the effect on the downstream 3-D core analysis accuracy is evaluated for a typical GII deflector design in order to assess the results against available plant measurements. (authors)« less

A probabilistic approach to aircraft design emphasizing stability and control uncertainties

NASA Astrophysics Data System (ADS)

Delaurentis, Daniel Andrew

In order to address identified deficiencies in current approaches to aerospace systems design, a new method has been developed. This new method for design is based on the premise that design is a decision making activity, and that deterministic analysis and synthesis can lead to poor, or misguided decision making. This is due to a lack of disciplinary knowledge of sufficient fidelity about the product, to the presence of uncertainty at multiple levels of the aircraft design hierarchy, and to a failure to focus on overall affordability metrics as measures of goodness. Design solutions are desired which are robust to uncertainty and are based on the maximum knowledge possible. The new method represents advances in the two following general areas. 1. Design models and uncertainty. The research performed completes a transition from a deterministic design representation to a probabilistic one through a modeling of design uncertainty at multiple levels of the aircraft design hierarchy, including: (1) Consistent, traceable uncertainty classification and representation; (2) Concise mathematical statement of the Probabilistic Robust Design problem; (3) Variants of the Cumulative Distribution Functions (CDFs) as decision functions for Robust Design; (4) Probabilistic Sensitivities which identify the most influential sources of variability. 2. Multidisciplinary analysis and design. Imbedded in the probabilistic methodology is a new approach for multidisciplinary design analysis and optimization (MDA/O), employing disciplinary analysis approximations formed through statistical experimentation and regression. These approximation models are a function of design variables common to the system level as well as other disciplines. For aircraft, it is proposed that synthesis/sizing is the proper avenue for integrating multiple disciplines. Research hypotheses are translated into a structured method, which is subsequently tested for validity. Specifically, the implementation involves the study of the relaxed static stability technology for a supersonic commercial transport aircraft. The probabilistic robust design method is exercised resulting in a series of robust design solutions based on different interpretations of "robustness". Insightful results are obtained and the ability of the method to expose trends in the design space are noted as a key advantage.

Two-strain competition in quasineutral stochastic disease dynamics.

PubMed

Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R

2014-10-01

We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

Optimal design of piezoelectric transformers: a rational approach based on an analytical model and a deterministic global optimization.

PubMed

Pigache, Francois; Messine, Frédéric; Nogarede, Bertrand

2007-07-01

This paper deals with a deterministic and rational way to design piezoelectric transformers in radial mode. The proposed approach is based on the study of the inverse problem of design and on its reformulation as a mixed constrained global optimization problem. The methodology relies on the association of the analytical models for describing the corresponding optimization problem and on an exact global optimization software, named IBBA and developed by the second author to solve it. Numerical experiments are presented and compared in order to validate the proposed approach.

Rare event computation in deterministic chaotic systems using genealogical particle analysis

NASA Astrophysics Data System (ADS)

Wouters, J.; Bouchet, F.

2016-09-01

In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in deterministic dynamical systems. We demonstrate that genealogical particle analysis algorithms can be successfully applied to a toy model of atmospheric dynamics, the Lorenz ’96 model. We furthermore use the Ornstein-Uhlenbeck system to illustrate a number of implementation issues. We also show how a time-dependent objective function based on the fluctuation path to a high threshold can greatly improve the performance of the estimator compared to a fixed-in-time objective function.

Pyrotechnic modeling for the NSI and pin puller

NASA Technical Reports Server (NTRS)

Powers, Joseph M.; Gonthier, Keith A.

1993-01-01

A discussion concerning the modeling of pyrotechnically driven actuators is presented in viewgraph format. The following topics are discussed: literature search, constitutive data for full-scale model, simple deterministic model, observed phenomena, and results from simple model.

MONALISA for stochastic simulations of Petri net models of biochemical systems.

PubMed

Balazki, Pavel; Lindauer, Klaus; Einloft, Jens; Ackermann, Jörg; Koch, Ina

2015-07-10

The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0.

Deterministic multi-zone ice accretion modeling

NASA Technical Reports Server (NTRS)

Yamaguchi, K.; Hansman, R. John, Jr.; Kazmierczak, Michael

1991-01-01

The focus here is on a deterministic model of the surface roughness transition behavior of glaze ice. The initial smooth/rough transition location, bead formation, and the propagation of the transition location are analyzed. Based on the hypothesis that the smooth/rough transition location coincides with the laminar/turbulent boundary layer transition location, a multizone model is implemented in the LEWICE code. In order to verify the effectiveness of the model, ice accretion predictions for simple cylinders calculated by the multizone LEWICE are compared to experimental ice shapes. The glaze ice shapes are found to be sensitive to the laminar surface roughness and bead thickness parameters controlling the transition location, while the ice shapes are found to be insensitive to the turbulent surface roughness.

Combining deterministic and stochastic velocity fields in the analysis of deep crustal seismic data

NASA Astrophysics Data System (ADS)

Larkin, Steven Paul

Standard crustal seismic modeling obtains deterministic velocity models which ignore the effects of wavelength-scale heterogeneity, known to exist within the Earth's crust. Stochastic velocity models are a means to include wavelength-scale heterogeneity in the modeling. These models are defined by statistical parameters obtained from geologic maps of exposed crystalline rock, and are thus tied to actual geologic structures. Combining both deterministic and stochastic velocity models into a single model allows a realistic full wavefield (2-D) to be computed. By comparing these simulations to recorded seismic data, the effects of wavelength-scale heterogeneity can be investigated. Combined deterministic and stochastic velocity models are created for two datasets, the 1992 RISC seismic experiment in southeastern California and the 1986 PASSCAL seismic experiment in northern Nevada. The RISC experiment was located in the transition zone between the Salton Trough and the southern Basin and Range province. A high-velocity body previously identified beneath the Salton Trough is constrained to pinch out beneath the Chocolate Mountains to the northeast. The lateral extent of this body is evidence for the ephemeral nature of rifting loci as a continent is initially rifted. Stochastic modeling of wavelength-scale structures above this body indicate that little more than 5% mafic intrusion into a more felsic continental crust is responsible for the observed reflectivity. Modeling of the wide-angle RISC data indicates that coda waves following PmP are initially dominated by diffusion of energy out of the near-surface basin as the wavefield reverberates within this low-velocity layer. At later times, this coda consists of scattered body waves and P to S conversions. Surface waves do not play a significant role in this coda. Modeling of the PASSCAL dataset indicates that a high-gradient crust-mantle transition zone or a rough Moho interface is necessary to reduce precritical PmP energy. Possibly related, inconsistencies in published velocity models are rectified by hypothesizing the existence of large, elongate, high-velocity bodies at the base of the crust oriented to and of similar scale as the basins and ranges at the surface. This structure would result in an anisotropic lower crust.

Forecasting risk along a river basin using a probabilistic and deterministic model for environmental risk assessment of effluents through ecotoxicological evaluation and GIS.

PubMed

Gutiérrez, Simón; Fernandez, Carlos; Barata, Carlos; Tarazona, José Vicente

2009-12-20

This work presents a computer model for Risk Assessment of Basins by Ecotoxicological Evaluation (RABETOX). The model is based on whole effluent toxicity testing and water flows along a specific river basin. It is capable of estimating the risk along a river segment using deterministic and probabilistic approaches. The Henares River Basin was selected as a case study to demonstrate the importance of seasonal hydrological variations in Mediterranean regions. As model inputs, two different ecotoxicity tests (the miniaturized Daphnia magna acute test and the D.magna feeding test) were performed on grab samples from 5 waste water treatment plant effluents. Also used as model inputs were flow data from the past 25 years, water velocity measurements and precise distance measurements using Geographical Information Systems (GIS). The model was implemented into a spreadsheet and the results were interpreted and represented using GIS in order to facilitate risk communication. To better understand the bioassays results, the effluents were screened through SPME-GC/MS analysis. The deterministic model, performed each month during one calendar year, showed a significant seasonal variation of risk while revealing that September represents the worst-case scenario with values up to 950 Risk Units. This classifies the entire area of study for the month of September as "sublethal significant risk for standard species". The probabilistic approach using Monte Carlo analysis was performed on 7 different forecast points distributed along the Henares River. A 0% probability of finding "low risk" was found at all forecast points with a more than 50% probability of finding "potential risk for sensitive species". The values obtained through both the deterministic and probabilistic approximations reveal the presence of certain substances, which might be causing sublethal effects in the aquatic species present in the Henares River.

Coupled CFD-PBE Predictions of Renal Stone Size Distributions in the Nephron in Microgravity

NASA Technical Reports Server (NTRS)

Kassemi, Mohammad; Griffin, Elise; Thompson, David

2016-01-01

In this paper, a deterministic model is developed to assess the risk of critical renal stone formation for astronauts during space travel. A Population Balance Equation (PBE) model is used to compute the size distribution of a population of nucleating, growing and agglomerating renal calculi as they are transported through different sections of the nephron. The PBE model is coupled to a Computational Fluid Dynamics (CFD) model that solves for steady state flow of urine and transport of renal calculi along with the concentrations of ionic species, calcium and oxalate, in the nephron using an Eulerian two-phase mathematical framework. Parametric simulation are performed to study stone size enhancement and steady state volume fraction distributions in the four main sections of the nephron under weightlessness conditions. Contribution of agglomeration to the stone size distribution and effect of wall friction on the stone volume fraction distributions are carefully examined. Case studies using measured astronaut urinary calcium and oxalate concentrations in microgravity as input indicate that under nominal conditions the largest stone sizes developed in Space will be still considerably below the critical range for problematic stone development. However, results also indicate that the highest stone volume fraction occurs next to the tubule and duct walls. This suggests that there is an increased potential for wall adhesion with the possibility of evolution towards critical stone sizes.

