A Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).

Stochastic four-way coupling of gas-solid flows for Large Eddy Simulations

NASA Astrophysics Data System (ADS)

Curran, Thomas; Denner, Fabian; van Wachem, Berend

2017-11-01

The interaction of solid particles with turbulence has for long been a topic of interest for predicting the behavior of industrially relevant flows. For the turbulent fluid phase, Large Eddy Simulation (LES) methods are widely used for their low computational cost, leaving only the sub-grid scales (SGS) of turbulence to be modelled. Although LES has seen great success in predicting the behavior of turbulent single-phase flows, the development of LES for turbulent gas-solid flows is still in its infancy. This contribution aims at constructing a model to describe the four-way coupling of particles in an LES framework, by considering the role particles play in the transport of turbulent kinetic energy across the scales. Firstly, a stochastic model reconstructing the sub-grid velocities for the particle tracking is presented. Secondly, to solve particle-particle interaction, most models involve a deterministic treatment of the collisions. We finally introduce a stochastic model for estimating the collision probability. All results are validated against fully resolved DNS-DPS simulations. The final goal of this contribution is to propose a global stochastic method adapted to two-phase LES simulation where the number of particles considered can be significantly increased. Financial support from PetroBras is gratefully acknowledged.

Vulnerability Assessment of Water Supply Systems: Status, Gaps and Opportunities

NASA Astrophysics Data System (ADS)

Wheater, H. S.

2015-12-01

Conventional frameworks for assessing the impacts of climate change on water resource systems use cascades of climate and hydrological models to provide 'top-down' projections of future water availability, but these are subject to high uncertainty and are model and scenario-specific. Hence there has been recent interest in 'bottom-up' frameworks, which aim to evaluate system vulnerability to change in the context of possible future climate and/or hydrological conditions. Such vulnerability assessments are generic, and can be combined with updated information from top-down assessments as they become available. While some vulnerability methods use hydrological models to estimate water availability, fully bottom-up schemes have recently been proposed that directly map system vulnerability as a function of feasible changes in water supply characteristics. These use stochastic algorithms, based on reconstruction or reshuffling methods, by which multiple water supply realizations can be generated under feasible ranges of change in water supply conditions. The paper reports recent successes, and points to areas of future improvement. Advances in stochastic modeling and optimization can address some technical limitations in flow reconstruction, while various data mining and system identification techniques can provide possibilities to better condition realizations for consistency with top-down scenarios. Finally, we show that probabilistic and Bayesian frameworks together can provide a potential basis to combine information obtained from fully bottom-up analyses with projections available from climate and/or hydrological models in a fully integrated risk assessment framework for deep uncertainty.

The role of phase dynamics in a stochastic model of a passively advected scalar

NASA Astrophysics Data System (ADS)

Moradi, Sara; Anderson, Johan

2016-05-01

Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form -βk/1 +k2 , where β is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of β, where we find that the energy spectrum follows a k-7 /2 scaling. Whereas for lower β there is a significant difference between a-synchronised and synchronised phase states, one could expect the formation of coherent modulations in the latter case.

Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs

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

Karagiannis, Georgios; Lin, Guang

2014-02-15

Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesianmore » model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.« less

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.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

PubMed

Harrison, Jonathan U; Yates, Christian A

2016-09-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.

A hybrid algorithm for coupling partial differential equation and compartment-based dynamics

PubMed Central

Yates, Christian A.

2016-01-01

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction–diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. PMID:27628171

Topology-selective jamming of fully-connected, code-division random-access networks

NASA Technical Reports Server (NTRS)

Polydoros, Andreas; Cheng, Unjeng

1990-01-01

The purpose is to introduce certain models of topology selective stochastic jamming and examine its impact on a class of fully-connected, spread-spectrum, slotted ALOHA-type random access networks. The theory covers dedicated as well as half-duplex units. The dominant role of the spatial duty factor is established, and connections with the dual concept of time selective jamming are discussed. The optimal choices of coding rate and link access parameters (from the users' side) and the jamming spatial fraction are numerically established for DS and FH spreading.

Optimal regeneration planning for old-growth forest: addressing scientific uncertainty in endangered species recovery through adaptive management

USGS Publications Warehouse

Moore, C.T.; Conroy, M.J.

2006-01-01

Stochastic and structural uncertainties about forest dynamics present challenges in the management of ephemeral habitat conditions for endangered forest species. Maintaining critical foraging and breeding habitat for the endangered red-cockaded woodpecker (Picoides borealis) requires an uninterrupted supply of old-growth forest. We constructed and optimized a dynamic forest growth model for the Piedmont National Wildlife Refuge (Georgia, USA) with the objective of perpetuating a maximum stream of old-growth forest habitat. Our model accommodates stochastic disturbances and hardwood succession rates, and uncertainty about model structure. We produced a regeneration policy that was indexed by current forest state and by current weight of evidence among alternative model forms. We used adaptive stochastic dynamic programming, which anticipates that model probabilities, as well as forest states, may change through time, with consequent evolution of the optimal decision for any given forest state. In light of considerable uncertainty about forest dynamics, we analyzed a set of competing models incorporating extreme, but plausible, parameter values. Under any of these models, forest silviculture practices currently recommended for the creation of woodpecker habitat are suboptimal. We endorse fully adaptive approaches to the management of endangered species habitats in which predictive modeling, monitoring, and assessment are tightly linked.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Chibbaro, Sergio; Pope, Stephen B.

2014-11-01

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

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

Minier, Jean-Pierre, E-mail: Jean-Pierre.Minier@edf.fr; Chibbaro, Sergio; Pope, Stephen B.

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangianmore » stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.« less

A stochastic multicriteria model for evidence-based decision making in drug benefit-risk analysis.

PubMed

Tervonen, Tommi; van Valkenhoef, Gert; Buskens, Erik; Hillege, Hans L; Postmus, Douwe

2011-05-30

Drug benefit-risk (BR) analysis is based on firm clinical evidence regarding various safety and efficacy outcomes. In this paper, we propose a new and more formal approach for constructing a supporting multi-criteria model that fully takes into account the evidence on efficacy and adverse drug reactions. Our approach is based on the stochastic multi-criteria acceptability analysis methodology, which allows us to compute the typical value judgments that support a decision, to quantify decision uncertainty, and to compute a comprehensive BR profile. We construct a multi-criteria model for the therapeutic group of second-generation antidepressants. We assess fluoxetine and venlafaxine together with placebo according to incidence of treatment response and three common adverse drug reactions by using data from a published study. Our model shows that there are clear trade-offs among the treatment alternatives. Copyright © 2011 John Wiley & Sons, Ltd.

Fully probabilistic control design in an adaptive critic framework.

PubMed

Herzallah, Randa; Kárný, Miroslav

2011-12-01

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem; in particular, very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic control algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this paper. Copyright © 2011 Elsevier Ltd. All rights reserved.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

Stochastic flux analysis of chemical reaction networks

PubMed Central

2013-01-01

Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153

Stochastic flux analysis of chemical reaction networks.

PubMed

Kahramanoğulları, Ozan; Lynch, James F

2013-12-07

Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.

Will systems biology offer new holistic paradigms to life sciences?

PubMed Central

Conti, Filippo; Valerio, Maria Cristina; Zbilut, Joseph P.

2008-01-01

A biological system, like any complex system, blends stochastic and deterministic features, displaying properties of both. In a certain sense, this blend is exactly what we perceive as the “essence of complexity” given we tend to consider as non-complex both an ideal gas (fully stochastic and understandable at the statistical level in the thermodynamic limit of a huge number of particles) and a frictionless pendulum (fully deterministic relative to its motion). In this commentary we make the statement that systems biology will have a relevant impact on nowadays biology if (and only if) will be able to capture the essential character of this blend that in our opinion is the generation of globally ordered collective modes supported by locally stochastic atomisms. PMID:19003440

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

Estimating radiative feedbacks from stochastic fluctuations in surface temperature and energy imbalance

NASA Astrophysics Data System (ADS)

Proistosescu, C.; Donohoe, A.; Armour, K.; Roe, G.; Stuecker, M. F.; Bitz, C. M.

2017-12-01

Joint observations of global surface temperature and energy imbalance provide for a unique opportunity to empirically constrain radiative feedbacks. However, the satellite record of Earth's radiative imbalance is relatively short and dominated by stochastic fluctuations. Estimates of radiative feedbacks obtained by regressing energy imbalance against surface temperature depend strongly on sampling choices and on assumptions about whether the stochastic fluctuations are primarily forced by atmospheric or oceanic variability (e.g. Murphy and Forster 2010, Dessler 2011, Spencer and Braswell 2011, Forster 2016). We develop a framework around a stochastic energy balance model that allows us to parse the different contributions of atmospheric and oceanic forcing based on their differing impacts on the covariance structure - or lagged regression - of temperature and radiative imbalance. We validate the framework in a hierarchy of general circulation models: the impact of atmospheric forcing is examined in unforced control simulations of fixed sea-surface temperature and slab ocean model versions; the impact of oceanic forcing is examined in coupled simulations with prescribed ENSO variability. With the impact of atmospheric and oceanic forcing constrained, we are able to predict the relationship between temperature and radiative imbalance in a fully coupled control simulation, finding that both forcing sources are needed to explain the structure of the lagged-regression. We further model the dependence of feedback estimates on sampling interval by considering the effects of a finite equilibration time for the atmosphere, and issues of smoothing and aliasing. Finally, we develop a method to fit the stochastic model to the short timeseries of temperature and radiative imbalance by performing a Bayesian inference based on a modified version of the spectral Whittle likelihood. We are thus able to place realistic joint uncertainty estimates on both stochastic forcing and radiative feedbacks derived from observational records. We find that these records are, as of yet, too short to be useful in constraining radiative feedbacks, and we provide estimates of how the uncertainty narrows as a function of record length.

Polymerization and oscillation stuttering in a filamentous model of the subcellular Min oscillation

NASA Astrophysics Data System (ADS)

Rutenberg, Andrew; Sengupta, Supratim; Sain, Anirban; Derr, Julien

2011-03-01

We present a computational model of the E. coli Min oscillation that involves polymerization of MinD filaments followed by depolymerization stimulated by filament-end zones of MinE. Our stochastic model is fully three-dimensional, and tracks the diffusion and interactions of every MinD and MinE molecule. We recover self-organized Min oscillations. We investigate the experimental phenomenon of oscillation stuttering, which we relate to the disruption of MinE tip-binding at the filament scale.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Baldovin-Stella stochastic volatility process and Wiener process mixtures

NASA Astrophysics Data System (ADS)

Peirano, P. P.; Challet, D.

2012-08-01

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distributions and show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

NASA Astrophysics Data System (ADS)

Barnes, Jeff P.; Trout, Colin J.; Lucarelli, Dennis; Clader, B. D.

2017-06-01

We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault-tolerant quantum error correcting circuit for a d =3 Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudothreshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

The role of predictive uncertainty in the operational management of reservoirs

NASA Astrophysics Data System (ADS)

Todini, E.

2014-09-01

The present work deals with the operational management of multi-purpose reservoirs, whose optimisation-based rules are derived, in the planning phase, via deterministic (linear and nonlinear programming, dynamic programming, etc.) or via stochastic (generally stochastic dynamic programming) approaches. In operation, the resulting deterministic or stochastic optimised operating rules are then triggered based on inflow predictions. In order to fully benefit from predictions, one must avoid using them as direct inputs to the reservoirs, but rather assess the "predictive knowledge" in terms of a predictive probability density to be operationally used in the decision making process for the estimation of expected benefits and/or expected losses. Using a theoretical and extremely simplified case, it will be shown why directly using model forecasts instead of the full predictive density leads to less robust reservoir management decisions. Moreover, the effectiveness and the tangible benefits for using the entire predictive probability density instead of the model predicted values will be demonstrated on the basis of the Lake Como management system, operational since 1997, as well as on the basis of a case study on the lake of Aswan.

Modeling cellular compartmentation in one-carbon metabolism

PubMed Central

Scotti, Marco; Stella, Lorenzo; Shearer, Emily J.; Stover, Patrick J.

2015-01-01

Folate-mediated one-carbon metabolism (FOCM) is associated with risk for numerous pathological states including birth defects, cancers, and chronic diseases. Although the enzymes that constitute the biological pathways have been well described and their interdependency through the shared use of folate cofactors appreciated, the biological mechanisms underlying disease etiologies remain elusive. The FOCM network is highly sensitive to nutritional status of several B-vitamins and numerous penetrant gene variants that alter network outputs, but current computational approaches do not fully capture the dynamics and stochastic noise of the system. Combining the stochastic approach with a rule-based representation will help model the intrinsic noise displayed by FOCM, address the limited flexibility of standard simulation methods for coarse-graining the FOCM-associated biochemical processes, and manage the combinatorial complexity emerging from reactions within FOCM that would otherwise be intractable. PMID:23408533

You can run, you can hide: The epidemiology and statistical mechanics of zombies

NASA Astrophysics Data System (ADS)

Alemi, Alexander A.; Bierbaum, Matthew; Myers, Christopher R.; Sethna, James P.

2015-11-01

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.

Optimization for Service Routes of Pallet Service Center Based on the Pallet Pool Mode

PubMed Central

He, Shiwei; Song, Rui

2016-01-01

Service routes optimization (SRO) of pallet service center should meet customers' demand firstly and then, through the reasonable method of lines organization, realize the shortest path of vehicle driving. The routes optimization of pallet service center is similar to the distribution problems of vehicle routing problem (VRP) and Chinese postman problem (CPP), but it has its own characteristics. Based on the relevant research results, the conditions of determining the number of vehicles, the one way of the route, the constraints of loading, and time windows are fully considered, and a chance constrained programming model with stochastic constraints is constructed taking the shortest path of all vehicles for a delivering (recycling) operation as an objective. For the characteristics of the model, a hybrid intelligent algorithm including stochastic simulation, neural network, and immune clonal algorithm is designed to solve the model. Finally, the validity and rationality of the optimization model and algorithm are verified by the case. PMID:27528865

Towards dropout training for convolutional neural networks.

PubMed

Wu, Haibing; Gu, Xiaodong

2015-11-01

Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weighted pooling. We also empirically show that the effect of convolutional dropout is not trivial, despite the dramatically reduced possibility of over-fitting due to the convolutional architecture. Elaborately designing dropout training simultaneously in max-pooling and fully-connected layers, we achieve state-of-the-art performance on MNIST, and very competitive results on CIFAR-10 and CIFAR-100, relative to other approaches without data augmentation. Finally, we compare max-pooling dropout and stochastic pooling, both of which introduce stochasticity based on multinomial distributions at pooling stage. Copyright © 2015 Elsevier Ltd. All rights reserved.

Combinatoric analysis of heterogeneous stochastic self-assembly.

PubMed

D'Orsogna, Maria R; Zhao, Bingyu; Berenji, Bijan; Chou, Tom

2013-09-28

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes

NASA Technical Reports Server (NTRS)

Adeniji-Fashola, A.; Chen, C. P.

1990-01-01

Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the Eulerian and Lagrangian modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.