A predictive computational model of the kinetic mechanism of stimulus-induced transducer methylation and feedback regulation through CheY in archaeal phototaxis and chemotaxis.

PubMed

Streif, Stefan; Oesterhelt, Dieter; Marwan, Wolfgang

2010-03-18

Photo- and chemotaxis of the archaeon Halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system. Certain members of the transducer family function as receptor proteins by directly sensing specific chemical or physical stimuli. Others interact with specific receptor proteins like the phototaxis photoreceptors sensory rhodopsin I and II, or require specific binding proteins as for example some chemotaxis transducers. Receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. Both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator CheY. By mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. The model (deterministic and in the form of ordinary differential equations) correctly predicts experimentally observed transducer demethylation (as detected by released methanol) in response to attractant and repellent stimuli of wildtype cells, a cheY deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient. We provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon H. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a CheY-dependent feedback on transducer demethylation.

Analyzing transmission dynamics of cholera with public health interventions.

PubMed

Posny, Drew; Wang, Jin; Mukandavire, Zindoga; Modnak, Chairat

2015-06-01

Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. These outbreaks have increased in frequency, severity, duration and endemicity in recent years. Mathematical models for infectious diseases play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. In this paper, we present a new deterministic cholera epidemiological model with three types of control measures incorporated into a cholera epidemic setting: treatment, vaccination and sanitation. Essential dynamical properties of the model with constant intervention controls which include local and global stabilities for the equilibria are carefully analyzed. Further, using optimal control techniques, we perform a study to investigate cost-effective solutions for time-dependent public health interventions in order to curb disease transmission in epidemic settings. Our results show that the basic reproductive number (R0) remains the model's epidemic threshold despite the inclusion of a package of cholera interventions. For time-dependent controls, the results suggest that these interventions closely interplay with each other, and the costs of controls directly affect the length and strength of each control in an optimal strategy. Copyright © 2015 Elsevier Inc. All rights reserved.

Developing a stochastic conflict resolution model for urban runoff quality management: Application of info-gap and bargaining theories

NASA Astrophysics Data System (ADS)

Ghodsi, Seyed Hamed; Kerachian, Reza; Estalaki, Siamak Malakpour; Nikoo, Mohammad Reza; Zahmatkesh, Zahra

2016-02-01

In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.

Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

NASA Technical Reports Server (NTRS)

Busby, Judy; Sondak, Doug; Staubach, Brent; Davis, Roger

1998-01-01

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.

Positive dwell time algorithm with minimum equal extra material removal in deterministic optical surfacing technology.

PubMed

Li, Longxiang; Xue, Donglin; Deng, Weijie; Wang, Xu; Bai, Yang; Zhang, Feng; Zhang, Xuejun

2017-11-10

In deterministic computer-controlled optical surfacing, accurate dwell time execution by computer numeric control machines is crucial in guaranteeing a high-convergence ratio for the optical surface error. It is necessary to consider the machine dynamics limitations in the numerical dwell time algorithms. In this paper, these constraints on dwell time distribution are analyzed, and a model of the equal extra material removal is established. A positive dwell time algorithm with minimum equal extra material removal is developed. Results of simulations based on deterministic magnetorheological finishing demonstrate the necessity of considering machine dynamics performance and illustrate the validity of the proposed algorithm. Indeed, the algorithm effectively facilitates the determinacy of sub-aperture optical surfacing processes.

Flow injection analysis simulations and diffusion coefficient determination by stochastic and deterministic optimization methods.

PubMed

Kucza, Witold

2013-07-25

Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg-Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches. Copyright © 2013 The Author. Published by Elsevier B.V. All rights reserved.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

Sampled-Data Consensus of Linear Multi-agent Systems With Packet Losses.

PubMed

Zhang, Wenbing; Tang, Yang; Huang, Tingwen; Kurths, Jurgen

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

Integrating Kinetic Model of E. coli with Genome Scale Metabolic Fluxes Overcomes Its Open System Problem and Reveals Bistability in Central Metabolism

PubMed Central

Mannan, Ahmad A.; Toya, Yoshihiro; Shimizu, Kazuyuki; McFadden, Johnjoe; Kierzek, Andrzej M.; Rocco, Andrea

2015-01-01

An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi-‘omics’ steady state data and a genome-scale metabolic network model. We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population. PMID:26469081

Interactive Reliability Model for Whisker-toughened Ceramics

NASA Technical Reports Server (NTRS)

Palko, Joseph L.

1993-01-01

Wider use of ceramic matrix composites (CMC) will require the development of advanced structural analysis technologies. The use of an interactive model to predict the time-independent reliability of a component subjected to multiaxial loads is discussed. The deterministic, three-parameter Willam-Warnke failure criterion serves as the theoretical basis for the reliability model. The strength parameters defining the model are assumed to be random variables, thereby transforming the deterministic failure criterion into a probabilistic criterion. The ability of the model to account for multiaxial stress states with the same unified theory is an improvement over existing models. The new model was coupled with a public-domain finite element program through an integrated design program. This allows a design engineer to predict the probability of failure of a component. A simple structural problem is analyzed using the new model, and the results are compared to existing models.

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

Distinct Sources of Deterministic and Stochastic Components of Action Timing Decisions in Rodent Frontal Cortex.

PubMed

Murakami, Masayoshi; Shteingart, Hanan; Loewenstein, Yonatan; Mainen, Zachary F

2017-05-17

The selection and timing of actions are subject to determinate influences such as sensory cues and internal state as well as to effectively stochastic variability. Although stochastic choice mechanisms are assumed by many theoretical models, their origin and mechanisms remain poorly understood. Here we investigated this issue by studying how neural circuits in the frontal cortex determine action timing in rats performing a waiting task. Electrophysiological recordings from two regions necessary for this behavior, medial prefrontal cortex (mPFC) and secondary motor cortex (M2), revealed an unexpected functional dissociation. Both areas encoded deterministic biases in action timing, but only M2 neurons reflected stochastic trial-by-trial fluctuations. This differential coding was reflected in distinct timescales of neural dynamics in the two frontal cortical areas. These results suggest a two-stage model in which stochastic components of action timing decisions are injected by circuits downstream of those carrying deterministic bias signals. Copyright © 2017 Elsevier Inc. All rights reserved.

Probability and Locality: Determinism Versus Indeterminism in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Dickson, William Michael

1995-01-01

Quantum mechanics is often taken to be necessarily probabilistic. However, this view of quantum mechanics appears to be more the result of historical accident than of careful analysis. Moreover, quantum mechanics in its usual form faces serious problems. Although the mathematical core of quantum mechanics--quantum probability theory- -does not face conceptual difficulties, the application of quantum probability to the physical world leads to problems. In particular, quantum mechanics seems incapable of describing our everyday macroscopic experience. Therefore, several authors have proposed new interpretations --including (but not limited to) modal interpretations, spontaneous localization interpretations, the consistent histories approach, and the Bohm theory--each of which deals with quantum-mechanical probabilities differently. Each of these interpretations promises to describe our macroscopic experience and, arguably, each succeeds. Is there any way to compare them? Perhaps, if we turn to another troubling aspect of quantum mechanics, non-locality. Non -locality is troubling because prima facie it threatens the compatibility of quantum mechanics with special relativity. This prima facie threat is mitigated by the no-signalling theorems in quantum mechanics, but nonetheless one may find a 'conflict of spirit' between nonlocality in quantum mechanics and special relativity. Do any of these interpretations resolve this conflict of spirit?. There is a strong relation between how an interpretation deals with quantum-mechanical probabilities and how it deals with non-locality. The main argument here is that only a completely deterministic interpretation can be completely local. That is, locality together with the empirical predictions of quantum mechanics (specifically, its strict correlations) entails determinism. But even with this entailment in hand, comparison of the various interpretations requires a look at each, to see how non-locality arises, or in the case of deterministic interpretations, whether it arises. The result of this investigation is that, at the least, deterministic interpretations are no worse off with respect to special relativity than indeterministic interpretations. This conclusion runs against a common view that deterministic interpretations, specifically the Bohm theory, have more difficulty with special relativity than other interpretations.

Developing deterioration models for Wyoming bridges.

DOT National Transportation Integrated Search

2016-05-01

Deterioration models for the Wyoming Bridge Inventory were developed using both stochastic and deterministic models. : The selection of explanatory variables is investigated and a new method using LASSO regression to eliminate human bias : in explana...

Review Article: Advances in modeling of bed particle entrainment sheared by turbulent flow

NASA Astrophysics Data System (ADS)

Dey, Subhasish; Ali, Sk Zeeshan

2018-06-01

Bed particle entrainment by turbulent wall-shear flow is a key topic of interest in hydrodynamics because it plays a major role to govern the planetary morphodynamics. In this paper, the state-of-the-art review of the essential mechanisms governing the bed particle entrainment by turbulent wall-shear flow and their mathematical modeling is presented. The paper starts with the appraisal of the earlier multifaceted ideas in modeling the particle entrainment highlighting the rolling, sliding, and lifting modes of entrainment. Then, various modeling approaches of bed particle entrainment, such as deterministic, stochastic, and spatiotemporal approaches, are critically analyzed. The modeling criteria of particle entrainment are distinguished for hydraulically smooth, transitional, and rough flow regimes. In this context, the responses of particle size, particle exposure, and packing condition to the near-bed turbulent flow that shears the particles to entrain are discussed. From the modern experimental outcomes, the conceptual mechanism of particle entrainment from the viewpoint of near-bed turbulent coherent structures is delineated. As the latest advancement of the subject, the paper sheds light on the origin of the primitive empirical formulations of bed particle entrainment deriving the scaling laws of threshold flow velocity of bed particle motion from the perspective of the phenomenological theory of turbulence. Besides, a model framework that provides a new look on the bed particle entrainment phenomenon stemming from the stochastic-cum-spatiotemporal approach is introduced. Finally, the future scope of research is articulated with open questions.

Short-range solar radiation forecasts over Sweden

NASA Astrophysics Data System (ADS)

Landelius, Tomas; Lindskog, Magnus; Körnich, Heiner; Andersson, Sandra

2018-04-01

In this article the performance for short-range solar radiation forecasts by the global deterministic and ensemble models from the European Centre for Medium-Range Weather Forecasts (ECMWF) is compared with an ensemble of the regional mesoscale model HARMONIE-AROME used by the national meteorological services in Sweden, Norway and Finland. Note however that only the control members and the ensemble means are included in the comparison. The models resolution differs considerably with 18 km for the ECMWF ensemble, 9 km for the ECMWF deterministic model, and 2.5 km for the HARMONIE-AROME ensemble. The models share the same radiation code. It turns out that they all underestimate systematically the Direct Normal Irradiance (DNI) for clear-sky conditions. Except for this shortcoming, the HARMONIE-AROME ensemble model shows the best agreement with the distribution of observed Global Horizontal Irradiance (GHI) and DNI values. During mid-day the HARMONIE-AROME ensemble mean performs best. The control member of the HARMONIE-AROME ensemble also scores better than the global deterministic ECMWF model. This is an interesting result since mesoscale models have so far not shown good results when compared to the ECMWF models. Three days with clear, mixed and cloudy skies are used to illustrate the possible added value of a probabilistic forecast. It is shown that in these cases the mesoscale ensemble could provide decision support to a grid operator in terms of forecasts of both the amount of solar power and its probabilities.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

PubMed

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

2016-08-25

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

Fitting-free algorithm for efficient quantification of collagen fiber alignment in SHG imaging applications.

PubMed

Hall, Gunnsteinn; Liang, Wenxuan; Li, Xingde

2017-10-01

Collagen fiber alignment derived from second harmonic generation (SHG) microscopy images can be important for disease diagnostics. Image processing algorithms are needed to robustly quantify the alignment in images with high sensitivity and reliability. Fourier transform (FT) magnitude, 2D power spectrum, and image autocorrelation have previously been used to extract fiber information from images by assuming a certain mathematical model (e.g. Gaussian distribution of the fiber-related parameters) and fitting. The fitting process is slow and fails to converge when the data is not Gaussian. Herein we present an efficient constant-time deterministic algorithm which characterizes the symmetricity of the FT magnitude image in terms of a single parameter, named the fiber alignment anisotropy R ranging from 0 (randomized fibers) to 1 (perfect alignment). This represents an important improvement of the technology and may bring us one step closer to utilizing the technology for various applications in real time. In addition, we present a digital image phantom-based framework for characterizing and validating the algorithm, as well as assessing the robustness of the algorithm against different perturbations.

Multi-point objective-oriented sequential sampling strategy for constrained robust design

NASA Astrophysics Data System (ADS)

Zhu, Ping; Zhang, Siliang; Chen, Wei

2015-03-01

Metamodelling techniques are widely used to approximate system responses of expensive simulation models. In association with the use of metamodels, objective-oriented sequential sampling methods have been demonstrated to be effective in balancing the need for searching an optimal solution versus reducing the metamodelling uncertainty. However, existing infilling criteria are developed for deterministic problems and restricted to one sampling point in one iteration. To exploit the use of multiple samples and identify the true robust solution in fewer iterations, a multi-point objective-oriented sequential sampling strategy is proposed for constrained robust design problems. In this article, earlier development of objective-oriented sequential sampling strategy for unconstrained robust design is first extended to constrained problems. Next, a double-loop multi-point sequential sampling strategy is developed. The proposed methods are validated using two mathematical examples followed by a highly nonlinear automotive crashworthiness design example. The results show that the proposed method can mitigate the effect of both metamodelling uncertainty and design uncertainty, and identify the robust design solution more efficiently than the single-point sequential sampling approach.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which verticesmore » (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.« less

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

PubMed Central

Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

2016-01-01

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

Counting and classifying attractors in high dimensional dynamical systems.

PubMed

Bagley, R J; Glass, L

1996-12-07

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

Using heuristic algorithms for capacity leasing and task allocation issues in telecommunication networks under fuzzy quality of service constraints

NASA Astrophysics Data System (ADS)

Huseyin Turan, Hasan; Kasap, Nihat; Savran, Huseyin

2014-03-01

Nowadays, every firm uses telecommunication networks in different amounts and ways in order to complete their daily operations. In this article, we investigate an optimisation problem that a firm faces when acquiring network capacity from a market in which there exist several network providers offering different pricing and quality of service (QoS) schemes. The QoS level guaranteed by network providers and the minimum quality level of service, which is needed for accomplishing the operations are denoted as fuzzy numbers in order to handle the non-deterministic nature of the telecommunication network environment. Interestingly, the mathematical formulation of the aforementioned problem leads to the special case of a well-known two-dimensional bin packing problem, which is famous for its computational complexity. We propose two different heuristic solution procedures that have the capability of solving the resulting nonlinear mixed integer programming model with fuzzy constraints. In conclusion, the efficiency of each algorithm is tested in several test instances to demonstrate the applicability of the methodology.

Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

NASA Astrophysics Data System (ADS)

Wiebenga, J. H.; Klaseboer, G.; van den Boogaard, A. H.

2011-08-01

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (>2σ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure.

On consciousness, resting state fMRI, and neurodynamics

PubMed Central

2010-01-01

Background During the last years, functional magnetic resonance imaging (fMRI) of the brain has been introduced as a new tool to measure consciousness, both in a clinical setting and in a basic neurocognitive research. Moreover, advanced mathematical methods and theories have arrived the field of fMRI (e.g. computational neuroimaging), and functional and structural brain connectivity can now be assessed non-invasively. Results The present work deals with a pluralistic approach to "consciousness'', where we connect theory and tools from three quite different disciplines: (1) philosophy of mind (emergentism and global workspace theory), (2) functional neuroimaging acquisitions, and (3) theory of deterministic and statistical neurodynamics – in particular the Wilson-Cowan model and stochastic resonance. Conclusions Based on recent experimental and theoretical work, we believe that the study of large-scale neuronal processes (activity fluctuations, state transitions) that goes on in the living human brain while examined with functional MRI during "resting state", can deepen our understanding of graded consciousness in a clinical setting, and clarify the concept of "consiousness" in neurocognitive and neurophilosophy research. PMID:20522270

Rescriptive and Descriptive Gauge Symmetry in Finite-Dimensional Dynamical Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurfil, Pini

2007-02-07

Gauge theories in physics constitute a fundamental tool for modeling interactions among electromagnetic, weak and strong forces. They have been used in a myriad of fields, ranging from sub-atomic physics to cosmology. The basic mathematical tool generating the gauge theories is that of symmetry, i.e. a redundancy in the description of the system. Although symmetries have long been recognized as a fundamental tool for solving ordinary differential equations, they have not been formally categorized as gauge theories. In this paper, we show how simple systems described by ordinary differential equations are prone to exhibit gauge symmetry, and discuss a fewmore » practical applications of this approach. In particular, we utilize the notion of gauge symmetry to question some common engineering misconceptions of chaotic and stochastic phenomena, and show that seemingly 'disordered' (deterministic) or 'random' (stochastic) behaviors can be 'ordered'. This brings into play the notion of observation; we show that temporal observations may be misleading when used for chaos detection. From a practical standpoint, we use gauge symmetry to considerably mitigate the numerical truncation error of numerical integrations.« less

Using sequential self-calibration method to identify conductivity distribution: Conditioning on tracer test data

USGS Publications Warehouse

Hu, B.X.; He, C.

2008-01-01

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases. ?? International Association for Mathematical Geology 2008.