Moderate stem-cell telomere shortening rate postpones cancer onset in a stochastic model

NASA Astrophysics Data System (ADS)

Holbek, Simon; Bendtsen, Kristian Moss; Juul, Jeppe

2013-10-01

Mammalian cells are restricted from proliferating indefinitely. Telomeres at the end of each chromosome are shortened at cell division and when they reach a critical length, the cell will enter permanent cell cycle arrest—a state known as senescence. This mechanism is thought to be tumor suppressing, as it helps prevent precancerous cells from dividing uncontrollably. Stem cells express the enzyme telomerase, which elongates the telomeres, thereby postponing senescence. However, unlike germ cells and most types of cancer cells, stem cells only express telomerase at levels insufficient to fully maintain the length of their telomeres, leading to a slow decline in proliferation potential. It is not yet fully understood how this decline influences the risk of cancer and the longevity of the organism. We here develop a stochastic model to explore the role of telomere dynamics in relation to both senescence and cancer. The model describes the accumulation of cancerous mutations in a multicellular organism and creates a coherent theoretical framework for interpreting the results of several recent experiments on telomerase regulation. We demonstrate that the longest average cancer-free lifespan before cancer onset is obtained when stem cells start with relatively long telomeres that are shortened at a steady rate at cell division. Furthermore, the risk of cancer early in life can be reduced by having a short initial telomere length. Finally, our model suggests that evolution will favor a shorter than optimal average cancer-free lifespan in order to postpone cancer onset until late in life.

Compressing random microstructures via stochastic Wang tilings.

PubMed

Novák, Jan; Kučerová, Anna; Zeman, Jan

2012-10-01

This Rapid Communication presents a stochastic Wang tiling-based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multidimensional media.

First assembly times and equilibration in stochastic coagulation-fragmentation

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

D’Orsogna, Maria R.; Department of Mathematics, CSUN, Los Angeles, California 91330-8313; Lei, Qi

2015-07-07

We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations ofmore » total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.« less

Stochastic and deterministic causes of streamer branching in liquid dielectrics

NASA Astrophysics Data System (ADS)

Jadidian, Jouya; Zahn, Markus; Lavesson, Nils; Widlund, Ola; Borg, Karl

2013-08-01

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching.

Micro-porous layer stochastic reconstruction and transport parameter determination

NASA Astrophysics Data System (ADS)

El Hannach, Mohamed; Singh, Randhir; Djilali, Ned; Kjeang, Erik

2015-05-01

The Micro-Porous Layer (MPL) is a porous, thin layer commonly used in fuel cells at the interfaces between the catalyst layers and gas diffusion media. It is generally made from spherical carbon nanoparticles and PTFE acting as hydrophobic agent. The scale and brittle nature of the MPL structure makes it challenging to study experimentally. In the present work, a 3D stochastic model is developed to virtually reconstruct the MPL structure. The carbon nanoparticle and PTFE phases are fully distinguished by the algorithm. The model is shown to capture the actual structural morphology of the MPL and is validated by comparing the results to available experimental data. The model shows a good capability in generating a realistic MPL successfully using a set of parameters introduced to capture specific morphological features of the MPL. A numerical model that resolves diffusive transport at the pore scale is used to compute the effective transport properties of the reconstructed MPLs. A parametric study is conducted to illustrate the capability of the model as an MPL design tool that can be used to guide and optimize the functionality of the material.

On Solar Cycle Predictions and Reconstructions

DTIC Science & Technology

2008-12-01

the At present it is still not fully clear whether solar activity optical assumptions (Wilson 1994; Beck el al. I995; Hathaway is purely stochastic... Beck et al. 1995). The Waldmeier effect was found to be a result of (or at least consistent with) var- ious dynamo models, starting with non-linear...Geophys. Res. Lett., 35, 1.20109 Beck . R., Hilbrecht, H., Reinsch, K., & Volker, P. 1995. Solar Astronomy Handbook (Richmond: Willmann-Bell) Beer. J

The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.

PubMed

Caravagna, Giulio; Mauri, Giancarlo; d'Onofrio, Alberto

2013-01-01

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i) the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii) a model of enzymatic futile cycle and (iii) a genetic toggle switch. In (ii) and (iii) we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.

High-resolution stochastic generation of extreme rainfall intensity for urban drainage modelling applications

NASA Astrophysics Data System (ADS)

Peleg, Nadav; Blumensaat, Frank; Molnar, Peter; Fatichi, Simone; Burlando, Paolo

2016-04-01

Urban drainage response is highly dependent on the spatial and temporal structure of rainfall. Therefore, measuring and simulating rainfall at a high spatial and temporal resolution is a fundamental step to fully assess urban drainage system reliability and related uncertainties. This is even more relevant when considering extreme rainfall events. However, the current space-time rainfall models have limitations in capturing extreme rainfall intensity statistics for short durations. Here, we use the STREAP (Space-Time Realizations of Areal Precipitation) model, which is a novel stochastic rainfall generator for simulating high-resolution rainfall fields that preserve the spatio-temporal structure of rainfall and its statistical characteristics. The model enables a generation of rain fields at 102 m and minute scales in a fast and computer-efficient way matching the requirements for hydrological analysis of urban drainage systems. The STREAP model was applied successfully in the past to generate high-resolution extreme rainfall intensities over a small domain. A sub-catchment in the city of Luzern (Switzerland) was chosen as a case study to: (i) evaluate the ability of STREAP to disaggregate extreme rainfall intensities for urban drainage applications; (ii) assessing the role of stochastic climate variability of rainfall in flow response and (iii) evaluate the degree of non-linearity between extreme rainfall intensity and system response (i.e. flow) for a small urban catchment. The channel flow at the catchment outlet is simulated by means of a calibrated hydrodynamic sewer model.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

NASA Astrophysics Data System (ADS)

Costa, Ariadne; Brochini, Ludmila; Kinouchi, Osame

2017-08-01

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

Neutral evolution in a biological population as diffusion in phenotype space: reproduction with local mutation but without selection.

PubMed

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-02

The process of "evolutionary diffusion," i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model

PubMed Central

Pedro, Sansao A.; Abelman, Shirley; Tonnang, Henri E. Z.

2016-01-01

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R0, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency. PMID:28002417

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

NASA Astrophysics Data System (ADS)

Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.

2017-06-01

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model.

PubMed

Pedro, Sansao A; Abelman, Shirley; Tonnang, Henri E Z

2016-12-01

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R0, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency.

Identifying Aircraft and Personnel Needs to Meet On-station Patrol Requirements

DTIC Science & Technology

2014-06-17

One option would be to develop a fully stochastic model that explicitly examined unplanned maintenance ( Marlow and Novak 2013; Mattila et al. 2008...stationed at the base and the serviceability rate, respectively (as in Marlow and Novak 2013). Next, if one assumes that, for the number of available AU...of Intelligent & Robotic Systems 70: 347-359. 7. Marlow D and Novak A (2013). Fleet Sizing Analysis Methodologies for the Royal Australian Navy’s

Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series

NASA Astrophysics Data System (ADS)

Fatichi, S.; Ivanov, V. Y.; Caporali, E.

2013-04-01

This study extends a stochastic downscaling methodology to generation of an ensemble of hourly time series of meteorological variables that express possible future climate conditions at a point-scale. The stochastic downscaling uses general circulation model (GCM) realizations and an hourly weather generator, the Advanced WEather GENerator (AWE-GEN). Marginal distributions of factors of change are computed for several climate statistics using a Bayesian methodology that can weight GCM realizations based on the model relative performance with respect to a historical climate and a degree of disagreement in projecting future conditions. A Monte Carlo technique is used to sample the factors of change from their respective marginal distributions. As a comparison with traditional approaches, factors of change are also estimated by averaging GCM realizations. With either approach, the derived factors of change are applied to the climate statistics inferred from historical observations to re-evaluate parameters of the weather generator. The re-parameterized generator yields hourly time series of meteorological variables that can be considered to be representative of future climate conditions. In this study, the time series are generated in an ensemble mode to fully reflect the uncertainty of GCM projections, climate stochasticity, as well as uncertainties of the downscaling procedure. Applications of the methodology in reproducing future climate conditions for the periods of 2000-2009, 2046-2065 and 2081-2100, using the period of 1962-1992 as the historical baseline are discussed for the location of Firenze (Italy). The inferences of the methodology for the period of 2000-2009 are tested against observations to assess reliability of the stochastic downscaling procedure in reproducing statistics of meteorological variables at different time scales.

Joint Stochastic Inversion of Pre-Stack 3D Seismic Data and Well Logs for High Resolution Hydrocarbon Reservoir Characterization

NASA Astrophysics Data System (ADS)

Torres-Verdin, C.

2007-05-01

This paper describes the successful implementation of a new 3D AVA stochastic inversion algorithm to quantitatively integrate pre-stack seismic amplitude data and well logs. The stochastic inversion algorithm is used to characterize flow units of a deepwater reservoir located in the central Gulf of Mexico. Conventional fluid/lithology sensitivity analysis indicates that the shale/sand interface represented by the top of the hydrocarbon-bearing turbidite deposits generates typical Class III AVA responses. On the other hand, layer- dependent Biot-Gassmann analysis shows significant sensitivity of the P-wave velocity and density to fluid substitution. Accordingly, AVA stochastic inversion, which combines the advantages of AVA analysis with those of geostatistical inversion, provided quantitative information about the lateral continuity of the turbidite reservoirs based on the interpretation of inverted acoustic properties (P-velocity, S-velocity, density), and lithotype (sand- shale) distributions. The quantitative use of rock/fluid information through AVA seismic amplitude data, coupled with the implementation of co-simulation via lithotype-dependent multidimensional joint probability distributions of acoustic/petrophysical properties, yields accurate 3D models of petrophysical properties such as porosity and permeability. Finally, by fully integrating pre-stack seismic amplitude data and well logs, the vertical resolution of inverted products is higher than that of deterministic inversions methods.

Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.

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

Preston, Leiph

Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fractionmore » of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.« less

Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.

Using animation quality metric to improve efficiency of global illumination computation for dynamic environments

NASA Astrophysics Data System (ADS)

Myszkowski, Karol; Tawara, Takehiro; Seidel, Hans-Peter

2002-06-01

In this paper, we consider applications of perception-based video quality metrics to improve the performance of global lighting computations for dynamic environments. For this purpose we extend the Visible Difference Predictor (VDP) developed by Daly to handle computer animations. We incorporate into the VDP the spatio-velocity CSF model developed by Kelly. The CSF model requires data on the velocity of moving patterns across the image plane. We use the 3D image warping technique to compensate for the camera motion, and we conservatively assume that the motion of animated objects (usually strong attractors of the visual attention) is fully compensated by the smooth pursuit eye motion. Our global illumination solution is based on stochastic photon tracing and takes advantage of temporal coherence of lighting distribution, by processing photons both in the spatial and temporal domains. The VDP is used to keep noise inherent in stochastic methods below the sensitivity level of the human observer. As a result a perceptually-consistent quality across all animation frames is obtained.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

Stochastic modeling of wetland-groundwater systems

NASA Astrophysics Data System (ADS)

Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca

2018-02-01

Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.

Neutral Evolution in a Biological Population as Diffusion in Phenotype Space: Reproduction with Local Mutation but without Selection

NASA Astrophysics Data System (ADS)

Lawson, Daniel John; Jensen, Henrik Jeldtoft

2007-03-01

The process of “evolutionary diffusion,” i.e., reproduction with local mutation but without selection in a biological population, resembles standard diffusion in many ways. However, evolutionary diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allows us to understand the large population limit, relates evolution to diffusion, and shows that independent local mutations act as a diffusion of interacting particles taking larger steps.

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

Jin, C.; Potts, I.; Reeks, M. W., E-mail: mike.reeks@ncl.ac.uk

We present a simple stochastic quadrant model for calculating the transport and deposition of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. In this way, we are able to account directly for the influence of ejection and sweeping events as others have done but without resorting tomore » the use of adjustable parameters. Deposition rate predictions for a wide range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition, deposition rates are compared with those obtained from continuous random walk models and Langevin equation based ejection and sweep models which noticeably give significantly lower deposition rates. Various statistics related to the particle near wall behavior are also presented. Finally, we consider the model limitations in using the model to calculate deposition in more complex flows where the near wall turbulence may be significantly different.« less

Evaluation of a Stochastic Inactivation Model for Heat-Activated Spores of Bacillus spp. ▿

PubMed Central

Corradini, Maria G.; Normand, Mark D.; Eisenberg, Murray; Peleg, Micha

2010-01-01

Heat activates the dormant spores of certain Bacillus spp., which is reflected in the “activation shoulder” in their survival curves. At the same time, heat also inactivates the already active and just activated spores, as well as those still dormant. A stochastic model based on progressively changing probabilities of activation and inactivation can describe this phenomenon. The model is presented in a fully probabilistic discrete form for individual and small groups of spores and as a semicontinuous deterministic model for large spore populations. The same underlying algorithm applies to both isothermal and dynamic heat treatments. Its construction does not require the assumption of the activation and inactivation kinetics or knowledge of their biophysical and biochemical mechanisms. A simplified version of the semicontinuous model was used to simulate survival curves with the activation shoulder that are reminiscent of experimental curves reported in the literature. The model is not intended to replace current models to predict dynamic inactivation but only to offer a conceptual alternative to their interpretation. Nevertheless, by linking the survival curve's shape to probabilities of events at the individual spore level, the model explains, and can be used to simulate, the irregular activation and survival patterns of individual and small groups of spores, which might be involved in food poisoning and spoilage. PMID:20453137

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.

Effects of Drift-Shell Splitting by Chorus Waves on Radiation Belt Electrons

NASA Astrophysics Data System (ADS)

Chan, A. A.; Zheng, L.; O'Brien, T. P., III; Tu, W.; Cunningham, G.; Elkington, S. R.; Albert, J.

2015-12-01

Drift shell splitting in the radiation belts breaks all three adiabatic invariants of charged particle motion via pitch angle scattering, and produces new diffusion terms that fully populate the diffusion tensor in the Fokker-Planck equation. Based on the stochastic differential equation method, the Radbelt Electron Model (REM) simulation code allows us to solve such a fully three-dimensional Fokker-Planck equation, and to elucidate the sources and transport mechanisms behind the phase space density variations. REM has been used to perform simulations with an empirical initial phase space density followed by a seed electron injection, with a Tsyganenko 1989 magnetic field model, and with chorus wave and ULF wave diffusion models. Our simulation results show that adding drift shell splitting changes the phase space location of the source to smaller L shells, which typically reduces local electron energization (compared to neglecting drift-shell splitting effects). Simulation results with and without drift-shell splitting effects are compared with Van Allen Probe measurements.