Ensemble assimilation of ARGO temperature profile, sea surface temperature and Altimetric satellite data into an eddy permitting primitive equation model of the North Atlantic ocean

NASA Astrophysics Data System (ADS)

Yan, Yajing; Barth, Alexander; Beckers, Jean-Marie; Candille, Guillem; Brankart, Jean-Michel; Brasseur, Pierre

2015-04-01

Sea surface height, sea surface temperature and temperature profiles at depth collected between January and December 2005 are assimilated into a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. 60 ensemble members are generated by adding realistic noise to the forcing parameters related to the temperature. The ensemble is diagnosed and validated by comparison between the ensemble spread and the model/observation difference, as well as by rank histogram before the assimilation experiments. Incremental analysis update scheme is applied in order to reduce spurious oscillations due to the model state correction. The results of the assimilation are assessed according to both deterministic and probabilistic metrics with observations used in the assimilation experiments and independent observations, which goes further than most previous studies and constitutes one of the original points of this paper. Regarding the deterministic validation, the ensemble means, together with the ensemble spreads are compared to the observations in order to diagnose the ensemble distribution properties in a deterministic way. Regarding the probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centred random variable (RCRV) score in order to investigate the reliability properties of the ensemble forecast system. The improvement of the assimilation is demonstrated using these validation metrics. Finally, the deterministic validation and the probabilistic validation are analysed jointly. The consistency and complementarity between both validations are highlighted. High reliable situations, in which the RMS error and the CRPS give the same information, are identified for the first time in this paper.

Comparison of numerical weather prediction based deterministic and probabilistic wind resource assessment methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jie; Draxl, Caroline; Hopson, Thomas

Numerical weather prediction (NWP) models have been widely used for wind resource assessment. Model runs with higher spatial resolution are generally more accurate, yet extremely computational expensive. An alternative approach is to use data generated by a low resolution NWP model, in conjunction with statistical methods. In order to analyze the accuracy and computational efficiency of different types of NWP-based wind resource assessment methods, this paper performs a comparison of three deterministic and probabilistic NWP-based wind resource assessment methodologies: (i) a coarse resolution (0.5 degrees x 0.67 degrees) global reanalysis data set, the Modern-Era Retrospective Analysis for Research and Applicationsmore » (MERRA); (ii) an analog ensemble methodology based on the MERRA, which provides both deterministic and probabilistic predictions; and (iii) a fine resolution (2-km) NWP data set, the Wind Integration National Dataset (WIND) Toolkit, based on the Weather Research and Forecasting model. Results show that: (i) as expected, the analog ensemble and WIND Toolkit perform significantly better than MERRA confirming their ability to downscale coarse estimates; (ii) the analog ensemble provides the best estimate of the multi-year wind distribution at seven of the nine sites, while the WIND Toolkit is the best at one site; (iii) the WIND Toolkit is more accurate in estimating the distribution of hourly wind speed differences, which characterizes the wind variability, at five of the available sites, with the analog ensemble being best at the remaining four locations; and (iv) the analog ensemble computational cost is negligible, whereas the WIND Toolkit requires large computational resources. Future efforts could focus on the combination of the analog ensemble with intermediate resolution (e.g., 10-15 km) NWP estimates, to considerably reduce the computational burden, while providing accurate deterministic estimates and reliable probabilistic assessments.« less

Analytical results for the statistical distribution related to a memoryless deterministic walk: dimensionality effect and mean-field models.

PubMed

Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto

2005-08-01

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial nonperiodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parametrized by the normalized incomplete beta function Id= I1/4 [1/2, (d+1) /2] . The joint distribution S(N) (mu,d) (t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is Sinfinity(1,d) (t,p) = [Gamma (1+ I(-1)(d)) (t+ I(-1)(d) ) /Gamma(t+p+ I(-1)(d)) ] delta(p,2), where t=0, 1,2, ... infinity, Gamma(z) is the gamma function and delta(i,j) is the Kronecker delta. The mean-field models are the random link models, which correspond to d-->infinity, and the random map model which, even for mu=0 , presents nontrivial cycle distribution [ S(N)(0,rm) (p) proportional to p(-1) ] : S(N)(0,rm) (t,p) =Gamma(N)/ {Gamma[N+1- (t+p) ] N( t+p)}. The fundamental quantities are the number of explored points n(e)=t+p and Id. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

Modelling ecosystem service flows under uncertainty with stochiastic SPAN

USGS Publications Warehouse

Johnson, Gary W.; Snapp, Robert R.; Villa, Ferdinando; Bagstad, Kenneth J.

2012-01-01

Ecosystem service models are increasingly in demand for decision making. However, the data required to run these models are often patchy, missing, outdated, or untrustworthy. Further, communication of data and model uncertainty to decision makers is often either absent or unintuitive. In this work, we introduce a systematic approach to addressing both the data gap and the difficulty in communicating uncertainty through a stochastic adaptation of the Service Path Attribution Networks (SPAN) framework. The SPAN formalism assesses ecosystem services through a set of up to 16 maps, which characterize the services in a study area in terms of flow pathways between ecosystems and human beneficiaries. Although the SPAN algorithms were originally defined deterministically, we present them here in a stochastic framework which combines probabilistic input data with a stochastic transport model in order to generate probabilistic spatial outputs. This enables a novel feature among ecosystem service models: the ability to spatially visualize uncertainty in the model results. The stochastic SPAN model can analyze areas where data limitations are prohibitive for deterministic models. Greater uncertainty in the model inputs (including missing data) should lead to greater uncertainty expressed in the model’s output distributions. By using Bayesian belief networks to fill data gaps and expert-provided trust assignments to augment untrustworthy or outdated information, we can account for uncertainty in input data, producing a model that is still able to run and provide information where strictly deterministic models could not. Taken together, these attributes enable more robust and intuitive modelling of ecosystem services under uncertainty.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Influence of changes in initial conditions for the simulation of dynamic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotyrba, Martin

2015-03-10

Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, sociology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a paradigm popularly referred to as the butterfly effect. Small differences in initial conditions field widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In this paperinfluence of changes in initial conditions will bemore » presented for the simulation of Lorenz system.« less

Implementation and verification of global optimization benchmark problems

NASA Astrophysics Data System (ADS)

Posypkin, Mikhail; Usov, Alexander

2017-12-01

The paper considers the implementation and verification of a test suite containing 150 benchmarks for global deterministic box-constrained optimization. A C++ library for describing standard mathematical expressions was developed for this purpose. The library automate the process of generating the value of a function and its' gradient at a given point and the interval estimates of a function and its' gradient on a given box using a single description. Based on this functionality, we have developed a collection of tests for an automatic verification of the proposed benchmarks. The verification has shown that literary sources contain mistakes in the benchmarks description. The library and the test suite are available for download and can be used freely.

Making sense of quantum operators, eigenstates and quantum measurements

NASA Astrophysics Data System (ADS)

Gire, Elizabeth; Manogue, Corinne

2012-02-01

Operators play a central role in the formalism of quantum mechanics. In particular, operators corresponding to observables encode important information about the results of quantum measurements. We interviewed upper-level undergraduate physics majors about their understanding of the role of operators in quantum measurements. Previous studies have shown that many students think of measurements on quantum systems as being deterministic and that measurements mathematically correspond to operators acting on the initial quantum state. This study is consistent with and expands on those results. We report on how two students make sense of a quantum measurement problem involving sequential measurements and the role that the eigenvalue equation plays in this sense-making.

Spatio-temporal modelling of rainfall in the Murray-Darling Basin

NASA Astrophysics Data System (ADS)

Nowak, Gen; Welsh, A. H.; O'Neill, T. J.; Feng, Lingbing

2018-02-01

The Murray-Darling Basin (MDB) is a large geographical region in southeastern Australia that contains many rivers and creeks, including Australia's three longest rivers, the Murray, the Murrumbidgee and the Darling. Understanding rainfall patterns in the MDB is very important due to the significant impact major events such as droughts and floods have on agricultural and resource productivity. We propose a model for modelling a set of monthly rainfall data obtained from stations in the MDB and for producing predictions in both the spatial and temporal dimensions. The model is a hierarchical spatio-temporal model fitted to geographical data that utilises both deterministic and data-derived components. Specifically, rainfall data at a given location are modelled as a linear combination of these deterministic and data-derived components. A key advantage of the model is that it is fitted in a step-by-step fashion, enabling appropriate empirical choices to be made at each step.

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

Stochastic Watershed Models for Risk Based Decision Making

NASA Astrophysics Data System (ADS)

Vogel, R. M.

2017-12-01

Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation

A stochastic chemostat model with an inhibitor and noise independent of population sizes

NASA Astrophysics Data System (ADS)

Sun, Shulin; Zhang, Xiaolu

2018-02-01

In this paper, a stochastic chemostat model with an inhibitor is considered, here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient. Firstly, we show that the system has a unique global positive solution. Secondly, by constructing some suitable Lyapunov functions, we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise. That is, the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied. However, the sufficient large noise can make the microorganisms become extinct with probability one, although the solutions to the original deterministic model may be persistent. Finally, the obtained analytical results are illustrated by computer simulations.

A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 1; Model Development and Parametric Response

NASA Technical Reports Server (NTRS)

Smialek, James L.

2002-01-01

An equation has been developed to model the iterative scale growth and spalling process that occurs during cyclic oxidation of high temperature materials. Parabolic scale growth and spalling of a constant surface area fraction have been assumed. Interfacial spallation of the only the thickest segments was also postulated. This simplicity allowed for representation by a simple deterministic summation series. Inputs are the parabolic growth rate constant, the spall area fraction, oxide stoichiometry, and cycle duration. Outputs include the net weight change behavior, as well as the total amount of oxygen and metal consumed, the total amount of oxide spalled, and the mass fraction of oxide spalled. The outputs all follow typical well-behaved trends with the inputs and are in good agreement with previous interfacial models.