A stochastic approach to uncertainty in the equations of MHD kinematics

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

Phillips, Edward G., E-mail: egphillips@math.umd.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2015-03-01

The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertaintymore » in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.« less

Species Associations in a Species-Rich Subtropical Forest Were Not Well-Explained by Stochastic Geometry of Biodiversity

PubMed Central

Wang, Qinggang; Bao, Dachuan; Guo, Yili; Lu, Junmeng; Lu, Zhijun; Xu, Yaozhan; Zhang, Kuihan; Liu, Haibo; Meng, Hongjie; Jiang, Mingxi; Qiao, Xiujuan; Huang, Handong

2014-01-01

The stochastic dilution hypothesis has been proposed to explain species coexistence in species-rich communities. The relative importance of the stochastic dilution effects with respect to other effects such as competition and habitat filtering required to be tested. In this study, using data from a 25-ha species-rich subtropical forest plot with a strong topographic structure at Badagongshan in central China, we analyzed overall species associations and fine-scale species interactions between 2,550 species pairs. The result showed that: (1) the proportion of segregation in overall species association analysis at 2 m neighborhood in this plot followed the prediction of the stochastic dilution hypothesis that segregations should decrease with species richness but that at 10 m neighborhood was higher than the prediction. (2) The proportion of no association type was lower than the expectation of stochastic dilution hypothesis. (3) Fine-scale species interaction analyses using Heterogeneous Poisson processes as null models revealed a high proportion (47%) of significant species effects. However, the assumption of separation of scale of this method was not fully met in this plot with a strong fine-scale topographic structure. We also found that for species within the same families, fine-scale positive species interactions occurred more frequently and negative ones occurred less frequently than expected by chance. These results suggested effects of environmental filtering other than species interaction in this forest. (4) We also found that arbor species showed a much higher proportion of significant fine-scale species interactions (66%) than shrub species (18%). We concluded that the stochastic dilution hypothesis only be partly supported and environmental filtering left discernible spatial signals in the spatial associations between species in this species-rich subtropical forest with a strong topographic structure. PMID:24824996

Species associations in a species-rich subtropical forest were not well-explained by stochastic geometry of biodiversity.

PubMed

Wang, Qinggang; Bao, Dachuan; Guo, Yili; Lu, Junmeng; Lu, Zhijun; Xu, Yaozhan; Zhang, Kuihan; Liu, Haibo; Meng, Hongjie; Jiang, Mingxi; Qiao, Xiujuan; Huang, Handong

2014-01-01

The stochastic dilution hypothesis has been proposed to explain species coexistence in species-rich communities. The relative importance of the stochastic dilution effects with respect to other effects such as competition and habitat filtering required to be tested. In this study, using data from a 25-ha species-rich subtropical forest plot with a strong topographic structure at Badagongshan in central China, we analyzed overall species associations and fine-scale species interactions between 2,550 species pairs. The result showed that: (1) the proportion of segregation in overall species association analysis at 2 m neighborhood in this plot followed the prediction of the stochastic dilution hypothesis that segregations should decrease with species richness but that at 10 m neighborhood was higher than the prediction. (2) The proportion of no association type was lower than the expectation of stochastic dilution hypothesis. (3) Fine-scale species interaction analyses using Heterogeneous Poisson processes as null models revealed a high proportion (47%) of significant species effects. However, the assumption of separation of scale of this method was not fully met in this plot with a strong fine-scale topographic structure. We also found that for species within the same families, fine-scale positive species interactions occurred more frequently and negative ones occurred less frequently than expected by chance. These results suggested effects of environmental filtering other than species interaction in this forest. (4) We also found that arbor species showed a much higher proportion of significant fine-scale species interactions (66%) than shrub species (18%). We concluded that the stochastic dilution hypothesis only be partly supported and environmental filtering left discernible spatial signals in the spatial associations between species in this species-rich subtropical forest with a strong topographic structure.

A Stochastic Seismic Model for the European Arctic

NASA Astrophysics Data System (ADS)

Hauser, J.; Dyer, K.; Pasyanos, M. E.; Bungum, H.; Faleide, J. I.; Clark, S. A.

2009-12-01

The development of three-dimensional seismic models for the crust and upper mantle has traditionally focused on finding one model that provides the best fit to the data, while observing some regularization constraints. Such deterministic models however ignore a fundamental property of many inverse problems in geophysics, non-uniqueness, that is, if a model can be found to satisfy given datasets an infinite number of alternative models will exist that satisfy the datasets equally well. The solution to the inverse problem presented here is therefore a stochastic model, an ensemble of models that satisfy all available data to the same degree, the posterior distribution. It is based on two sources of information, (1) the data, in this work surface-wave group velocities, regional body-wave travel times, gravity data, compiled 1D velocity models, and thickness relationships between sedimentary rocks and underlying crystalline rocks, and (2) prior information, which is independent from the data. A Monte Carlo Markov Chain (MCMC) algorithm allows us to sample models from the prior distribution and test them against the data to generate the posterior distribution. While being computationally much more expensive, such a stochastic inversion provides a more complete picture of solution space and allows to seamlessly combine various datasets. The resulting stochastic model gives an overview of the different structures that can explain the observed datasets while taking the uncertainties in the data into account. Stochastic models are important for improving seismic monitoring capabilities as they allow to not only predict new observables but also their uncertainties. The model introduced here for the crust and upper mantle structure of the European Arctic is parametrized by a series of 8 layers in an equidistant mesh. Within each layer the seismic parameters (Vp, Vs and density) can vary linearly with depth. This allows to model changes of seismic parameters within the sediments and the crystalline crust without introducing artificial discontinuities that would result from parametrizing the structure using layers with constant seismic parameters. The complex geology of the region, encompassing oceanic crust, continental shelf regions, rift basins and old cratonic crust, and the non-uniform coverage of the region by data with varying levels of uncertainty makes the European Arctic a challenging setting for any imaging technique and therefore an ideal environment for demonstrating the practical advantages of a stochastic model. Maps of sediment thickness and thickness of the crystalline crust derived from the posterior distribution are in good agreement with knowledge of the regional tectonic setting. The predicted uncertainties, which are more important than the absolute values, correlate well with the variation in data coverage and data quality in the region. This indicates that the technique behaves as expected, thus we are properly tuning the methodology by allowing the Markov Chain adequate time to fully sample the model space.

Single-molecule stochastic times in a reversible bimolecular reaction

NASA Astrophysics Data System (ADS)

Keller, Peter; Valleriani, Angelo

2012-08-01

In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.

Stochastic process of pragmatic information for 2D spiral wave turbulence in globally and locally coupled Alief-Panfilov oscillators

NASA Astrophysics Data System (ADS)

Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi

2017-09-01

Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.

Alcoholism Detection by Data Augmentation and Convolutional Neural Network with Stochastic Pooling.

PubMed

Wang, Shui-Hua; Lv, Yi-Ding; Sui, Yuxiu; Liu, Shuai; Wang, Su-Jing; Zhang, Yu-Dong

2017-11-17

Alcohol use disorder (AUD) is an important brain disease. It alters the brain structure. Recently, scholars tend to use computer vision based techniques to detect AUD. We collected 235 subjects, 114 alcoholic and 121 non-alcoholic. Among the 235 image, 100 images were used as training set, and data augmentation method was used. The rest 135 images were used as test set. Further, we chose the latest powerful technique-convolutional neural network (CNN) based on convolutional layer, rectified linear unit layer, pooling layer, fully connected layer, and softmax layer. We also compared three different pooling techniques: max pooling, average pooling, and stochastic pooling. The results showed that our method achieved a sensitivity of 96.88%, a specificity of 97.18%, and an accuracy of 97.04%. Our method was better than three state-of-the-art approaches. Besides, stochastic pooling performed better than other max pooling and average pooling. We validated CNN with five convolution layers and two fully connected layers performed the best. The GPU yielded a 149× acceleration in training and a 166× acceleration in test, compared to CPU.

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 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.

Uncertainty-based Optimization Algorithms in Designing Fractionated Spacecraft

PubMed Central

Ning, Xin; Yuan, Jianping; Yue, Xiaokui

2016-01-01

A fractionated spacecraft is an innovative application of a distributive space system. To fully understand the impact of various uncertainties on its development, launch and in-orbit operation, we use the stochastic missioncycle cost to comprehensively evaluate the survivability, flexibility, reliability and economy of the ways of dividing the various modules of the different configurations of fractionated spacecraft. We systematically describe its concept and then analyze its evaluation and optimal design method that exists during recent years and propose the stochastic missioncycle cost for comprehensive evaluation. We also establish the models of the costs such as module development, launch and deployment and the impacts of their uncertainties respectively. Finally, we carry out the Monte Carlo simulation of the complete missioncycle costs of various configurations of the fractionated spacecraft under various uncertainties and give and compare the probability density distribution and statistical characteristics of its stochastic missioncycle cost, using the two strategies of timing module replacement and non-timing module replacement. The simulation results verify the effectiveness of the comprehensive evaluation method and show that our evaluation method can comprehensively evaluate the adaptability of the fractionated spacecraft under different technical and mission conditions. PMID:26964755

A dissipative random velocity field for fully developed fluid turbulence

NASA Astrophysics Data System (ADS)

Chevillard, Laurent; Pereira, Rodrigo; Garban, Christophe

2016-11-01

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments, including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion shows that energy transfers indeed take place, justifying the dissipative nature of this random field.

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

Jadidian, Jouya; Zahn, Markus; Lavesson, Nils

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer headmore » is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching.« less

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.

PubMed

Herzallah, Randa

2015-03-01

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochasticity in the Expression of LamB and its Affect on λ phage Infection

NASA Astrophysics Data System (ADS)

Chapman, Emily; Wu, Xiao-Lun

2006-03-01

λ phage binds to E. Coli's lamB protein and injects its DNA into the cell. The phage quickly replicates and after a latent period the bacteria bursts, emitting mature phages. We developed a mathematical model based on the known physical events that occur when a λ phage infects an E.Coli cell. The results of these models predict that the bacteria and phage populations become extinct unless the parameters of the model are very finely tuned, which is untrue in the nature. The lamB protein is part of the maltose regulon and can be repressed to minimal levels when grown in the absence of inducer. Therefore, a cell that is not expressing any lamB protein at that moment is resistant against phage infection. We studied the dynamic relationship between λ phage and E. Coli when the concentration of phage greatly outnumbers the concentration of bacteria. We study how the stochasticity of the expression of lamB affects the percentage of cells that the λ phage infects. We show that even in the case when the maltose regulon is fully induced a percentage of cells continue to persist against phage infection.

Kappa and Rater Accuracy: Paradigms and Parameters.

PubMed

Conger, Anthony J

2017-12-01

Drawing parallels to classical test theory, this article clarifies the difference between rater accuracy and reliability and demonstrates how category marginal frequencies affect rater agreement and Cohen's kappa (κ). Category assignment paradigms are developed: comparing raters to a standard (index) versus comparing two raters to one another (concordance), using both nonstochastic and stochastic category membership. Using a probability model to express category assignments in terms of rater accuracy and random error, it is shown that observed agreement (Po) depends only on rater accuracy and number of categories; however, expected agreement (Pe) and κ depend additionally on category frequencies. Moreover, category frequencies affect Pe and κ solely through the variance of the category proportions, regardless of the specific frequencies underlying the variance. Paradoxically, some judgment paradigms involving stochastic categories are shown to yield higher κ values than their nonstochastic counterparts. Using the stated probability model, assignments to categories were generated for 552 combinations of paradigms, rater and category parameters, category frequencies, and number of stimuli. Observed means and standard errors for Po, Pe, and κ were fully consistent with theory expectations. Guidelines for interpretation of rater accuracy and reliability are offered, along with a discussion of alternatives to the basic model.

cuTauLeaping: A GPU-Powered Tau-Leaping Stochastic Simulator for Massive Parallel Analyses of Biological Systems

PubMed Central

Besozzi, Daniela; Pescini, Dario; Mauri, Giancarlo

2014-01-01

Tau-leaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tau-leaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU) provides power-efficient high-performance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tau-leaping simulations, by fully exploiting the Nvidia's Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tau-leaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPU-based tau-leaping implementation when the number of parallel simulations increases, with a break-even directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep analysis to study the oscillatory regimes in the Ras/cAMP/PKA pathway in S. cerevisiae. PMID:24663957

Infinitely divisible cascades to model the statistics of natural images.

PubMed

Chainais, Pierre

2007-12-01

We propose to model the statistics of natural images thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDC). IDC were first introduced in one dimension to provide multifractal time series to model the so-called intermittency phenomenon in hydrodynamical turbulence. We have extended the definition of scalar infinitely divisible cascades from 1 to N dimensions and commented on the relevance of such a model in fully developed turbulence in [1]. In this article, we focus on the particular 2 dimensional case. IDC appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDC for applications to procedural texture synthesis.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

A cloud model based multi-attribute decision making approach for selection and evaluation of groundwater management schemes

NASA Astrophysics Data System (ADS)

Lu, Hongwei; Ren, Lixia; Chen, Yizhong; Tian, Peipei; Liu, Jia

2017-12-01

Due to the uncertainty (i.e., fuzziness, stochasticity and imprecision) existed simultaneously during the process for groundwater remediation, the accuracy of ranking results obtained by the traditional methods has been limited. This paper proposes a cloud model based multi-attribute decision making framework (CM-MADM) with Monte Carlo for the contaminated-groundwater remediation strategies selection. The cloud model is used to handle imprecise numerical quantities, which can describe the fuzziness and stochasticity of the information fully and precisely. In the proposed approach, the contaminated concentrations are aggregated via the backward cloud generator and the weights of attributes are calculated by employing the weight cloud module. A case study on the remedial alternative selection for a contaminated site suffering from a 1,1,1-trichloroethylene leakage problem in Shanghai, China is conducted to illustrate the efficiency and applicability of the developed approach. Totally, an attribute system which consists of ten attributes were used for evaluating each alternative through the developed method under uncertainty, including daily total pumping rate, total cost and cloud model based health risk. Results indicated that A14 was evaluated to be the most preferred alternative for the 5-year, A5 for the 10-year, A4 for the 15-year and A6 for the 20-year remediation.

Relatively slow stochastic gene-state switching in the presence of positive feedback significantly broadens the region of bimodality through stabilizing the uninduced phenotypic state.

PubMed

Ge, Hao; Wu, Pingping; Qian, Hong; Xie, Xiaoliang Sunney

2018-03-01

Within an isogenic population, even in the same extracellular environment, individual cells can exhibit various phenotypic states. The exact role of stochastic gene-state switching regulating the transition among these phenotypic states in a single cell is not fully understood, especially in the presence of positive feedback. Recent high-precision single-cell measurements showed that, at least in bacteria, switching in gene states is slow relative to the typical rates of active transcription and translation. Hence using the lac operon as an archetype, in such a region of operon-state switching, we present a fluctuating-rate model for this classical gene regulation module, incorporating the more realistic operon-state switching mechanism that was recently elucidated. We found that the positive feedback mechanism induces bistability (referred to as deterministic bistability), and that the parameter range for its occurrence is significantly broadened by stochastic operon-state switching. We further show that in the absence of positive feedback, operon-state switching must be extremely slow to trigger bistability by itself. However, in the presence of positive feedback, which stabilizes the induced state, the relatively slow operon-state switching kinetics within the physiological region are sufficient to stabilize the uninduced state, together generating a broadened parameter region of bistability (referred to as stochastic bistability). We illustrate the opposite phenotype-transition rate dependence upon the operon-state switching rates in the two types of bistability, with the aid of a recently proposed rate formula for fluctuating-rate models. The rate formula also predicts a maximal transition rate in the intermediate region of operon-state switching, which is validated by numerical simulations in our model. Overall, our findings suggest a biological function of transcriptional "variations" among genetically identical cells, for the emergence of bistability and transition between phenotypic states.

Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.

PubMed

Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard

2012-01-01

Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting hospitals to effectively manage time and resources in clinical pathway.