Using emergent order to shape a space society

NASA Technical Reports Server (NTRS)

Graps, Amara L.

1993-01-01

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Using Artificial Neural Networks to Predict the Presence of Overpressured Zones in the Anadarko Basin, Oklahoma

NASA Astrophysics Data System (ADS)

Cranganu, Constantin

2007-10-01

Many sedimentary basins throughout the world exhibit areas with abnormal pore-fluid pressures (higher or lower than normal or hydrostatic pressure). Predicting pore pressure and other parameters (depth, extension, magnitude, etc.) in such areas are challenging tasks. The compressional acoustic (sonic) log (DT) is often used as a predictor because it responds to changes in porosity or compaction produced by abnormal pore-fluid pressures. Unfortunately, the sonic log is not commonly recorded in most oil and/or gas wells. We propose using an artificial neural network to synthesize sonic logs by identifying the mathematical dependency between DT and the commonly available logs, such as normalized gamma ray (GR) and deep resistivity logs (REID). The artificial neural network process can be divided into three steps: (1) Supervised training of the neural network; (2) confirmation and validation of the model by blind-testing the results in wells that contain both the predictor (GR, REID) and the target values (DT) used in the supervised training; and 3) applying the predictive model to all wells containing the required predictor data and verifying the accuracy of the synthetic DT data by comparing the back-predicted synthetic predictor curves (GRNN, REIDNN) to the recorded predictor curves used in training (GR, REID). Artificial neural networks offer significant advantages over traditional deterministic methods. They do not require a precise mathematical model equation that describes the dependency between the predictor values and the target values and, unlike linear regression techniques, neural network methods do not overpredict mean values and thereby preserve original data variability. One of their most important advantages is that their predictions can be validated and confirmed through back-prediction of the input data. This procedure was applied to predict the presence of overpressured zones in the Anadarko Basin, Oklahoma. The results are promising and encouraging.

A Probabilistic Framework for the Validation and Certification of Computer Simulations

NASA Technical Reports Server (NTRS)

Ghanem, Roger; Knio, Omar

2000-01-01

The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.

Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

NASA Technical Reports Server (NTRS)

McClelland, Ryan S.

2016-01-01

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.

Simplified continuous simulation model for investigating effects of controlled drainage on long-term soil moisture dynamics with a shallow groundwater table.

PubMed

Sun, Huaiwei; Tong, Juxiu; Luo, Wenbing; Wang, Xiugui; Yang, Jinzhong

2016-08-01

Accurate modeling of soil water content is required for a reasonable prediction of crop yield and of agrochemical leaching in the field. However, complex mathematical models faced the difficult-to-calibrate parameters and the distinct knowledge between the developers and users. In this study, a deterministic model is presented and is used to investigate the effects of controlled drainage on soil moisture dynamics in a shallow groundwater area. This simplified one-dimensional model is formulated to simulate soil moisture in the field on a daily basis and takes into account only the vertical hydrological processes. A linear assumption is proposed and is used to calculate the capillary rise from the groundwater. The pipe drainage volume is calculated by using a steady-state approximation method and the leakage rate is calculated as a function of soil moisture. The model is successfully calibrated by using field experiment data from four different pipe drainage treatments with several field observations. The model was validated by comparing the simulations with observed soil water content during the experimental seasons. The comparison results demonstrated the robustness and effectiveness of the model in the prediction of average soil moisture values. The input data required to run the model are widely available and can be measured easily in the field. It is observed that controlled drainage results in lower groundwater contribution to the root zone and lower depth of percolation to the groundwater, thus helping in the maintenance of a low level of soil salinity in the root zone.

Population density equations for stochastic processes with memory kernels

NASA Astrophysics Data System (ADS)

Lai, Yi Ming; de Kamps, Marc

2017-06-01

We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

Kinetics of Thermal Unimolecular Decomposition of Acetic Anhydride: An Integrated Deterministic and Stochastic Model.

PubMed

Mai, Tam V-T; Duong, Minh V; Nguyen, Hieu T; Lin, Kuang C; Huynh, Lam K

2017-04-27

An integrated deterministic and stochastic model within the master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) framework was first used to characterize temperature- and pressure-dependent behaviors of thermal decomposition of acetic anhydride in a wide range of conditions (i.e., 300-1500 K and 0.001-100 atm). Particularly, using potential energy surface and molecular properties obtained from high-level electronic structure calculations at CCSD(T)/CBS, macroscopic thermodynamic properties and rate coefficients of the title reaction were derived with corrections for hindered internal rotation and tunneling treatments. Being in excellent agreement with the scattered experimental data, the results from deterministic and stochastic frameworks confirmed and complemented each other to reveal that the main decomposition pathway proceeds via a 6-membered-ring transition state with the 0 K barrier of 35.2 kcal·mol -1 . This observation was further understood and confirmed by the sensitivity analysis on the time-resolved species profiles and the derived rate coefficients with respect to the ab initio barriers. Such an agreement suggests the integrated model can be confidently used for a wide range of conditions as a powerful postfacto and predictive tool in detailed chemical kinetic modeling and simulation for the title reaction and thus can be extended to complex chemical reactions.

Probabilistic dose-response modeling: case study using dichloromethane PBPK model results.

PubMed

Marino, Dale J; Starr, Thomas B

2007-12-01

A revised assessment of dichloromethane (DCM) has recently been reported that examines the influence of human genetic polymorphisms on cancer risks using deterministic PBPK and dose-response modeling in the mouse combined with probabilistic PBPK modeling in humans. This assessment utilized Bayesian techniques to optimize kinetic variables in mice and humans with mean values from posterior distributions used in the deterministic modeling in the mouse. To supplement this research, a case study was undertaken to examine the potential impact of probabilistic rather than deterministic PBPK and dose-response modeling in mice on subsequent unit risk factor (URF) determinations. Four separate PBPK cases were examined based on the exposure regimen of the NTP DCM bioassay. These were (a) Same Mouse (single draw of all PBPK inputs for both treatment groups); (b) Correlated BW-Same Inputs (single draw of all PBPK inputs for both treatment groups except for bodyweights (BWs), which were entered as correlated variables); (c) Correlated BW-Different Inputs (separate draws of all PBPK inputs for both treatment groups except that BWs were entered as correlated variables); and (d) Different Mouse (separate draws of all PBPK inputs for both treatment groups). Monte Carlo PBPK inputs reflect posterior distributions from Bayesian calibration in the mouse that had been previously reported. A minimum of 12,500 PBPK iterations were undertaken, in which dose metrics, i.e., mg DCM metabolized by the GST pathway/L tissue/day for lung and liver were determined. For dose-response modeling, these metrics were combined with NTP tumor incidence data that were randomly selected from binomial distributions. Resultant potency factors (0.1/ED(10)) were coupled with probabilistic PBPK modeling in humans that incorporated genetic polymorphisms to derive URFs. Results show that there was relatively little difference, i.e., <10% in central tendency and upper percentile URFs, regardless of the case evaluated. Independent draws of PBPK inputs resulted in the slightly higher URFs. Results were also comparable to corresponding values from the previously reported deterministic mouse PBPK and dose-response modeling approach that used LED(10)s to derive potency factors. This finding indicated that the adjustment from ED(10) to LED(10) in the deterministic approach for DCM compensated for variability resulting from probabilistic PBPK and dose-response modeling in the mouse. Finally, results show a similar degree of variability in DCM risk estimates from a number of different sources including the current effort even though these estimates were developed using very different techniques. Given the variety of different approaches involved, 95th percentile-to-mean risk estimate ratios of 2.1-4.1 represent reasonable bounds on variability estimates regarding probabilistic assessments of DCM.

Complex Population Dynamics and the Coalescent Under Neutrality

PubMed Central

Volz, Erik M.

2012-01-01

Estimates of the coalescent effective population size Ne can be poorly correlated with the true population size. The relationship between Ne and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of Ne such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics. PMID:22042576

Statistically Qualified Neuro-Analytic system and Method for Process Monitoring

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

1998-11-04

An apparatus and method for monitoring a process involves development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two steps: deterministic model adaption and stochastic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics,augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation emor minimization technique. Stochastic model adaptation involves qualifying any remaining uncertaintymore » in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system.« less

Nonlinear unitary quantum collapse model with self-generated noise

NASA Astrophysics Data System (ADS)

Geszti, Tamás

2018-04-01

Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.

DIETARY EXPOSURES OF YOUNG CHILDREN, PART 3: MODELLING

EPA Science Inventory

A deterministic model was used to model dietary exposure of young children. Parameters included pesticide residue on food before handling, surface pesticide loading, transfer efficiencies and children's activity patterns. Three components of dietary pesticide exposure were includ...