Developing Stochastic Models as Inputs for High-Frequency Ground Motion Simulations

NASA Astrophysics Data System (ADS)

Savran, William Harvey

High-frequency ( 10 Hz) deterministic ground motion simulations are challenged by our understanding of the small-scale structure of the earth's crust and the rupture process during an earthquake. We will likely never obtain deterministic models that can accurately describe these processes down to the meter scale length required for broadband wave propagation. Instead, we can attempt to explain the behavior, in a statistical sense, by including stochastic models defined by correlations observed in the natural earth and through physics based simulations of the earthquake rupture process. Toward this goal, we develop stochastic models to address both of the primary considerations for deterministic ground motion simulations: namely, the description of the material properties in the crust, and broadband earthquake source descriptions. Using borehole sonic log data recorded in Los Angeles basin, we estimate the spatial correlation structure of the small-scale fluctuations in P-wave velocities by determining the best-fitting parameters of a von Karman correlation function. We find that Hurst exponents, nu, between 0.0-0.2, vertical correlation lengths, az, of 15-150m, an standard deviation, sigma of about 5% characterize the variability in the borehole data. Usin these parameters, we generated a stochastic model of velocity and density perturbations and combined with leading seismic velocity models to perform a validation exercise for the 2008, Chino Hills, CA using heterogeneous media. We find that models of velocity and density perturbations can have significant effects on the wavefield at frequencies as low as 0.3 Hz, with ensemble median values of various ground motion metrics varying up to +/-50%, at certain stations, compared to those computed solely from the CVM. Finally, we develop a kinematic rupture generator based on dynamic rupture simulations on geometrically complex faults. We analyze 100 dynamic rupture simulations on strike-slip faults ranging from Mw 6.4-7.2. We find that our dynamic simulations follow empirical scaling relationships for inter-plate strike-slip events, and provide source spectra comparable with an o -2 model. Our rupture generator reproduces GMPE medians and intra-event standard deviations spectral accelerations for an ensemble of 10 Hz fully-deterministic ground motion simulations, as compared to NGA West2 GMPE relationships up to 0.2 seconds.

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

Groundwater Model Validation

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

Ahmed E. Hassan

2006-01-24

Models have an inherent uncertainty. The difficulty in fully characterizing the subsurface environment makes uncertainty an integral component of groundwater flow and transport models, which dictates the need for continuous monitoring and improvement. Building and sustaining confidence in closure decisions and monitoring networks based on models of subsurface conditions require developing confidence in the models through an iterative process. The definition of model validation is postulated as a confidence building and long-term iterative process (Hassan, 2004a). Model validation should be viewed as a process not an end result. Following Hassan (2004b), an approach is proposed for the validation process ofmore » stochastic groundwater models. The approach is briefly summarized herein and detailed analyses of acceptance criteria for stochastic realizations and of using validation data to reduce input parameter uncertainty are presented and applied to two case studies. During the validation process for stochastic models, a question arises as to the sufficiency of the number of acceptable model realizations (in terms of conformity with validation data). Using a hierarchical approach to make this determination is proposed. This approach is based on computing five measures or metrics and following a decision tree to determine if a sufficient number of realizations attain satisfactory scores regarding how they represent the field data used for calibration (old) and used for validation (new). The first two of these measures are applied to hypothetical scenarios using the first case study and assuming field data consistent with the model or significantly different from the model results. In both cases it is shown how the two measures would lead to the appropriate decision about the model performance. Standard statistical tests are used to evaluate these measures with the results indicating they are appropriate measures for evaluating model realizations. The use of validation data to constrain model input parameters is shown for the second case study using a Bayesian approach known as Markov Chain Monte Carlo. The approach shows a great potential to be helpful in the validation process and in incorporating prior knowledge with new field data to derive posterior distributions for both model input and output.« less

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.

Gambling with Superconducting Fluctuations

NASA Astrophysics Data System (ADS)

Foltyn, Marek; Zgirski, Maciej

2015-08-01

Josephson junctions and superconducting nanowires, when biased close to superconducting critical current, can switch to a nonzero voltage state by thermal or quantum fluctuations. The process is understood as an escape of a Brownian particle from a metastable state. Since this effect is fully stochastic, we propose to use it for generating random numbers. We present protocol for obtaining random numbers and test the experimentally harvested data for their fidelity. Our work is prerequisite for using the Josephson junction as a tool for stochastic (probabilistic) determination of physical parameters such as magnetic flux, temperature, and current.

A simplified model for dynamics of cell rolling and cell-surface adhesion

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

Cimrák, Ivan, E-mail: ivan.cimrak@fri.uniza.sk

2015-03-10

We propose a three dimensional model for the adhesion and rolling of biological cells on surfaces. We study cells moving in shear flow above a wall to which they can adhere via specific receptor-ligand bonds based on receptors from selectin as well as integrin family. The computational fluid dynamics are governed by the lattice-Boltzmann method. The movement and the deformation of the cells is described by the immersed boundary method. Both methods are fully coupled by implementing a two-way fluid-structure interaction. The adhesion mechanism is modelled by adhesive bonds including stochastic rules for their creation and rupture. We explore amore » simplified model with dissociation rate independent of the length of the bonds. We demonstrate that this model is able to resemble the mesoscopic properties, such as velocity of rolling cells.« less

Systematic parameter inference in stochastic mesoscopic modeling

NASA Astrophysics Data System (ADS)

Lei, Huan; Yang, Xiu; Li, Zhen; Karniadakis, George Em

2017-02-01

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are "sparse". The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Unification theory of optimal life histories and linear demographic models in internal stochasticity.

PubMed

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

PubMed Central

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

Seeking parsimony in hydrology and water resources technology

NASA Astrophysics Data System (ADS)

Koutsoyiannis, D.

2009-04-01

The principle of parsimony, also known as the principle of simplicity, the principle of economy and Ockham's razor, advises scientists to prefer the simplest theory among those that fit the data equally well. In this, it is an epistemic principle but reflects an ontological characterization that the universe is ultimately parsimonious. Is this principle useful and can it really be reconciled with, and implemented to, our modelling approaches of complex hydrological systems, whose elements and events are extraordinarily numerous, different and unique? The answer underlying the mainstream hydrological research of the last two decades seems to be negative. Hopes were invested to the power of computers that would enable faithful and detailed representation of the diverse system elements and the hydrological processes, based on merely "first principles" and resulting in "physically-based" models that tend to approach in complexity the real world systems. Today the account of such research endeavour seems not positive, as it did not improve model predictive capacity and processes comprehension. A return to parsimonious modelling seems to be again the promising route. The experience from recent research and from comparisons of parsimonious and complicated models indicates that the former can facilitate insight and comprehension, improve accuracy and predictive capacity, and increase efficiency. In addition - and despite aspiration that "physically based" models will have lower data requirements and, even, they ultimately become "data-free" - parsimonious models require fewer data to achieve the same accuracy with more complicated models. Naturally, the concepts that reconcile the simplicity of parsimonious models with the complexity of hydrological systems are probability theory and statistics. Probability theory provides the theoretical basis for moving from a microscopic to a macroscopic view of phenomena, by mapping sets of diverse elements and events of hydrological systems to single numbers (a probability or an expected value), and statistics provides the empirical basis of summarizing data, making inference from them, and supporting decision making in water resource management. Unfortunately, the current state of the art in probability, statistics and their union, often called stochastics, is not fully satisfactory for the needs of modelling of hydrological and water resource systems. A first problem is that stochastic modelling has traditionally relied on classical statistics, which is based on the independent "coin-tossing" prototype, rather than on the study of real-world systems whose behaviour is very different from the classical prototype. A second problem is that the stochastic models (particularly the multivariate ones) are often not parsimonious themselves. Therefore, substantial advancement of stochastics is necessary in a new paradigm of parsimonious hydrological modelling. These ideas are illustrated using several examples, namely: (a) hydrological modelling of a karst system in Bosnia and Herzegovina using three different approaches ranging from parsimonious to detailed "physically-based"; (b) parsimonious modelling of a peculiar modified catchment in Greece; (c) a stochastic approach that can replace parameter-excessive ARMA-type models with a generalized algorithm that produces any shape of autocorrelation function (consistent with the accuracy provided by the data) using a couple of parameters; (d) a multivariate stochastic approach which replaces a huge number of parameters estimated from data with coefficients estimated by the principle of maximum entropy; and (e) a parsimonious approach for decision making in multi-reservoir systems using a handful of parameters instead of thousands of decision variables.

NF-κB dynamics show digital activation and analog information processing in cells

NASA Astrophysics Data System (ADS)

Tay, Savas; Hughey, Jake; Lee, Timothy; Lipniacki, Tomasz; Covert, Markus; Quake, Stephen

2010-03-01

Cells operate in ever changing environments using extraordinary communication capabilities. Cell-to-cell communication is mediated by signaling molecules that form spatiotemporal concentration gradients, which requires cells to respond to a wide range of signal intensities. We used high-throughput microfluidic cell culture, quantitative gene expression analysis and mathematical modeling to investigate how single mammalian cells respond to different concentrations of the signaling molecule TNF-α via the transcription factor NF-κB. We measured NF-κB activity in thousands of live cells under TNF-α doses covering four orders of magnitude. In contrast to population studies, the activation is a stochastic, switch-like process at the single cell level with fewer cells responding at lower doses. The activated cells respond fully and express early genes independent of the TNF-α concentration, while only high dose stimulation results in the expression of late genes. Cells also encode a set of analog parameters such as the NF-κB peak intensity, response time and number of oscillations to modulate the outcome. We developed a stochastic model that reproduces both the digital and analog dynamics as well as the gene expression profiles at all measured conditions, constituting a broadly applicable model for TNF-α induced NF-κB signaling in various types of cells.

On Designing Multicore-Aware Simulators for Systems Biology Endowed with OnLine Statistics

PubMed Central

Calcagno, Cristina; Coppo, Mario

2014-01-01

The paper arguments are on enabling methodologies for the design of a fully parallel, online, interactive tool aiming to support the bioinformatics scientists .In particular, the features of these methodologies, supported by the FastFlow parallel programming framework, are shown on a simulation tool to perform the modeling, the tuning, and the sensitivity analysis of stochastic biological models. A stochastic simulation needs thousands of independent simulation trajectories turning into big data that should be analysed by statistic and data mining tools. In the considered approach the two stages are pipelined in such a way that the simulation stage streams out the partial results of all simulation trajectories to the analysis stage that immediately produces a partial result. The simulation-analysis workflow is validated for performance and effectiveness of the online analysis in capturing biological systems behavior on a multicore platform and representative proof-of-concept biological systems. The exploited methodologies include pattern-based parallel programming and data streaming that provide key features to the software designers such as performance portability and efficient in-memory (big) data management and movement. Two paradigmatic classes of biological systems exhibiting multistable and oscillatory behavior are used as a testbed. PMID:25050327

On designing multicore-aware simulators for systems biology endowed with OnLine statistics.

PubMed

Aldinucci, Marco; Calcagno, Cristina; Coppo, Mario; Damiani, Ferruccio; Drocco, Maurizio; Sciacca, Eva; Spinella, Salvatore; Torquati, Massimo; Troina, Angelo

2014-01-01

The paper arguments are on enabling methodologies for the design of a fully parallel, online, interactive tool aiming to support the bioinformatics scientists .In particular, the features of these methodologies, supported by the FastFlow parallel programming framework, are shown on a simulation tool to perform the modeling, the tuning, and the sensitivity analysis of stochastic biological models. A stochastic simulation needs thousands of independent simulation trajectories turning into big data that should be analysed by statistic and data mining tools. In the considered approach the two stages are pipelined in such a way that the simulation stage streams out the partial results of all simulation trajectories to the analysis stage that immediately produces a partial result. The simulation-analysis workflow is validated for performance and effectiveness of the online analysis in capturing biological systems behavior on a multicore platform and representative proof-of-concept biological systems. The exploited methodologies include pattern-based parallel programming and data streaming that provide key features to the software designers such as performance portability and efficient in-memory (big) data management and movement. Two paradigmatic classes of biological systems exhibiting multistable and oscillatory behavior are used as a testbed.

Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides

DTIC Science & Technology

2009-01-01

STOCHASTIC LANCHESTER AIR-TO-AIR CAMPAIGN MODEL MODEL DESCRIPTION AND USERS GUIDES—2009 REPORT PA702T1 Rober t V. Hemm Jr. Dav id A . Lee...LMI © 2009. ALL RIGHTS RESERVED. Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides—2009 PA702T1/JANUARY...2009 Executive Summary This report documents the latest version of the Stochastic Lanchester Air-to-Air Campaign Model (SLAACM), developed by LMI for

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

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

PubMed

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

Regional-specific Stochastic Simulation of Spatially-distributed Ground-motion Time Histories using Wavelet Packet Analysis

NASA Astrophysics Data System (ADS)

Huang, D.; Wang, G.

2014-12-01

Stochastic simulation of spatially distributed ground-motion time histories is important for performance-based earthquake design of geographically distributed systems. In this study, we develop a novel technique to stochastically simulate regionalized ground-motion time histories using wavelet packet analysis. First, a transient acceleration time history is characterized by wavelet-packet parameters proposed by Yamamoto and Baker (2013). The wavelet-packet parameters fully characterize ground-motion time histories in terms of energy content, time- frequency-domain characteristics and time-frequency nonstationarity. This study further investigates the spatial cross-correlations of wavelet-packet parameters based on geostatistical analysis of 1500 regionalized ground motion data from eight well-recorded earthquakes in California, Mexico, Japan and Taiwan. The linear model of coregionalization (LMC) is used to develop a permissible spatial cross-correlation model for each parameter group. The geostatistical analysis of ground-motion data from different regions reveals significant dependence of the LMC structure on regional site conditions, which can be characterized by the correlation range of Vs30 in each region. In general, the spatial correlation and cross-correlation of wavelet-packet parameters are stronger if the site condition is more homogeneous. Using the regional-specific spatial cross-correlation model and cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground-motion time histories can be synthesized. Case studies and blind tests demonstrated that the simulated ground motions generally agree well with the actual recorded data, if the influence of regional-site conditions is considered. The developed method has great potential to be used in computational-based seismic analysis and loss estimation in a regional scale.

Stochastic effects in a seasonally forced epidemic model

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.

2010-10-01

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Casein Kinase II Regulation of the Hot1 Transcription Factor Promotes Stochastic Gene Expression*

PubMed Central

Burns, Laura T.; Wente, Susan R.

2014-01-01

In Saccharomyces cerevisiae, Hog1 MAPK is activated and induces a transcriptional program in response to hyperosmotic stress. Several Hog1-responsive genes exhibit stochastic transcription, resulting in cell-to-cell variability in mRNA and protein levels. However, the mechanisms governing stochastic gene activity are not fully defined. Here we uncover a novel role for casein kinase II (CK2) in the cellular response to hyperosmotic stress. CK2 interacts with and phosphorylates the Hot1 transcription factor; however, Hot1 phosphorylation is not sufficient for controlling the stochastic response. The CK2 protein itself is required to negatively regulate mRNA expression of Hot1-responsive genes and Hot1 enrichment at target promoters. Single-cell gene expression analysis reveals altered activation of Hot1-targeted STL1 in ck2 mutants, resulting in a bimodal to unimodal shift in expression. Together, this work reveals a novel CK2 function during the hyperosmotic stress response that promotes cell-to-cell variability in gene expression. PMID:24817120

[Gene method for inconsistent hydrological frequency calculation. I: Inheritance, variability and evolution principles of hydrological genes].

PubMed

Xie, Ping; Wu, Zi Yi; Zhao, Jiang Yan; Sang, Yan Fang; Chen, Jie

2018-04-01

A stochastic hydrological process is influenced by both stochastic and deterministic factors. A hydrological time series contains not only pure random components reflecting its inheri-tance characteristics, but also deterministic components reflecting variability characteristics, such as jump, trend, period, and stochastic dependence. As a result, the stochastic hydrological process presents complicated evolution phenomena and rules. To better understand these complicated phenomena and rules, this study described the inheritance and variability characteristics of an inconsistent hydrological series from two aspects: stochastic process simulation and time series analysis. In addition, several frequency analysis approaches for inconsistent time series were compared to reveal the main problems in inconsistency study. Then, we proposed a new concept of hydrological genes origined from biological genes to describe the inconsistent hydrolocal processes. The hydrologi-cal genes were constructed using moments methods, such as general moments, weight function moments, probability weight moments and L-moments. Meanwhile, the five components, including jump, trend, periodic, dependence and pure random components, of a stochastic hydrological process were defined as five hydrological bases. With this method, the inheritance and variability of inconsistent hydrological time series were synthetically considered and the inheritance, variability and evolution principles were fully described. Our study would contribute to reveal the inheritance, variability and evolution principles in probability distribution of hydrological elements.

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

NASA Astrophysics Data System (ADS)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

On Using Surrogates with Genetic Programming.

PubMed

Hildebrandt, Torsten; Branke, Jürgen

2015-01-01

One way to accelerate evolutionary algorithms with expensive fitness evaluations is to combine them with surrogate models. Surrogate models are efficiently computable approximations of the fitness function, derived by means of statistical or machine learning techniques from samples of fully evaluated solutions. But these models usually require a numerical representation, and therefore cannot be used with the tree representation of genetic programming (GP). In this paper, we present a new way to use surrogate models with GP. Rather than using the genotype directly as input to the surrogate model, we propose using a phenotypic characterization. This phenotypic characterization can be computed efficiently and allows us to define approximate measures of equivalence and similarity. Using a stochastic, dynamic job shop scenario as an example of simulation-based GP with an expensive fitness evaluation, we show how these ideas can be used to construct surrogate models and improve the convergence speed and solution quality of GP.

Agent based reasoning for the non-linear stochastic models of long-range memory

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Gontis, V.

2012-02-01

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment II.

PubMed

Liu, Meng; Wang, Ke

2010-12-07

This is a continuation of our paper [Liu, M., Wang, K., 2010. Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment, J. Theor. Biol. 264, 934-944]. Taking both white noise and colored noise into account, a stochastic single-species model under regime switching in a polluted environment is studied. Sufficient conditions for extinction, stochastic nonpersistence in the mean, stochastic weak persistence and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is obtained. The results show that a different type of noise has a different effect on the survival results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

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

Spill, Fabian, E-mail: fspill@bu.edu; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; Guerrero, Pilar

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and smallmore » in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less

Stochastic Coloured Petrinet Based Healthcare Infrastructure Interdependency Model

NASA Astrophysics Data System (ADS)

Nukavarapu, Nivedita; Durbha, Surya

2016-06-01

The Healthcare Critical Infrastructure (HCI) protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI) such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN) modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

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.

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Economic consequences of paratuberculosis control in dairy cattle: A stochastic modeling study.

PubMed

Smith, R L; Al-Mamun, M A; Gröhn, Y T

2017-03-01

The cost of paratuberculosis to dairy herds, through decreased milk production, early culling, and poor reproductive performance, has been well-studied. The benefit of control programs, however, has been debated. A recent stochastic compartmental model for paratuberculosis transmission in US dairy herds was modified to predict herd net present value (NPV) over 25 years in herds of 100 and 1000 dairy cattle with endemic paratuberculosis at initial prevalence of 10% and 20%. Control programs were designed by combining 5 tests (none, fecal culture, ELISA, PCR, or calf testing), 3 test-related culling strategies (all test-positive, high-positive, or repeated positive), 2 test frequencies (annual and biannual), 3 hygiene levels (standard, moderate, or improved), and 2 cessation decisions (testing ceased after 5 negative whole-herd tests or testing continued). Stochastic dominance was determined for each herd scenario; no control program was fully dominant for maximizing herd NPV in any scenario. Use of the ELISA test was generally preferred in all scenarios, but no paratuberculosis control was highly preferred for the small herd with 10% initial prevalence and was frequently preferred in other herd scenarios. Based on their effect on paratuberculosis alone, hygiene improvements were not found to be as cost-effective as test-and-cull strategies in most circumstances. Global sensitivity analysis found that economic parameters, such as the price of milk, had more influence on NPV than control program-related parameters. We conclude that paratuberculosis control can be cost effective, and multiple control programs can be applied for equivalent economic results. Copyright © 2017 Elsevier B.V. All rights reserved.

Suitability of Synthetic Driving Profiles from Traffic Micro-Simulation for Real-World Energy Analysis: Preprint

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

Hou, Yunfei; Wood, Eric; Burton, Evan

A shift towards increased levels of driving automation is generally expected to result in improved safety and traffic congestion outcomes. However, little empirical data exists to estimate the impact that automated driving could have on energy consumption and greenhouse gas emissions. In the absence of empirical data on differences between drive cycles from present day vehicles (primarily operated by humans) and future vehicles (partially or fully operated by computers) one approach is to model both situations over identical traffic conditions. Such an exercise requires traffic micro-simulation to not only accurately model vehicle operation under high levels of automation, but alsomore » (and potentially more challenging) vehicle operation under present day human drivers. This work seeks to quantify the ability of a commercial traffic micro-simulation program to accurately model real-world drive cycles in vehicles operated primarily by humans in terms of driving speed, acceleration, and simulated fuel economy. Synthetic profiles from models of freeway and arterial facilities near Atlanta, Georgia, are compared to empirical data collected from real-world drivers on the same facilities. Empirical and synthetic drive cycles are then simulated in a powertrain efficiency model to enable comparison on the basis of fuel economy. Synthetic profiles from traffic micro-simulation were found to exhibit low levels of transient behavior relative to the empirical data. Even with these differences, the synthetic and empirical data in this study agree well in terms of driving speed and simulated fuel economy. The differences in transient behavior between simulated and empirical data suggest that larger stochastic contributions in traffic micro-simulation (relative to those present in the traffic micro-simulation tool used in this study) are required to fully capture the arbitrary elements of human driving. Interestingly, the lack of stochastic contributions from models of human drivers in this study did not result in a significant discrepancy between fuel economy simulations based on synthetic and empirical data; a finding with implications on the potential energy efficiency gains of automated vehicle technology.« less

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.

Simulation of Stochastic Processes by Coupled ODE-PDE

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Effects of stochastic sodium channels on extracellular excitation of myelinated nerve fibers.

PubMed

Mino, Hiroyuki; Grill, Warren M

2002-06-01

The effects of the stochastic gating properties of sodium channels on the extracellular excitation properties of mammalian nerve fibers was determined by computer simulation. To reduce computation time, a hybrid multicompartment cable model including five central nodes of Ranvier containing stochastic sodium channels and 16 flanking nodes containing detenninistic membrane dynamics was developed. The excitation properties of the hybrid cable model were comparable with those of a full stochastic cable model including 21 nodes of Ranvier containing stochastic sodium channels, indicating the validity of the hybrid cable model. The hybrid cable model was used to investigate whether or not the excitation properties of extracellularly activated fibers were influenced by the stochastic gating of sodium channels, including spike latencies, strength-duration (SD), current-distance (IX), and recruitment properties. The stochastic properties of the sodium channels in the hybrid cable model had the greatest impact when considering the temporal dynamics of nerve fibers, i.e., a large variability in latencies, while they did not influence the SD, IX, or recruitment properties as compared with those of the conventional deterministic cable model. These findings suggest that inclusion of stochastic nodes is not important for model-based design of stimulus waveforms for activation of motor nerve fibers. However, in cases where temporal fine structure is important, for example in sensory neural prostheses in the auditory and visual systems, the stochastic properties of the sodium channels may play a key role in the design of stimulus waveforms.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

NASA Astrophysics Data System (ADS)

Chang, Zhengbo; Meng, Xinzhu; Lu, Xiao

2017-04-01

This paper presents a stochastic SIRS epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis, and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model. We firstly investigate the boundness and extinction of the stochastic system. Furthermore, we use Ito's formula, the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases. The results indicate that stochastic fluctuations can suppress the disease outbreak. Finally, numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results.

Inner Core Anisotropy: Can Seismic Observations be Reconciled with Ab Initio Calculations of Elasticity?

NASA Astrophysics Data System (ADS)

Song, X.; Jordan, T. H.

2016-12-01

Body-wave and normal-mode observations have revealed an inner-core structure that is radially layered, axially anisotropic, and hemispherically asymmetric. Previous theoretical studies have examined the consistency of these features with the elasticity of iron crystals thought to dominate inner-core composition, but a fully consistent model has been elusive. Here we compare the seismic observation with effective-medium models derived from ab initio calculations of the elasticity tensors for hcp-Fe and bcc-Fe. Our estimates are based on Jordan's (GJI, 2015) effective medium theory, which is derived from a self-consistent, second-order Born approximation. The theory provides closed-form expressions for the effective elastic parameters of 3D anisotropic, heterogeneous media in which the local anisotropy is a constant hexagonal stiffness tensor C stochastically oriented about a constant symmetry axis \\hat{s} and the statistics of the small-scale heterogeneities are transversely isotropic in the plane perpendicular to \\hat{s}. The stochastic model is then described by a dimensionless "aspect ratio of the heterogeneity", 0 ≤ η < ∞, and a dimensionless "orientation ratio of the anisotropy", 0 ≤ ξ < ∞. The latter determines the degree to which the axis of C is aligned with \\hat{s}. We compute the loci of models with \\hat{s} oriented along the Earth's rotational axis ( \\hat{s} = north) by varying ξ and η for various ab initio estimates of C. We show that a lot of widely used estimates of C are inconsistent with most published normal-mode models of inner-core anisotropy. In particular, if the P-wave fast axis aligns with the rotational axis, which is required to satisfy the body-wave observations, then these hcp-Fe models predict that the fast polarization of the S waves is in the plane perpendicular to \\hat{s}, which disagrees with most normal-mode models. We have attempted to resolve this discrepancy by examining alternative hcp-Fe models, including radially anisotropic distributions of stochastic anisotropy and heterogeneity (i.e., where \\hat{s} = \\hat{r}), as well as bcc-Fe models. Our calculations constrain the form of C needed to satisfy the seismological inferences.

Quantum simulation of a quantum stochastic walk

NASA Astrophysics Data System (ADS)

Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.

2017-03-01

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.

Stochastic Human Exposure and Dose Simulation Model for Pesticides

EPA Science Inventory

SHEDS-Pesticides (Stochastic Human Exposure and Dose Simulation Model for Pesticides) is a physically-based stochastic model developed to quantify exposure and dose of humans to multimedia, multipathway pollutants. Probabilistic inputs are combined in physical/mechanistic algorit...

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction

DTIC Science & Technology

2016-02-25

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction We have completed a short program of theoretical research...on dimensional reduction and approximation of models based on quantum stochastic differential equations. Our primary results lie in the area of...2211 quantum probability, quantum stochastic differential equations REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR

On predicting monitoring system effectiveness

NASA Astrophysics Data System (ADS)

Cappello, Carlo; Sigurdardottir, Dorotea; Glisic, Branko; Zonta, Daniele; Pozzi, Matteo

2015-03-01

While the objective of structural design is to achieve stability with an appropriate level of reliability, the design of systems for structural health monitoring is performed to identify a configuration that enables acquisition of data with an appropriate level of accuracy in order to understand the performance of a structure or its condition state. However, a rational standardized approach for monitoring system design is not fully available. Hence, when engineers design a monitoring system, their approach is often heuristic with performance evaluation based on experience, rather than on quantitative analysis. In this contribution, we propose a probabilistic model for the estimation of monitoring system effectiveness based on information available in prior condition, i.e. before acquiring empirical data. The presented model is developed considering the analogy between structural design and monitoring system design. We assume that the effectiveness can be evaluated based on the prediction of the posterior variance or covariance matrix of the state parameters, which we assume to be defined in a continuous space. Since the empirical measurements are not available in prior condition, the estimation of the posterior variance or covariance matrix is performed considering the measurements as a stochastic variable. Moreover, the model takes into account the effects of nuisance parameters, which are stochastic parameters that affect the observations but cannot be estimated using monitoring data. Finally, we present an application of the proposed model to a real structure. The results show how the model enables engineers to predict whether a sensor configuration satisfies the required performance.

Systematic parameter inference in stochastic mesoscopic modeling

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

Lei, Huan; Yang, Xiu; Li, Zhen

2017-02-01

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the priormore » knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.« less

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

NASA Astrophysics Data System (ADS)

Chen, Can; Kang, Yanmei

2017-01-01

A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.

Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

NASA Astrophysics Data System (ADS)

Sudakov, Ivan

Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

Effects of Stochastic Traffic Flow Model on Expected System Performance

DTIC Science & Technology

2012-12-01

NSWC-PCD has made considerable improvements to their pedestrian flow modeling . In addition to the linear paths, the 2011 version now includes...using stochastic paths. 2.2 Linear Paths vs. Stochastic Paths 2.2.1 Linear Paths and Direct Maximum Pd Calculation Modeling pedestrian traffic flow...as a stochastic process begins with the linear path model . Let the detec- tion area be R x C voxels. This creates C 2 total linear paths, path(Cs

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.

Full particle orbit effects in regular and stochastic magnetic fields

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

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

DOE PAGES

Ogawa, Shun; Cambon, Benjamin P.; Leoncini, Xavier; ...

2016-07-18

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, themore » particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.« less

Full particle orbit effects in regular and stochastic magnetic fields

NASA Astrophysics Data System (ADS)

Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel; del Castillo-Negrete, Diego; Dif-Pradalier, Guilhem; Garbet, Xavier

2016-07-01

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

Stochastic stability assessment of a semi-free piston engine generator concept

NASA Astrophysics Data System (ADS)

Kigezi, T. N.; Gonzalez Anaya, J. A.; Dunne, J. F.

2016-09-01

Small engines, as power generators with low-noise and vibration characteristics, are needed in two niche application areas: as electric vehicle range extenders and as domestic micro Combined Heat and Power systems. A recent semi-free piston design known as the AMOCATIC generator fully meets this requirement. The engine potentially allows for high energy conversion efficiencies at resonance derived from having a mass and spring assembly. As with free-piston engines in general, stability and control of piston motion has been cited as the prime challenge limiting the technology's widespread application. Using physical principles, we derive in this paper two important results: an energy balance criterion and a related general stability criterion for a semi-free piston engine. Control is achieved by systematically designing a Proportional Integral (PI) controller using a control-oriented engine model for which a specific stability condition is stated. All results are presented in closed form throughout the paper. Simulation results under stochastic pressure conditions show that the proposed energy balance, stability criterion, and PI controller, operate as predicted to yield stable engine operation at fixed compression ratio.