Mesoscopic and continuum modelling of angiogenesis

PubMed Central

Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

2016-01-01

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. PMID:24615007

Statistical Physics of Complex Substitutive Systems

NASA Astrophysics Data System (ADS)

Jin, Qing

Diffusion processes are central to human interactions. Despite extensive studies that span multiple disciplines, our knowledge is limited to spreading processes in non-substitutive systems. Yet, a considerable number of ideas, products, and behaviors spread by substitution; to adopt a new one, agents must give up an existing one. This captures the spread of scientific constructs--forcing scientists to choose, for example, a deterministic or probabilistic worldview, as well as the adoption of durable items, such as mobile phones, cars, or homes. In this dissertation, I develop a statistical physics framework to describe, quantify, and understand substitutive systems. By empirically exploring three collected high-resolution datasets pertaining to such systems, I build a mechanistic model describing substitutions, which not only analytically predicts the universal macroscopic phenomenon discovered in the collected datasets, but also accurately captures the trajectories of individual items in a complex substitutive system, demonstrating a high degree of regularity and universality in substitutive systems. I also discuss the origins and insights of the parameters in the substitution model and possible generalization form of the mathematical framework. The systematical study of substitutive systems presented in this dissertation could potentially guide the understanding and prediction of all spreading phenomena driven by substitutions, from electric cars to scientific paradigms, and from renewable energy to new healthy habits.

Stochastic Optimization For Water Resources Allocation

NASA Astrophysics Data System (ADS)

Yamout, G.; Hatfield, K.

2003-12-01

For more than 40 years, water resources allocation problems have been addressed using deterministic mathematical optimization. When data uncertainties exist, these methods could lead to solutions that are sub-optimal or even infeasible. While optimization models have been proposed for water resources decision-making under uncertainty, no attempts have been made to address the uncertainties in water allocation problems in an integrated approach. This paper presents an Integrated Dynamic, Multi-stage, Feedback-controlled, Linear, Stochastic, and Distributed parameter optimization approach to solve a problem of water resources allocation. It attempts to capture (1) the conflict caused by competing objectives, (2) environmental degradation produced by resource consumption, and finally (3) the uncertainty and risk generated by the inherently random nature of state and decision parameters involved in such a problem. A theoretical system is defined throughout its different elements. These elements consisting mainly of water resource components and end-users are described in terms of quantity, quality, and present and future associated risks and uncertainties. Models are identified, modified, and interfaced together to constitute an integrated water allocation optimization framework. This effort is a novel approach to confront the water allocation optimization problem while accounting for uncertainties associated with all its elements; thus resulting in a solution that correctly reflects the physical problem in hand.

Models, solution, methods and their applicability of dynamic location problems (DLPs) (a gap analysis for further research)

NASA Astrophysics Data System (ADS)

Seyedhosseini, Seyed Mohammad; Makui, Ahmad; Shahanaghi, Kamran; Torkestani, Sara Sadat

2016-09-01

Determining the best location to be profitable for the facility's lifetime is the important decision of public and private firms, so this is why discussion about dynamic location problems (DLPs) is a critical significance. This paper presented a comprehensive review from 1968 up to most recent on published researches about DLPs and classified them into two parts. First, mathematical models developed based on different characteristics: type of parameters (deterministic, probabilistic or stochastic), number and type of objective function, numbers of commodity and modes, relocation time, number of relocation and relocating facilities, time horizon, budget and capacity constraints and their applicability. In second part, It have been also presented solution algorithms, main specification, applications and some real-world case studies of DLPs. At the ends, we concluded that in the current literature of DLPs, distribution systems and production-distribution systems with simple assumption of the tackle to the complexity of these models studied more than any other fields, as well as the concept of variety of services (hierarchical network), reliability, sustainability, relief management, waiting time for services (queuing theory) and risk of facility disruption need for further investigation. All of the available categories based on different criteria, solution methods and applicability of them, gaps and analysis which have been done in this paper suggest the ways for future research.

Mechanisms that enhance sustainability of p53 pulses.

PubMed

Kim, Jae Kyoung; Jackson, Trachette L

2013-01-01

The tumor suppressor p53 protein shows various dynamic responses depending on the types and extent of cellular stresses. In particular, in response to DNA damage induced by γ-irradiation, cells generate a series of p53 pulses. Recent research has shown the importance of sustaining repeated p53 pulses for recovery from DNA damage. However, far too little attention has been paid to understanding how cells can sustain p53 pulses given the complexities of genetic heterogeneity and intrinsic noise. Here, we explore potential molecular mechanisms that enhance the sustainability of p53 pulses by developing a new mathematical model of the p53 regulatory system. This model can reproduce many experimental results that describe the dynamics of p53 pulses. By simulating the model both deterministically and stochastically, we found three potential mechanisms that improve the sustainability of p53 pulses: 1) the recently identified positive feedback loop between p53 and Rorα allows cells to sustain p53 pulses with high amplitude over a wide range of conditions, 2) intrinsic noise can often prevent the dampening of p53 pulses even after mutations, and 3) coupling of p53 pulses in neighboring cells via cytochrome-c significantly reduces the chance of failure in sustaining p53 pulses in the presence of heterogeneity among cells. Finally, in light of these results, we propose testable experiments that can reveal important mechanisms underlying p53 dynamics.

Location of coating defects and assessment of level of cathodic protection on underground pipelines using AC impedance, deterministic and non-deterministic models

NASA Astrophysics Data System (ADS)

Castaneda-Lopez, Homero

A methodology for detecting and locating defects or discontinuities on the outside covering of coated metal underground pipelines subjected to cathodic protection has been addressed. On the basis of wide range AC impedance signals for various frequencies applied to a steel-coated pipeline system and by measuring its corresponding transfer function under several laboratory simulation scenarios, a physical laboratory setup of an underground cathodic-protected, coated pipeline was built. This model included different variables and elements that exist under real conditions, such as soil resistivity, soil chemical composition, defect (holiday) location in the pipeline covering, defect area and geometry, and level of cathodic protection. The AC impedance data obtained under different working conditions were used to fit an electrical transmission line model. This model was then used as a tool to fit the impedance signal for different experimental conditions and to establish trends in the impedance behavior without the necessity of further experimental work. However, due to the chaotic nature of the transfer function response of this system under several conditions, it is believed that non-deterministic models based on pattern recognition algorithms are suitable for field condition analysis. A non-deterministic approach was used for experimental analysis by applying an artificial neural network (ANN) algorithm based on classification analysis capable of studying the pipeline system and differentiating the variables that can change impedance conditions. These variables include level of cathodic protection, location of discontinuities (holidays), and severity of corrosion. This work demonstrated a proof-of-concept for a well-known technique and a novel algorithm capable of classifying impedance data for experimental results to predict the exact location of the active holidays and defects on the buried pipelines. Laboratory findings from this procedure are promising, and efforts to develop it for field conditions should continue.

Hidden order in crackling noise during peeling of an adhesive tape.

PubMed

Kumar, Jagadish; Ciccotti, M; Ananthakrishna, G

2008-04-01

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.

ON JOINT DETERMINISTIC GRID MODELING AND SUB-GRID VARIABILITY CONCEPTUAL FRAMEWORK FOR MODEL EVALUATION

EPA Science Inventory

The general situation, (but exemplified in urban areas), where a significant degree of sub-grid variability (SGV) exists in grid models poses problems when comparing gridbased air quality modeling results with observations. Typically, grid models ignore or parameterize processes ...

Hierarchial mark-recapture models: a framework for inference about demographic processes

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

2004-01-01

The development of sophisticated mark-recapture models over the last four decades has provided fundamental tools for the study of wildlife populations, allowing reliable inference about population sizes and demographic rates based on clearly formulated models for the sampling processes. Mark-recapture models are now routinely described by large numbers of parameters. These large models provide the next challenge to wildlife modelers: the extraction of signal from noise in large collections of parameters. Pattern among parameters can be described by strong, deterministic relations (as in ultrastructural models) but is more flexibly and credibly modeled using weaker, stochastic relations. Trend in survival rates is not likely to be manifest by a sequence of values falling precisely on a given parametric curve; rather, if we could somehow know the true values, we might anticipate a regression relation between parameters and explanatory variables, in which true value equals signal plus noise. Hierarchical models provide a useful framework for inference about collections of related parameters. Instead of regarding parameters as fixed but unknown quantities, we regard them as realizations of stochastic processes governed by hyperparameters. Inference about demographic processes is based on investigation of these hyperparameters. We advocate the Bayesian paradigm as a natural, mathematically and scientifically sound basis for inference about hierarchical models. We describe analysis of capture-recapture data from an open population based on hierarchical extensions of the Cormack-Jolly-Seber model. In addition to recaptures of marked animals, we model first captures of animals and losses on capture, and are thus able to estimate survival probabilities w (i.e., the complement of death or permanent emigration) and per capita growth rates f (i.e., the sum of recruitment and immigration rates). Covariation in these rates, a feature of demographic interest, is explicitly described in the model.

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria

NASA Astrophysics Data System (ADS)

Joo, Jaewook; Eric, Harvill; Albert, Reka

2007-03-01

Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial populations and a deterministic model, we have shown in [Joo et al 2005] that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of the initial phage concentration and other phage and host parameters such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates, and the phage burst size. Here we investigate the effects of stochastic fluctuations on bacterial invasion facilitated by bacteriophage, and examine the validity of the deterministic approach. We use both numerical and analytical methods of stochastic processes to identify the source of noise and assess its magnitude. We show that the conclusions obtained from the deterministic model are robust against stochastic fluctuations, yet deviations become prominently large when the phage are more pathological to the invading bacterial strain.

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Modelling the interaction between flooding events and economic growth

NASA Astrophysics Data System (ADS)

Grames, J.; Prskawetz, A.; Grass, D.; Blöschl, G.