Post-transcriptional regulation tends to attenuate the mRNA noise and to increase the mRNA gain

NASA Astrophysics Data System (ADS)

Shi, Changhong; Wang, Shuqiang; Zhou, Tianshou; Jiang, Yiguo

2015-10-01

Post-transcriptional regulation is ubiquitous in prokaryotic and eukaryotic cells, but how it impacts gene expression remains to be fully explored. Here, we analyze a simple gene model in which we assume that mRNAs are produced in a constitutive manner but are regulated post-transcriptionally by a decapping enzyme that switches between the active state and the inactive state. We derive the analytical mRNA distribution governed by a chemical master equation, which can be well used to analyze the mechanism of how post-transcription regulation influences the mRNA expression level including the mRNA noise. We demonstrate that the mean mRNA level in the stochastic case is always higher than that in the deterministic case due to the stochastic effect of the enzyme, but the size of the increased part depends mainly on the switching rates between two enzyme states. More interesting is that we find that in contrast to transcriptional regulation, post-transcriptional regulation tends to attenuate noise in mRNA. Our results provide insight into the role of post-transcriptional regulation in controlling the transcriptional noise.

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.

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.

Hybrid ODE/SSA methods and the cell cycle model

NASA Astrophysics Data System (ADS)

Wang, S.; Chen, M.; Cao, Y.

2017-07-01

Stochastic effect in cellular systems has been an important topic in systems biology. Stochastic modeling and simulation methods are important tools to study stochastic effect. Given the low efficiency of stochastic simulation algorithms, the hybrid method, which combines an ordinary differential equation (ODE) system with a stochastic chemically reacting system, shows its unique advantages in the modeling and simulation of biochemical systems. The efficiency of hybrid method is usually limited by reactions in the stochastic subsystem, which are modeled and simulated using Gillespie's framework and frequently interrupt the integration of the ODE subsystem. In this paper we develop an efficient implementation approach for the hybrid method coupled with traditional ODE solvers. We also compare the efficiency of hybrid methods with three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments with three biochemical models are presented. A detailed discussion is presented for the performances of three ODE solvers.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

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.

Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Sharma, Sandeep; Alavi, Ali

2017-01-01

In this article we report a stochastic evaluation of the recently proposed multireference linearized coupled cluster theory [S. Sharma and A. Alavi, J. Chem. Phys. 143, 102815 (2015)]. In this method, both the zeroth-order and first-order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth-order wavefunction follows a set of stochastic processes identical to the one used in the full configuration interaction quantum Monte Carlo (FCIQMC) method. To sample the first-order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first-order wavefunction from the zeroth-order wavefunction. The second-order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first-order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. The method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard complete active space self consistent field theory with perturbative correction, we find the singlet-triplet gap to be in good agreement with the experimental values.

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Some Stochastic-Duel Models of Combat.

DTIC Science & Technology

1983-03-01

AD-R127 879 SOME STOCHASTIC- DUEL MODELS OF CONBAT(U) NAVAL - / POSTGRADUATE SCHOOL MONTEREY CA J S CHOE MAR 83 UNCLASSiIED FC1/Ehhh1; F/ 12/ ,iE...SCHOOL Monterey, California DTIC ELECTE :MAY 10 1983 "T !H ES IS SOME STOCHASTIC- DUEL MODELS OF COMBAT by Jum Soo Choe March 1983 Thesis Advisor: J. G...TYPE OF RETORT a PERIOD COVIOCe Master’s Thesis Some Stochastic- Duel Models of Combat March 1983 S. PERFORINGi *no. 44POOi umet 7. AUTHORW.) a

A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints

DOE PAGES

Wu, Fei; Sioshansi, Ramteen

2017-05-25

Electric vehicles (EVs) hold promise to improve the energy efficiency and environmental impacts of transportation. However, widespread EV use can impose significant stress on electricity-distribution systems due to their added charging loads. This paper proposes a centralized EV charging-control model, which schedules the charging of EVs that have flexibility. This flexibility stems from EVs that are parked at the charging station for a longer duration of time than is needed to fully recharge the battery. The model is formulated as a two-stage stochastic optimization problem. The model captures the use of distributed energy resources and uncertainties around EV arrival timesmore » and charging demands upon arrival, non-EV loads on the distribution system, energy prices, and availability of energy from the distributed energy resources. We use a Monte Carlo-based sample-average approximation technique and an L-shaped method to solve the resulting optimization problem efficiently. We also apply a sequential sampling technique to dynamically determine the optimal size of the randomly sampled scenario tree to give a solution with a desired quality at minimal computational cost. Here, we demonstrate the use of our model on a Central-Ohio-based case study. We show the benefits of the model in reducing charging costs, negative impacts on the distribution system, and unserved EV-charging demand compared to simpler heuristics. Lastly, we also conduct sensitivity analyses, to show how the model performs and the resulting costs and load profiles when the design of the station or EV-usage parameters are changed.« less

Stochastic backscatter modelling for the prediction of pollutant removal from an urban street canyon: A large-eddy simulation

NASA Astrophysics Data System (ADS)

O'Neill, J. J.; Cai, X.-M.; Kinnersley, R.

2016-10-01

The large-eddy simulation (LES) approach has recently exhibited its appealing capability of capturing turbulent processes inside street canyons and the urban boundary layer aloft, and its potential for deriving the bulk parameters adopted in low-cost operational urban dispersion models. However, the thin roof-level shear layer may be under-resolved in most LES set-ups and thus sophisticated subgrid-scale (SGS) parameterisations may be required. In this paper, we consider the important case of pollutant removal from an urban street canyon of unit aspect ratio (i.e. building height equal to street width) with the external flow perpendicular to the street. We show that by employing a stochastic SGS model that explicitly accounts for backscatter (energy transfer from unresolved to resolved scales), the pollutant removal process is better simulated compared with the use of a simpler (fully dissipative) but widely-used SGS model. The backscatter induces additional mixing within the shear layer which acts to increase the rate of pollutant removal from the street canyon, giving better agreement with a recent wind-tunnel experiment. The exchange velocity, an important parameter in many operational models that determines the mass transfer between the urban canopy and the external flow, is predicted to be around 15% larger with the backscatter SGS model; consequently, the steady-state mean pollutant concentration within the street canyon is around 15% lower. A database of exchange velocities for various other urban configurations could be generated and used as improved input for operational street canyon models.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

A spatial stochastic programming model for timber and core area management under risk of stand-replacing fire

Treesearch

Dung Tuan Nguyen

2012-01-01

Forest harvest scheduling has been modeled using deterministic and stochastic programming models. Past models seldom address explicit spatial forest management concerns under the influence of natural disturbances. In this research study, we employ multistage full recourse stochastic programming models to explore the challenges and advantages of building spatial...

A spatial stochastic programming model for timber and core area management under risk of fires

Treesearch

Yu Wei; Michael Bevers; Dung Nguyen; Erin Belval

2014-01-01

Previous stochastic models in harvest scheduling seldom address explicit spatial management concerns under the influence of natural disturbances. We employ multistage stochastic programming models to explore the challenges and advantages of building spatial optimization models that account for the influences of random stand-replacing fires. Our exploratory test models...

Recent Advances in Voltammetry

PubMed Central

Batchelor-McAuley, Christopher; Kätelhön, Enno; Barnes, Edward O; Compton, Richard G; Laborda, Eduardo; Molina, Angela

2015-01-01

Recent progress in the theory and practice of voltammetry is surveyed and evaluated. The transformation over the last decade of the level of modelling and simulation of experiments has realised major advances such that electrochemical techniques can be fully developed and applied to real chemical problems of distinct complexity. This review focuses on the topic areas of: multistep electrochemical processes, voltammetry in ionic liquids, the development and interpretation of theories of electron transfer (Butler–Volmer and Marcus–Hush), advances in voltammetric pulse techniques, stochastic random walk models of diffusion, the influence of migration under conditions of low support, voltammetry at rough and porous electrodes, and nanoparticle electrochemistry. The review of the latter field encompasses both the study of nanoparticle-modified electrodes, including stripping voltammetry and the new technique of ‘nano-impacts’. PMID:26246984

Real-time management of a multipurpose water reservoir with a heteroscedastic inflow model

NASA Astrophysics Data System (ADS)

Pianosi, F.; Soncini-Sessa, R.

2009-10-01

Stochastic dynamic programming has been extensively used as a method for designing optimal regulation policies for water reservoirs. However, the potential of this method is dramatically reduced by its computational burden, which often forces to introduce strong approximations in the model of the system, especially in the description of the reservoir inflow. In this paper, an approach to partially remedy this problem is proposed and applied to a real world case study. It foresees solving the management problem on-line, using a reduced model of the system and the inflow forecast provided by a dynamic model. By doing so, all the hydrometeorological information that is available in real-time is fully exploited. The model here proposed for the inflow forecasting is a nonlinear, heteroscedastic model that provides both the expected value and the standard deviation of the inflow through dynamic relations. The effectiveness of such model for the purpose of the reservoir regulation is evaluated through simulation and comparison with the results provided by conventional homoscedastic inflow models.

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

Switchable genetic oscillator operating in quasi-stable mode

PubMed Central

Strelkowa, Natalja; Barahona, Mauricio

2010-01-01

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes. PMID:20097721

Multiscale Stochastic Fracture Mechanics of Composites Informed by In-situ XCT Tests

DTIC Science & Technology

2016-02-02

TERMS EOARD, Materials, nano -scale manufacturing 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18, NUMBER OF PAGES 7 19a...relation to CFRP have been fully realised, with additional outcomes in related topics such as studies of UHPFRC and development of new nano -graphene

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment.

PubMed

Liu, Meng; Wang, Ke

2010-06-07

A new single-species model disturbed by both white noise and colored noise in a polluted environment is developed and analyzed. Sufficient criteria for extinction, stochastic nonpersistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the species are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. The results show that both white and colored environmental noises have sufficient effect to the survival results. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Some mechanistic requirements for major transitions

PubMed Central

2016-01-01

Major transitions in nature and human society are accompanied by a substantial change towards higher complexity in the core of the evolving system. New features are established, novel hierarchies emerge, new regulatory mechanisms are required and so on. An obvious way to achieve higher complexity is integration of autonomous elements into new organized systems whereby the previously independent units give up their autonomy at least in part. In this contribution, we reconsider the more than 40 years old hypercycle model and analyse it by the tools of stochastic chemical kinetics. An open system is implemented in the form of a flow reactor. The formation of new dynamically organized units through integration of competitors is identified with transcritical bifurcations. In the stochastic model, the fully organized state is quasi-stationary whereas the unorganized state corresponds to a population with natural selection. The stability of the organized state depends strongly on the number of individual subspecies, n, that have to be integrated: two and three classes of individuals, and , readily form quasi-stationary states. The four-membered deterministic dynamical system, , is stable but in the stochastic approach self-enhancing fluctuations drive it into extinction. In systems with five and more classes of individuals, , the state of cooperation is unstable and the solutions of the deterministic ODEs exhibit large amplitude oscillations. In the stochastic system self-enhancing fluctuations lead to extinction as observed with . Interestingly, cooperative systems in nature are commonly two-membered as shown by numerous examples of binary symbiosis. A few cases of symbiosis of three partners, called three-way symbiosis, have been found and were analysed within the past decade. Four-way symbiosis is rather rare but was reported to occur in fungus-growing ants. The model reported here can be used to illustrate the interplay between competition and cooperation whereby we obtain a hint on the role that resources play in major transitions. Abundance of resources seems to be an indispensable prerequisite of radical innovation that apparently needs substantial investments. Economists often claim that scarcity is driving innovation. Our model sheds some light on this apparent contradiction. In a nutshell, the answer is: scarcity drives optimization and increase in efficiency but abundance is required for radical novelty and the development of new features. This article is part of the themed issue ‘The major synthetic evolutionary transitions’. PMID:27431517

Model selection for integrated pest management with stochasticity.

PubMed

Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel

2018-04-07

In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.

Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control

NASA Astrophysics Data System (ADS)

Gao, Shujing; Zhong, Deming; Zhang, Yan

2018-04-01

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.

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.

From Complex to Simple: Interdisciplinary Stochastic Models

ERIC Educational Resources Information Center

Mazilu, D. A.; Zamora, G.; Mazilu, I.

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

One-Week Module on Stochastic Groundwater Modeling

ERIC Educational Resources Information Center

Mays, David C.

2010-01-01

This article describes a one-week introduction to stochastic groundwater modeling, intended for the end of a first course on groundwater hydrology, or the beginning of a second course on stochastic hydrogeology or groundwater modeling. The motivation for this work is to strengthen groundwater education, which has been identified among the factors…

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.

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

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Stochastic growth logistic model with aftereffect for batch fermentation process

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

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

A stochastically fully connected conditional random field framework for super resolution OCT

NASA Astrophysics Data System (ADS)

Boroomand, A.; Tan, B.; Wong, A.; Bizheva, K.

2017-02-01

A number of factors can degrade the resolution and contrast of OCT images, such as: (1) changes of the OCT pointspread function (PSF) resulting from wavelength dependent scattering and absorption of light along the imaging depth (2) speckle noise, as well as (3) motion artifacts. We propose a new Super Resolution OCT (SR OCT) imaging framework that takes advantage of a Stochastically Fully Connected Conditional Random Field (SF-CRF) model to generate a Super Resolved OCT (SR OCT) image of higher quality from a set of Low-Resolution OCT (LR OCT) images. The proposed SF-CRF SR OCT imaging is able to simultaneously compensate for all of the factors mentioned above, that degrade the OCT image quality, using a unified computational framework. The proposed SF-CRF SR OCT imaging framework was tested on a set of simulated LR human retinal OCT images generated from a high resolution, high contrast retinal image, and on a set of in-vivo, high resolution, high contrast rat retinal OCT images. The reconstructed SR OCT images show considerably higher spatial resolution, less speckle noise and higher contrast compared to other tested methods. Visual assessment of the results demonstrated the usefulness of the proposed approach in better preservation of fine details and structures of the imaged sample, retaining biological tissue boundaries while reducing speckle noise using a unified computational framework. Quantitative evaluation using both Contrast to Noise Ratio (CNR) and Edge Preservation (EP) parameter also showed superior performance of the proposed SF-CRF SR OCT approach compared to other image processing approaches.

Waterbodies Extraction from LANDSAT8-OLI Imagery Using Awater Indexs-Guied Stochastic Fully-Connected Conditional Random Field Model and the Support Vector Machine

NASA Astrophysics Data System (ADS)

Wang, X.; Xu, L.

2018-04-01

One of the most important applications of remote sensing classification is water extraction. The water index (WI) based on Landsat images is one of the most common ways to distinguish water bodies from other land surface features. But conventional WI methods take into account spectral information only form a limited number of bands, and therefore the accuracy of those WI methods may be constrained in some areas which are covered with snow/ice, clouds, etc. An accurate and robust water extraction method is the key to the study at present. The support vector machine (SVM) using all bands spectral information can reduce for these classification error to some extent. Nevertheless, SVM which barely considers spatial information is relatively sensitive to noise in local regions. Conditional random field (CRF) which considers both spatial information and spectral information has proven to be able to compensate for these limitations. Hence, in this paper, we develop a systematic water extraction method by taking advantage of the complementarity between the SVM and a water index-guided stochastic fully-connected conditional random field (SVM-WIGSFCRF) to address the above issues. In addition, we comprehensively evaluate the reliability and accuracy of the proposed method using Landsat-8 operational land imager (OLI) images of one test site. We assess the method's performance by calculating the following accuracy metrics: Omission Errors (OE) and Commission Errors (CE); Kappa coefficient (KP) and Total Error (TE). Experimental results show that the new method can improve target detection accuracy under complex and changeable environments.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

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.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

PubMed

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-10-15

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

PubMed Central

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. PMID:26478601

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

Probing quantum frustrated systems via factorization of the ground state.

PubMed

Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio

2010-05-21

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.

Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models.

PubMed

Sato, Tatsuhiko; Furusawa, Yoshiya

2012-10-01

Estimation of the survival fractions of cells irradiated with various particles over a wide linear energy transfer (LET) range is of great importance in the treatment planning of charged-particle therapy. Two computational models were developed for estimating survival fractions based on the concept of the microdosimetric kinetic model. They were designated as the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models. The former model takes into account the stochastic natures of both domain and cell nucleus specific energies, whereas the latter model represents the stochastic nature of domain specific energy by its approximated mean value and variance to reduce the computational time. The probability densities of the domain and cell nucleus specific energies are the fundamental quantities for expressing survival fractions in these models. These densities are calculated using the microdosimetric and LET-estimator functions implemented in the Particle and Heavy Ion Transport code System (PHITS) in combination with the convolution or database method. Both the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models can reproduce the measured survival fractions for high-LET and high-dose irradiations, whereas a previously proposed microdosimetric kinetic model predicts lower values for these fractions, mainly due to intrinsic ignorance of the stochastic nature of cell nucleus specific energies in the calculation. The models we developed should contribute to a better understanding of the mechanism of cell inactivation, as well as improve the accuracy of treatment planning of charged-particle therapy.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Natural Human Mobility Patterns and Spatial Spread of Infectious Diseases

NASA Astrophysics Data System (ADS)

Belik, Vitaly; Geisel, Theo; Brockmann, Dirk

2011-08-01

We investigate a model for spatial epidemics explicitly taking into account bidirectional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reaction-diffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that, in contrast to the diffusive systems, our model predicts a saturation of the velocity with an increasing traveling rate. Furthermore, we show that a fully stochastic system exhibits a novel threshold for the attack ratio of an outbreak that is absent in diffusion and force of infection models. These insights not only capture natural features of human mobility relevant for the geographical epidemic spread, they may serve as a starting point for modeling important dynamical processes in human and animal epidemiology, population ecology, biology, and evolution.

Arctic Sea Ice: Trends, Stability and Variability

NASA Astrophysics Data System (ADS)

Moon, Woosok

A stochastic Arctic sea-ice model is derived and analyzed in detail to interpret the recent decay and associated variability of Arctic sea-ice under changes in greenhouse gas forcing widely referred to as global warming. The approach begins from a deterministic model of the heat flux balance through the air/sea/ice system, which uses observed monthly-averaged heat fluxes to drive a time evolution of sea-ice thickness. This model reproduces the observed seasonal cycle of the ice cover and it is to this that stochastic noise---representing high frequency variability---is introduced. The model takes the form of a single periodic non-autonomous stochastic ordinary differential equation. Following an introductory chapter, the two that follow focus principally on the properties of the deterministic model in order to identify the main properties governing the stability of the ice cover. In chapter 2 the underlying time-dependent solutions to the deterministic model are analyzed for their stability. It is found that the response time-scale of the system to perturbations is dominated by the destabilizing sea-ice albedo feedback, which is operative in the summer, and the stabilizing long wave radiative cooling of the ice surface, which is operative in the winter. This basic competition is found throughout the thesis to define the governing dynamics of the system. In particular, as greenhouse gas forcing increases, the sea-ice albedo feedback becomes more effective at destabilizing the system. Thus, any projections of the future state of Arctic sea-ice will depend sensitively on the treatment of the ice-albedo feedback. This in turn implies that the treatment a fractional ice cover as the ice areal extent changes rapidly, must be handled with the utmost care. In chapter 3, the idea of a two-season model, with just winter and summer, is revisited. By breaking the seasonal cycle up in this manner one can simplify the interpretation of the basic dynamics. Whereas in the fully time-dependent seasonal model one finds stable seasonal ice cover (vanishing in the summer but reappearing in the winter), in previous two-season models such a state could not be found. In this chapter the sufficient conditions are found for a stable seasonal ice cover, which reside in including a time variation in the shortwave radiance during summer. This provides a qualitative interpretation of the continuous and reversible shift from perennial to seasonally-varying states in the more complex deterministic model. In order to put the stochastic model into a realistic observational framework, in chapter 4, the analysis of daily satellite retrievals of ice albedo and ice extent is described. Both the basic statistics are examined and a new method, called multi-fractal temporally weighted detrended fluctuation analysis, is applied. Because the basic data are taken on daily time scales, the full fidelity of the retrieved data is accessed and we find time scales from days and weeks to seasonal and decadal. Importantly, the data show a white-noise structure on annual to biannual time scales and this provides the basis for using a Wiener process for the noise in the stochastic Arctic sea-ice model. In chapter 5 a generalized perturbation analysis of a non-autonomous stochastic differential equation is developed and then applied to interpreting the variability of Arctic sea-ice as greenhouse gas forcing increases. The resulting analytic expressions of the statistical moments provide insight into the transient and memory-delay effects associated with the basic competition in the system: the ice-albedo feedback and long wave radiative stabilization along with the asymmetry in the nonlinearity of the deterministic contributions to the model and the magnitude and structure of the stochastic noise. A systematic study of the impact of the noise structure, from additive to multiplicative, is undertaken in chapters 6 and 7. Finally, in chapter 8 the matter of including a fractional ice cover into a deterministic model is addressed. It is found that a simple but crucial mistake is made in one of the most widely used model schemes and this has a major impact given the important role of areal fraction in the ice-albedo feedback in such a model. The thesis is summarized in chapter 9.

Validation of the Poisson Stochastic Radiative Transfer Model

NASA Technical Reports Server (NTRS)

Zhuravleva, Tatiana; Marshak, Alexander

2004-01-01

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough

PubMed Central

Black, Andrew J.; McKane, Alan J.

2010-01-01

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields

NASA Astrophysics Data System (ADS)

Lauterbach, S.; Fina, M.; Wagner, W.

2018-04-01

Since structural engineering requires highly developed and optimized structures, the thickness dependency is one of the most controversially debated topics. This paper deals with stability analysis of lightweight thin structures combined with arbitrary geometrical imperfections. Generally known design guidelines only consider imperfections for simple shapes and loading, whereas for complex structures the lower-bound design philosophy still holds. Herein, uncertainties are considered with an empirical knockdown factor representing a lower bound of existing measurements. To fully understand and predict expected bearable loads, numerical investigations are essential, including geometrical imperfections. These are implemented into a stand-alone program code with a stochastic approach to compute random fields as geometric imperfections that are applied to nodes of the finite element mesh of selected structural examples. The stochastic approach uses the Karhunen-Loève expansion for the random field discretization. For this approach, the so-called correlation length l_c controls the random field in a powerful way. This parameter has a major influence on the buckling shape, and also on the stability load. First, the impact of the correlation length is studied for simple structures. Second, since most structures for engineering devices are more complex and combined structures, these are intensively discussed with the focus on constrained random fields for e.g. flange-web-intersections. Specific constraints for those random fields are pointed out with regard to the finite element model. Further, geometrical imperfections vanish where the structure is supported.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

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

Xie, Fei; Huang, Yongxi

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE PAGES

Xie, Fei; Huang, Yongxi

2018-02-04

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Machine learning from computer simulations with applications in rail vehicle dynamics

NASA Astrophysics Data System (ADS)

Taheri, Mehdi; Ahmadian, Mehdi

2016-05-01

The application of stochastic modelling for learning the behaviour of a multibody dynamics (MBD) models is investigated. Post-processing data from a simulation run are used to train the stochastic model that estimates the relationship between model inputs (suspension relative displacement and velocity) and the output (sum of suspension forces). The stochastic model can be used to reduce the computational burden of the MBD model by replacing a computationally expensive subsystem in the model (suspension subsystem). With minor changes, the stochastic modelling technique is able to learn the behaviour of a physical system and integrate its behaviour within MBD models. The technique is highly advantageous for MBD models where real-time simulations are necessary, or with models that have a large number of repeated substructures, e.g. modelling a train with a large number of railcars. The fact that the training data are acquired prior to the development of the stochastic model discards the conventional sampling plan strategies like Latin Hypercube sampling plans where simulations are performed using the inputs dictated by the sampling plan. Since the sampling plan greatly influences the overall accuracy and efficiency of the stochastic predictions, a sampling plan suitable for the process is developed where the most space-filling subset of the acquired data with ? number of sample points that best describes the dynamic behaviour of the system under study is selected as the training data.

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.

A chance-constrained stochastic approach to intermodal container routing problems.

PubMed

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost. PMID:29438389

A stochastic SIS epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

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.

Stochastic volatility of the futures prices of emission allowances: A Bayesian approach

NASA Astrophysics Data System (ADS)

Kim, Jungmu; Park, Yuen Jung; Ryu, Doojin

2017-01-01

Understanding the stochastic nature of the spot volatility of emission allowances is crucial for risk management in emissions markets. In this study, by adopting a stochastic volatility model with or without jumps to represent the dynamics of European Union Allowances (EUA) futures prices, we estimate the daily volatilities and model parameters by using the Markov Chain Monte Carlo method for stochastic volatility (SV), stochastic volatility with return jumps (SVJ) and stochastic volatility with correlated jumps (SVCJ) models. Our empirical results reveal three important features of emissions markets. First, the data presented herein suggest that EUA futures prices exhibit significant stochastic volatility. Second, the leverage effect is noticeable regardless of whether or not jumps are included. Third, the inclusion of jumps has a significant impact on the estimation of the volatility dynamics. Finally, the market becomes very volatile and large jumps occur at the beginning of a new phase. These findings are important for policy makers and regulators.

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.

Examining Solutions to Missing Data in Longitudinal Nursing Research

PubMed Central

Roberts, Mary B.; Sullivan, Mary C.; Winchester, Suzy B.

2017-01-01

Purpose Longitudinal studies are highly valuable in pediatrics because they provide useful data about developmental patterns of child health and behavior over time. When data are missing, the value of the research is impacted. The study’s purpose was to: (1) introduce a 3-step approach to assess and address missing data; (2) illustrate this approach using categorical and continuous level variables from a longitudinal study of premature infants. Methods A three-step approach with simulations was followed to assess the amount and pattern of missing data and to determine the most appropriate imputation method for the missing data. Patterns of missingness were Missing Completely at Random, Missing at Random, and Not Missing at Random. Missing continuous-level data were imputed using mean replacement, stochastic regression, multiple imputation, and fully conditional specification. Missing categorical-level data were imputed using last value carried forward, hot-decking, stochastic regression, and fully conditional specification. Simulations were used to evaluate these imputation methods under different patterns of missingness at different levels of missing data. Results The rate of missingness was 16–23% for continuous variables and 1–28% for categorical variables. Fully conditional specification imputation provided the least difference in mean and standard deviation estimates for continuous measures. Fully conditional specification imputation was acceptable for categorical measures. Results obtained through simulation reinforced and confirmed these findings. Practice Implications Significant investments are made in the collection of longitudinal data. The prudent handling of missing data can protect these investments and potentially improve the scientific information contained in pediatric longitudinal studies. PMID:28425202

Stochastic Game Analysis and Latency Awareness for Self-Adaptation

DTIC Science & Technology

2014-01-01

this paper, we introduce a formal analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to quantify the...Additional Key Words and Phrases: Proactive adaptation, Stochastic multiplayer games , Latency 1. INTRODUCTION When planning how to adapt, self-adaptive...contribution of this paper is twofold: (1) A novel analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to

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.

Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances

NASA Astrophysics Data System (ADS)

Zhang, Weiwei; Meng, Xinzhu

2018-02-01

In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

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

Thomas, Vaughan L.; Gayme, Dennice F.; Lieu, Binh K.

2014-10-15

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate thatmore » the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.« less

Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems.

PubMed

Tang, Ying; Yuan, Ruoshi; Ma, Yian

2013-01-01

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems

NASA Astrophysics Data System (ADS)

Tang, Ying; Yuan, Ruoshi; Ma, Yian

2013-01-01

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

Modeling the lake eutrophication stochastic ecosystem and the research of its stability.

PubMed

Wang, Bo; Qi, Qianqian

2018-06-01

In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e., nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0,  0.388644) and (0.66003825,  1.0), there only exists a stable equilibrium state and the additive noise intensity could not change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be capable of effectively explaining the regime shift theory and agreed with the realistic analyze. These conclusions also confirms the two paths for the system to move from one stable state to another proposed by Beisner et al. [3], which may help understand the occurrence mechanism related to the lake eutrophication from the view point of the stochastic model and mathematical analysis. Copyright © 2018 Elsevier Inc. All rights reserved.

Importance of vesicle release stochasticity in neuro-spike communication.

PubMed

Ramezani, Hamideh; Akan, Ozgur B

2017-07-01

Aim of this paper is proposing a stochastic model for vesicle release process, a part of neuro-spike communication. Hence, we study biological events occurring in this process and use microphysiological simulations to observe functionality of these events. Since the most important source of variability in vesicle release probability is opening of voltage dependent calcium channels (VDCCs) followed by influx of calcium ions through these channels, we propose a stochastic model for this event, while using a deterministic model for other variability sources. To capture the stochasticity of calcium influx to pre-synaptic neuron in our model, we study its statistics and find that it can be modeled by a distribution defined based on Normal and Logistic distributions.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Stochastic Modeling of Laminar-Turbulent Transition

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Choudhari, Meelan

2002-01-01

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Stochastic modeling of consumer preferences for health care institutions.

PubMed

Malhotra, N K

1983-01-01

This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.

Fusion of Hard and Soft Information in Nonparametric Density Estimation

DTIC Science & Technology

2015-06-10

and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum...particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output...an essential step in simulation analysis and stochastic optimization is the generation of probability densities for input random variables; see for

The threshold of a stochastic avian-human influenza epidemic model with psychological effect

NASA Astrophysics Data System (ADS)

Zhang, Fengrong; Zhang, Xinhong

2018-02-01

In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

NASA Astrophysics Data System (ADS)

Xue, Chi; Goldenfeld, Nigel

2017-12-01

The "kill the winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the kill the winner paradigm and show that the stable coexistence state of the deterministic kill the winner model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes the high diversity of the ecosystem by generating a persistent population flux of species.

Stochastic mixed-mode oscillations in a three-species predator-prey model

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

The timing and probability of treatment switch under cost uncertainty: an application to patients with gastrointestinal stromal tumor.

PubMed

de Mello-Sampayo, Felipa

2014-03-01

Cost fluctuations render the outcome of any treatment switch uncertain, so that decision makers might have to wait for more information before optimally switching treatments, especially when the incremental cost per quality-adjusted life year (QALY) gained cannot be fully recovered later on. To analyze the timing of treatment switch under cost uncertainty. A dynamic stochastic model for the optimal timing of a treatment switch is developed and applied to a problem in medical decision taking, i.e. to patients with unresectable gastrointestinal stromal tumour (GIST). The theoretical model suggests that cost uncertainty reduces expected net benefit. In addition, cost volatility discourages switching treatments. The stochastic model also illustrates that as technologies become less cost competitive, the cost uncertainty becomes more dominant. With limited substitutability, higher quality of technologies will increase the demand for those technologies disregarding the cost uncertainty. The results of the empirical application suggest that the first-line treatment may be the better choice when considering lifetime welfare. Under uncertainty and irreversibility, low-risk patients must begin the second-line treatment as soon as possible, which is precisely when the second-line treatment is least valuable. As the costs of reversing current treatment impacts fall, it becomes more feasible to provide the option-preserving treatment to these low-risk individuals later on. Copyright © 2014 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Tsunamis: stochastic models of occurrence and generation mechanisms

USGS Publications Warehouse

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

Addressing model uncertainty through stochastic parameter perturbations within the High Resolution Rapid Refresh (HRRR) ensemble

NASA Astrophysics Data System (ADS)

Wolff, J.; Jankov, I.; Beck, J.; Carson, L.; Frimel, J.; Harrold, M.; Jiang, H.