2015-06-01

Socio-hydrology describes the interaction between the socio-economy and water. Recent models analyze the interplay of community risk-coping culture, flooding damage and economic growth (Di Baldassarre et al., 2013; Viglione et al., 2014). These models descriptively explain the feedbacks between socio-economic development and natural disasters like floods. Contrary to these descriptive models, our approach develops an optimization model, where the intertemporal decision of an economic agent interacts with the hydrological system. In order to build this first economic growth model describing the interaction between the consumption and investment decisions of an economic agent and the occurrence of flooding events, we transform an existing descriptive stochastic model into an optimal deterministic model. The intermediate step is to formulate and simulate a descriptive deterministic model. We develop a periodic water function to approximate the former discrete stochastic time series of rainfall events. Due to the non-autonomous exogenous periodic rainfall function the long-term path of consumption and investment will be periodic.

Linking Inflammation, Cardiorespiratory Variability, and Neural Control in Acute Inflammation via Computational Modeling

PubMed Central

Dick, Thomas E.; Molkov, Yaroslav I.; Nieman, Gary; Hsieh, Yee-Hsee; Jacono, Frank J.; Doyle, John; Scheff, Jeremy D.; Calvano, Steve E.; Androulakis, Ioannis P.; An, Gary; Vodovotz, Yoram

2012-01-01

Acute inflammation leads to organ failure by engaging catastrophic feedback loops in which stressed tissue evokes an inflammatory response and, in turn, inflammation damages tissue. Manifestations of this maladaptive inflammatory response include cardio-respiratory dysfunction that may be reflected in reduced heart rate and ventilatory pattern variabilities. We have developed signal-processing algorithms that quantify non-linear deterministic characteristics of variability in biologic signals. Now, coalescing under the aegis of the NIH Computational Biology Program and the Society for Complexity in Acute Illness, two research teams performed iterative experiments and computational modeling on inflammation and cardio-pulmonary dysfunction in sepsis as well as on neural control of respiration and ventilatory pattern variability. These teams, with additional collaborators, have recently formed a multi-institutional, interdisciplinary consortium, whose goal is to delineate the fundamental interrelationship between the inflammatory response and physiologic variability. Multi-scale mathematical modeling and complementary physiological experiments will provide insight into autonomic neural mechanisms that may modulate the inflammatory response to sepsis and simultaneously reduce heart rate and ventilatory pattern variabilities associated with sepsis. This approach integrates computational models of neural control of breathing and cardio-respiratory coupling with models that combine inflammation, cardiovascular function, and heart rate variability. The resulting integrated model will provide mechanistic explanations for the phenomena of respiratory sinus-arrhythmia and cardio-ventilatory coupling observed under normal conditions, and the loss of these properties during sepsis. This approach holds the potential of modeling cross-scale physiological interactions to improve both basic knowledge and clinical management of acute inflammatory diseases such as sepsis and trauma. PMID:22783197

Linking Inflammation, Cardiorespiratory Variability, and Neural Control in Acute Inflammation via Computational Modeling.

PubMed

Dick, Thomas E; Molkov, Yaroslav I; Nieman, Gary; Hsieh, Yee-Hsee; Jacono, Frank J; Doyle, John; Scheff, Jeremy D; Calvano, Steve E; Androulakis, Ioannis P; An, Gary; Vodovotz, Yoram

2012-01-01

Acute inflammation leads to organ failure by engaging catastrophic feedback loops in which stressed tissue evokes an inflammatory response and, in turn, inflammation damages tissue. Manifestations of this maladaptive inflammatory response include cardio-respiratory dysfunction that may be reflected in reduced heart rate and ventilatory pattern variabilities. We have developed signal-processing algorithms that quantify non-linear deterministic characteristics of variability in biologic signals. Now, coalescing under the aegis of the NIH Computational Biology Program and the Society for Complexity in Acute Illness, two research teams performed iterative experiments and computational modeling on inflammation and cardio-pulmonary dysfunction in sepsis as well as on neural control of respiration and ventilatory pattern variability. These teams, with additional collaborators, have recently formed a multi-institutional, interdisciplinary consortium, whose goal is to delineate the fundamental interrelationship between the inflammatory response and physiologic variability. Multi-scale mathematical modeling and complementary physiological experiments will provide insight into autonomic neural mechanisms that may modulate the inflammatory response to sepsis and simultaneously reduce heart rate and ventilatory pattern variabilities associated with sepsis. This approach integrates computational models of neural control of breathing and cardio-respiratory coupling with models that combine inflammation, cardiovascular function, and heart rate variability. The resulting integrated model will provide mechanistic explanations for the phenomena of respiratory sinus-arrhythmia and cardio-ventilatory coupling observed under normal conditions, and the loss of these properties during sepsis. This approach holds the potential of modeling cross-scale physiological interactions to improve both basic knowledge and clinical management of acute inflammatory diseases such as sepsis and trauma.

Modelling the epidemiology of Escherichia coli ST131 and the impact of interventions on the community and healthcare centres.

PubMed

Talaminos, A; López-Cerero, L; Calvillo, J; Pascual, A; Roa, L M; Rodríguez-Baño, J

2016-07-01

ST131 Escherichia coli is an emergent clonal group that has achieved successful worldwide spread through a combination of virulence and antimicrobial resistance. Our aim was to develop a mathematical model, based on current knowledge of the epidemiology of ESBL-producing and non-ESBL-producing ST131 E. coli, to provide a framework enabling a better understanding of its spread within the community, in hospitals and long-term care facilities, and the potential impact of specific interventions on the rates of infection. A model belonging to the SEIS (Susceptible-Exposed-Infected-Susceptible) class of compartmental models, with specific modifications, was developed. Quantification of the model is based on the law of mass preservation, which helps determine the relationships between flows of individuals and different compartments. Quantification is deterministic or probabilistic depending on subpopulation size. The assumptions for the model are based on several developed epidemiological studies. Based on the assumptions of the model, an intervention capable of sustaining a 25% reduction in person-to-person transmission shows a significant reduction in the rate of infections caused by ST131; the impact is higher for non-ESBL-producing ST131 isolates than for ESBL producers. On the other hand, an isolated intervention reducing exposure to antimicrobial agents has much more limited impact on the rate of ST131 infection. Our results suggest that interventions achieving a continuous reduction in the transmission of ST131 in households, nursing homes and hospitals offer the best chance of reducing the burden of the infections caused by these isolates.

MIMICKING COUNTERFACTUAL OUTCOMES TO ESTIMATE CAUSAL EFFECTS.

PubMed

Lok, Judith J

2017-04-01

In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates, and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Structural nested models have been applied in this setting. Structural nested models are based on counterfactuals: the outcome a person would have had had treatment been withheld after a certain time. Previous work on continuous-time structural nested models assumes that counterfactuals depend deterministically on observed data, while conjecturing that this assumption can be relaxed. This article proves that one can mimic counterfactuals by constructing random variables, solutions to a differential equation, that have the same distribution as the counterfactuals, even given past observed data. These "mimicking" variables can be used to estimate the parameters of structural nested models without assuming the treatment effect to be deterministic.

Amplification of intrinsic fluctuations by the Lorenz equations

NASA Astrophysics Data System (ADS)

Fox, Ronald F.; Elston, T. C.

1993-07-01

Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations.

Uniqueness of Nash equilibrium in vaccination games.

PubMed

Bai, Fan

2016-12-01

One crucial condition for the uniqueness of Nash equilibrium set in vaccination games is that the attack ratio monotonically decreases as the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in heterogeneous mixing population. Based on the final size relations obtained from the deterministic epidemic models, we prove that the attack ratios can be expressed in terms of the vaccine coverage levels, and also prove that the attack ratios are decreasing functions of vaccine coverage levels. Some thresholds are presented, which depend on the vaccine efficacy. It is proved that for vaccination games in homogeneous mixing population, there is a unique Nash equilibrium for each game.

Automated Assume-Guarantee Reasoning by Abstraction Refinement

NASA Technical Reports Server (NTRS)

Pasareanu, Corina S.; Giannakopoulous, Dimitra; Glannakopoulou, Dimitra

2008-01-01

Current automated approaches for compositional model checking in the assume-guarantee style are based on learning of assumptions as deterministic automata. We propose an alternative approach based on abstraction refinement. Our new method computes the assumptions for the assume-guarantee rules as conservative and not necessarily deterministic abstractions of some of the components, and refines those abstractions using counter-examples obtained from model checking them together with the other components. Our approach also exploits the alphabets of the interfaces between components and performs iterative refinement of those alphabets as well as of the abstractions. We show experimentally that our preliminary implementation of the proposed alternative achieves similar or better performance than a previous learning-based implementation.

Deterministic Impulsive Vacuum Foundations for Quantum-Mechanical Wavefunctions

NASA Astrophysics Data System (ADS)

Valentine, John S.

2013-09-01

By assuming that a fermion de-constitutes immediately at source, that its constituents, as bosons, propagate uniformly as scalar vacuum terms with phase (radial) symmetry, and that fermions are unique solutions for specific phase conditions, we find a model that self-quantizes matter from continuous waves, unifying bosons and fermion ontologies in a single basis, in a constitution-invariant process. Vacuum energy has a wavefunction context, as a mass-energy term that enables wave collapse and increases its amplitude, with gravitational field as the gradient of the flux density. Gravitational and charge-based force effects emerge as statistics without special treatment. Confinement, entanglement, vacuum statistics, forces, and wavefunction terms emerge from the model's deterministic foundations.

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

NASA Technical Reports Server (NTRS)

Murphey, Thomas W.; Mikulas, Martin M.

2001-01-01

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

INTEGRATED PLANNING MODEL - EPA APPLICATIONS

EPA Science Inventory

The Integrated Planning Model (IPM) is a multi-regional, dynamic, deterministic linear programming (LP) model of the electric power sector in the continental lower 48 states and the District of Columbia. It provides forecasts up to year 2050 of least-cost capacity expansion, elec...

On the applicability of low-dimensional models for convective flow reversals at extreme Prandtl numbers

NASA Astrophysics Data System (ADS)

Mannattil, Manu; Pandey, Ambrish; Verma, Mahendra K.; Chakraborty, Sagar

2017-12-01

Constructing simpler models, either stochastic or deterministic, for exploring the phenomenon of flow reversals in fluid systems is in vogue across disciplines. Using direct numerical simulations and nonlinear time series analysis, we illustrate that the basic nature of flow reversals in convecting fluids can depend on the dimensionless parameters describing the system. Specifically, we find evidence of low-dimensional behavior in flow reversals occurring at zero Prandtl number, whereas we fail to find such signatures for reversals at infinite Prandtl number. Thus, even in a single system, as one varies the system parameters, one can encounter reversals that are fundamentally different in nature. Consequently, we conclude that a single general low-dimensional deterministic model cannot faithfully characterize flow reversals for every set of parameter values.

Modeling Uncertainties in EEG Microstates: Analysis of Real and Imagined Motor Movements Using Probabilistic Clustering-Driven Training of Probabilistic Neural Networks.

PubMed

Dinov, Martin; Leech, Robert

2017-01-01

Part of the process of EEG microstate estimation involves clustering EEG channel data at the global field power (GFP) maxima, very commonly using a modified K-means approach. Clustering has also been done deterministically, despite there being uncertainties in multiple stages of the microstate analysis, including the GFP peak definition, the clustering itself and in the post-clustering assignment of microstates back onto the EEG timecourse of interest. We perform a fully probabilistic microstate clustering and labeling, to account for these sources of uncertainty using the closest probabilistic analog to KM called Fuzzy C-means (FCM). We train softmax multi-layer perceptrons (MLPs) using the KM and FCM-inferred cluster assignments as target labels, to then allow for probabilistic labeling of the full EEG data instead of the usual correlation-based deterministic microstate label assignment typically used. We assess the merits of the probabilistic analysis vs. the deterministic approaches in EEG data recorded while participants perform real or imagined motor movements from a publicly available data set of 109 subjects. Though FCM group template maps that are almost topographically identical to KM were found, there is considerable uncertainty in the subsequent assignment of microstate labels. In general, imagined motor movements are less predictable on a time point-by-time point basis, possibly reflecting the more exploratory nature of the brain state during imagined, compared to during real motor movements. We find that some relationships may be more evident using FCM than using KM and propose that future microstate analysis should preferably be performed probabilistically rather than deterministically, especially in situations such as with brain computer interfaces, where both training and applying models of microstates need to account for uncertainty. Probabilistic neural network-driven microstate assignment has a number of advantages that we have discussed, which are likely to be further developed and exploited in future studies. In conclusion, probabilistic clustering and a probabilistic neural network-driven approach to microstate analysis is likely to better model and reveal details and the variability hidden in current deterministic and binarized microstate assignment and analyses.

Modeling Uncertainties in EEG Microstates: Analysis of Real and Imagined Motor Movements Using Probabilistic Clustering-Driven Training of Probabilistic Neural Networks

PubMed Central

Dinov, Martin; Leech, Robert

2017-01-01

Part of the process of EEG microstate estimation involves clustering EEG channel data at the global field power (GFP) maxima, very commonly using a modified K-means approach. Clustering has also been done deterministically, despite there being uncertainties in multiple stages of the microstate analysis, including the GFP peak definition, the clustering itself and in the post-clustering assignment of microstates back onto the EEG timecourse of interest. We perform a fully probabilistic microstate clustering and labeling, to account for these sources of uncertainty using the closest probabilistic analog to KM called Fuzzy C-means (FCM). We train softmax multi-layer perceptrons (MLPs) using the KM and FCM-inferred cluster assignments as target labels, to then allow for probabilistic labeling of the full EEG data instead of the usual correlation-based deterministic microstate label assignment typically used. We assess the merits of the probabilistic analysis vs. the deterministic approaches in EEG data recorded while participants perform real or imagined motor movements from a publicly available data set of 109 subjects. Though FCM group template maps that are almost topographically identical to KM were found, there is considerable uncertainty in the subsequent assignment of microstate labels. In general, imagined motor movements are less predictable on a time point-by-time point basis, possibly reflecting the more exploratory nature of the brain state during imagined, compared to during real motor movements. We find that some relationships may be more evident using FCM than using KM and propose that future microstate analysis should preferably be performed probabilistically rather than deterministically, especially in situations such as with brain computer interfaces, where both training and applying models of microstates need to account for uncertainty. Probabilistic neural network-driven microstate assignment has a number of advantages that we have discussed, which are likely to be further developed and exploited in future studies. In conclusion, probabilistic clustering and a probabilistic neural network-driven approach to microstate analysis is likely to better model and reveal details and the variability hidden in current deterministic and binarized microstate assignment and analyses. PMID:29163110

The forecasting research of early warning systems for atmospheric pollutants: A case in Yangtze River Delta region

NASA Astrophysics Data System (ADS)

Song, Yiliao; Qin, Shanshan; Qu, Jiansheng; Liu, Feng

2015-10-01

The issue of air quality regarding PM pollution levels in China is a focus of public attention. To address that issue, to date, a series of studies is in progress, including PM monitoring programs, PM source apportionment, and the enactment of new ambient air quality index standards. However, related research concerning computer modeling for PM future trends estimation is rare, despite its significance to forecasting and early warning systems. Thereby, a study regarding deterministic and interval forecasts of PM is performed. In this study, data on hourly and 12 h-averaged air pollutants are applied to forecast PM concentrations within the Yangtze River Delta (YRD) region of China. The characteristics of PM emissions have been primarily examined and analyzed using different distribution functions. To improve the distribution fitting that is crucial for estimating PM levels, an artificial intelligence algorithm is incorporated to select the optimal parameters. Following that step, an ANF model is used to conduct deterministic forecasts of PM. With the identified distributions and deterministic forecasts, different levels of PM intervals are estimated. The results indicate that the lognormal or gamma distributions are highly representative of the recorded PM data with a goodness-of-fit R2 of approximately 0.998. Furthermore, the results of the evaluation metrics (MSE, MAPE and CP, AW) also show high accuracy within the deterministic and interval forecasts of PM, indicating that this method enables the informative and effective quantification of future PM trends.

On the notion of free will in the Free Will Theorem

NASA Astrophysics Data System (ADS)

Landsman, Klaas

2017-02-01

The (Strong) Free Will Theorem (FWT) of Conway and Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to "freely choose" the settings of their experiments). This makes the theorem philosophically vulnerable, especially if it is construed as a proof of indeterminism or even of libertarian free will (as Conway & Kochen suggest). However, Cator and Landsman (Foundations of Physics 44, 781-791, 2014) previously gave a reformulation of the FWT that does not presuppose indeterminism, but rather assumes a mathematically specific form of such "free choices" even in a deterministic world (based on a non-probabilistic independence assumption). In the present paper, which is a philosophical sequel to the one just mentioned, I argue that the concept of free will used in the latter version of the FWT is essentially the one proposed by Lewis (1981), also known as 'local miracle compatibilism' (of which I give a mathematical interpretation that might be of some independent interest also beyond its application to the FWT). As such, the (reformulated) FWT in my view challenges compatibilist free will à la Lewis (albeit in a contrived way via bipartite EPR-type experiments), falling short of supporting libertarian free will.

Modeling and analysis of cosmetic treatment effects on human skin

NASA Astrophysics Data System (ADS)

Lunderstaedt, Reinhart A.; Hopermann, Hermann; Hillemann, Thomas

2000-10-01

In view of treatment effects of cosmetics, quality management becomes more and more important. Due to the efficiency reasons it is desirable to quantify these effects and predict them as a function of time. For this, a mathematical model of the skin's surface (epidermis) is needed. Such a model cannot be worked out purely analytically. It can only be derived with the help of measurement data. The signals of interest as output of different measurement devices consist of two parts: noise of high (spatial) frequencies (stochastic signal) and periodic functions (deterministic signal) of low (spatial) frequencies. Both parts can be separated by correlation analysis. The paper introduces in addition to the Fourier Transform (FT) with the Wavelet Transform (WT), a brand new, highly sophisticated method with excellent properties for both modeling the skin's surface as well as evaluating treatment effects. Its main physical advantage is (in comparison to the FT) that local irregularities in the measurement signal (e.g. by scars) remain at their place and are not represented as mean square values as it is the case when applying the FT. The method has just now been installed in industry and will there be used in connection with a new in vivo measurement device for quality control of cosmetic products. As texture parameter for an integral description of the human skin the fractal dimension D is used which is appropriate for classification of different skin regions and treatment effects as well.