2016-12-01

It is well known that global and regional numerical weather prediction ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system for addressing the deficiencies in ensemble modeling is the use of stochastic physics to represent model-related uncertainty. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), Stochastic Perturbation of Physics Tendencies (SPPT), or some combination of all three. The focus of this study is to assess the model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) when using stochastic approaches. For this purpose, the test utilized a single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model, with ensemble members produced by employing stochastic methods. Parameter perturbations were employed in the Rapid Update Cycle (RUC) land surface model and Mellor-Yamada-Nakanishi-Niino (MYNN) planetary boundary layer scheme. Results will be presented in terms of bias, error, spread, skill, accuracy, reliability, and sharpness using the Model Evaluation Tools (MET) verification package. Due to the high level of complexity of running a frequently updating (hourly), high spatial resolution (3 km), large domain (CONUS) ensemble system, extensive high performance computing (HPC) resources were needed to meet this objective. Supercomputing resources were provided through the National Center for Atmospheric Research (NCAR) Strategic Capability (NSC) project support, allowing for a more extensive set of tests over multiple seasons, consequently leading to more robust results. Through the use of these stochastic innovations and powerful supercomputing at NCAR, further insights and advancements in ensemble forecasting at convection-permitting scales will be possible.

Decentralized system identification using stochastic subspace identification on wireless smart sensor networks

NASA Astrophysics Data System (ADS)

Sim, Sung-Han; Spencer, Billie F., Jr.; Park, Jongwoong; Jung, Hyungjo

2012-04-01

Wireless Smart Sensor Networks (WSSNs) facilitates a new paradigm to structural identification and monitoring for civil infrastructure. Conventional monitoring systems based on wired sensors and centralized data acquisition and processing have been considered to be challenging and costly due to cabling and expensive equipment and maintenance costs. WSSNs have emerged as a technology that can overcome such difficulties, making deployment of a dense array of sensors on large civil structures both feasible and economical. However, as opposed to wired sensor networks in which centralized data acquisition and processing is common practice, WSSNs require decentralized computing algorithms to reduce data transmission due to the limitation associated with wireless communication. Thus, several system identification methods have been implemented to process sensor data and extract essential information, including Natural Excitation Technique with Eigensystem Realization Algorithm, Frequency Domain Decomposition (FDD), and Random Decrement Technique (RDT); however, Stochastic Subspace Identification (SSI) has not been fully utilized in WSSNs, while SSI has the strong potential to enhance the system identification. This study presents a decentralized system identification using SSI in WSSNs. The approach is implemented on MEMSIC's Imote2 sensor platform and experimentally verified using a 5-story shear building model.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

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

Castillo-Negrete, Diego del; Blazevski, Daniel

2016-04-15

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in three-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands andmore » remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in large helical device and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.« less

Stochastic soil water balance under seasonal climates

PubMed Central

Feng, Xue; Porporato, Amilcare; Rodriguez-Iturbe, Ignacio

2015-01-01

The analysis of soil water partitioning in seasonally dry climates necessarily requires careful consideration of the periodic climatic forcing at the intra-annual timescale in addition to daily scale variabilities. Here, we introduce three new extensions to a stochastic soil moisture model which yields seasonal evolution of soil moisture and relevant hydrological fluxes. These approximations allow seasonal climatic forcings (e.g. rainfall and potential evapotranspiration) to be fully resolved, extending the analysis of soil water partitioning to account explicitly for the seasonal amplitude and the phase difference between the climatic forcings. The results provide accurate descriptions of probabilistic soil moisture dynamics under seasonal climates without requiring extensive numerical simulations. We also find that the transfer of soil moisture between the wet to the dry season is responsible for hysteresis in the hydrological response, showing asymmetrical trajectories in the mean soil moisture and in the transient Budyko's curves during the ‘dry-down‘ versus the ‘rewetting‘ phases of the year. Furthermore, in some dry climates where rainfall and potential evapotranspiration are in-phase, annual evapotranspiration can be shown to increase because of inter-seasonal soil moisture transfer, highlighting the importance of soil water storage in the seasonal context. PMID:25663808

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

PubMed

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

A stochastic visco-hyperelastic model of human placenta tissue for finite element crash simulations.

PubMed

Hu, Jingwen; Klinich, Kathleen D; Miller, Carl S; Rupp, Jonathan D; Nazmi, Giseli; Pearlman, Mark D; Schneider, Lawrence W

2011-03-01

Placental abruption is the most common cause of fetal deaths in motor-vehicle crashes, but studies on the mechanical properties of human placenta are rare. This study presents a new method of developing a stochastic visco-hyperelastic material model of human placenta tissue using a combination of uniaxial tensile testing, specimen-specific finite element (FE) modeling, and stochastic optimization techniques. In our previous study, uniaxial tensile tests of 21 placenta specimens have been performed using a strain rate of 12/s. In this study, additional uniaxial tensile tests were performed using strain rates of 1/s and 0.1/s on 25 placenta specimens. Response corridors for the three loading rates were developed based on the normalized data achieved by test reconstructions of each specimen using specimen-specific FE models. Material parameters of a visco-hyperelastic model and their associated standard deviations were tuned to match both the means and standard deviations of all three response corridors using a stochastic optimization method. The results show a very good agreement between the tested and simulated response corridors, indicating that stochastic analysis can improve estimation of variability in material model parameters. The proposed method can be applied to develop stochastic material models of other biological soft tissues.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Parameters of control when facing stochastic demand: a DEA approach applied to Bangladeshi vaccination sites.

PubMed

Dervaux, B; Leleu, H; Valdmanis, V; Walker, D

2003-12-01

An aim of vaccination programs is near-complete coverage. One method for achieving this is for health facilities providing these services to operate frequently and for many hours during each session. However, if vaccine vials are not fully used, the remainder is often discarded, considered as waste. Without an active appointment schedule process, there is no way for facility staff to control the stochastic demand of potential patients, and hence reduce waste. And yet reducing the hours of operation or number of sessions per week could hinder access to vaccination services. In lieu of any formal system of controlling demand, we propose to model the optimal number of hours and sessions in order to maximize outputs, the number and type of vaccines provided given inputs, using Data Envelopment Analysis (DEA). Inputs are defined as the amount of vaccine wastage and the number of full-time equivalent staff, size of the facility, number of hours of operation and the number of sessions. Outputs are defined as the number and type of vaccines aimed at children and pregnant women. This analysis requires two models: one DEA model with possible reallocations between the number of hours and the number of sessions but with the total amount of time fixed and one model without this kind of reallocation in scheduling. Comparing these two scores we can identify the "gain" that would be possible were the scheduling of hours and sessions modified while controlling for all other types of inefficiency. By modeling an output-based model, we maintain the objective of increasing coverage while assisting decision-makers determining optimal operating processes.

Dynamics of a stochastic HIV-1 infection model with logistic growth

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan

2017-03-01

This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.

Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for Detection System Design

DTIC Science & Technology

2013-11-01

STOCHASTIC RADIATIVE TRANSFER MODEL FOR CONTAMINATED ROUGH SURFACES: A...of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid ...COVERED (From - To) Jan 2013 - Sep 2013 4. TITLE AND SUBTITLE Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

PubMed

Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

2014-12-01

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Evaluation of Stochastic Rainfall Models in Capturing Climate Variability for Future Drought and Flood Risk Assessment

NASA Astrophysics Data System (ADS)

Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.

2016-12-01

One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

NASA Astrophysics Data System (ADS)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using all three stochastic approaches to address model uncertainty. Results from the stochastic perturbation testing were compared to a baseline multi-physics control ensemble. For probabilistic forecast performance the Model Evaluation Tools (MET) verification package was used.

Partial ASL extensions for stochastic programming.

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

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data

NASA Astrophysics Data System (ADS)

Darmon, David

2018-03-01

In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

Studying Resist Stochastics with the Multivariate Poisson Propagation Model

DOE PAGES

Naulleau, Patrick; Anderson, Christopher; Chao, Weilun; ...

2014-01-01

Progress in the ultimate performance of extreme ultraviolet resist has arguably decelerated in recent years suggesting an approach to stochastic limits both in photon counts and material parameters. Here we report on the performance of a variety of leading extreme ultraviolet resist both with and without chemical amplification. The measured performance is compared to stochastic modeling results using the Multivariate Poisson Propagation Model. The results show that the best materials are indeed nearing modeled performance limits.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Stochastic Ocean Eddy Perturbations in a Coupled General Circulation Model.

NASA Astrophysics Data System (ADS)

Howe, N.; Williams, P. D.; Gregory, J. M.; Smith, R. S.

2014-12-01

High-resolution ocean models, which are eddy permitting and resolving, require large computing resources to produce centuries worth of data. Also, some previous studies have suggested that increasing resolution does not necessarily solve the problem of unresolved scales, because it simply introduces a new set of unresolved scales. Applying stochastic parameterisations to ocean models is one solution that is expected to improve the representation of small-scale (eddy) effects without increasing run-time. Stochastic parameterisation has been shown to have an impact in atmosphere-only models and idealised ocean models, but has not previously been studied in ocean general circulation models. Here we apply simple stochastic perturbations to the ocean temperature and salinity tendencies in the low-resolution coupled climate model, FAMOUS. The stochastic perturbations are implemented according to T(t) = T(t-1) + (ΔT(t) + ξ(t)), where T is temperature or salinity, ΔT is the corresponding deterministic increment in one time step, and ξ(t) is Gaussian noise. We use high-resolution HiGEM data coarse-grained to the FAMOUS grid to provide information about the magnitude and spatio-temporal correlation structure of the noise to be added to the lower resolution model. Here we present results of adding white and red noise, showing the impacts of an additive stochastic perturbation on mean climate state and variability in an AOGCM.

Physics of traffic gridlock in a city.

PubMed

Kerner, Boris S

2011-10-01

Based on simulations of stochastic three-phase and two-phase traffic flow models, we reveal that at a signalized city intersection under small link inflow rates at which a vehicle queue developed during the red phase of the light signal dissolves fully during the green phase, i.e., no traffic gridlock should be expected, nevertheless, spontaneous traffic breakdown with subsequent city gridlock occurs with some probability after a random time delay. In most cases, this traffic breakdown is initiated by a phase transition from free flow to a synchronized flow occurring upstream of the queue at the light signal. The probability of traffic breakdown at the light signal is an increasing function of the link inflow rate and duration of the red phase of the light signal.

Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread

NASA Astrophysics Data System (ADS)

Billings, Lora; Bollt, Erik M.; Schwartz, Ira B.

2002-06-01

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

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

Wang, Hong; Aziz, H M Abdul; Young, Stan

Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections.more » In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.« less

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies

NASA Astrophysics Data System (ADS)

Williams, Paul; Howe, Nicola; Gregory, Jonathan; Smith, Robin; Joshi, Manoj

2016-04-01

In climate simulations, the impacts of the sub-grid scales on the resolved scales are conventionally represented using deterministic closure schemes, which assume that the impacts are uniquely determined by the resolved scales. Stochastic parameterization relaxes this assumption, by sampling the sub-grid variability in a computationally inexpensive manner. This presentation shows that the simulated climatological state of the ocean is improved in many respects by implementing a simple stochastic parameterization of ocean eddies into a coupled atmosphere-ocean general circulation model. Simulations from a high-resolution, eddy-permitting ocean model are used to calculate the eddy statistics needed to inject realistic stochastic noise into a low-resolution, non-eddy-permitting version of the same model. A suite of four stochastic experiments is then run to test the sensitivity of the simulated climate to the noise definition, by varying the noise amplitude and decorrelation time within reasonable limits. The addition of zero-mean noise to the ocean temperature tendency is found to have a non-zero effect on the mean climate. Specifically, in terms of the ocean temperature and salinity fields both at the surface and at depth, the noise reduces many of the biases in the low-resolution model and causes it to more closely resemble the high-resolution model. The variability of the strength of the global ocean thermohaline circulation is also improved. It is concluded that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost. Therefore, stochastic parameterizations of ocean eddies have the potential to significantly improve climate simulations. Reference PD Williams, NJ Howe, JM Gregory, RS Smith, and MM Joshi (2016) Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies. Journal of Climate, under revision.

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

Stochastic-field cavitation model

NASA Astrophysics Data System (ADS)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A cavitation model based on Eulerian stochastic fields

NASA Astrophysics Data System (ADS)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Stochastic-field cavitation model

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

Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.

2013-07-15

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less

Modeling of stochastic motion of bacteria propelled spherical microbeads

NASA Astrophysics Data System (ADS)

Arabagi, Veaceslav; Behkam, Bahareh; Cheung, Eugene; Sitti, Metin

2011-06-01

This work proposes a stochastic dynamic model of bacteria propelled spherical microbeads as potential swimming microrobotic bodies. Small numbers of S. marcescens bacteria are attached with their bodies to surfaces of spherical microbeads. Average-behavior stochastic models that are normally adopted when studying such biological systems are generally not effective for cases in which a small number of agents are interacting in a complex manner, hence a stochastic model is proposed to simulate the behavior of 8-41 bacteria assembled on a curved surface. Flexibility of the flagellar hook is studied via comparing simulated and experimental results for scenarios of increasing bead size and the number of attached bacteria on a bead. Although requiring more experimental data to yield an exact, certain flagellar hook stiffness value, the examined results favor a stiffer flagella. The stochastic model is intended to be used as a design and simulation tool for future potential targeted drug delivery and disease diagnosis applications of bacteria propelled microrobots.

Ground motion simulation for the 23 August 2011, Mineral, Virginia earthquake using physics-based and stochastic broadband methods

USGS Publications Warehouse

Sun, Xiaodan; Hartzell, Stephen; Rezaeian, Sanaz

2015-01-01

Three broadband simulation methods are used to generate synthetic ground motions for the 2011 Mineral, Virginia, earthquake and compare with observed motions. The methods include a physics‐based model by Hartzell et al. (1999, 2005), a stochastic source‐based model by Boore (2009), and a stochastic site‐based model by Rezaeian and Der Kiureghian (2010, 2012). The ground‐motion dataset consists of 40 stations within 600 km of the epicenter. Several metrics are used to validate the simulations: (1) overall bias of response spectra and Fourier spectra (from 0.1 to 10 Hz); (2) spatial distribution of residuals for GMRotI50 peak ground acceleration (PGA), peak ground velocity, and pseudospectral acceleration (PSA) at various periods; (3) comparison with ground‐motion prediction equations (GMPEs) for the eastern United States. Our results show that (1) the physics‐based model provides satisfactory overall bias from 0.1 to 10 Hz and produces more realistic synthetic waveforms; (2) the stochastic site‐based model also yields more realistic synthetic waveforms and performs superiorly for frequencies greater than about 1 Hz; (3) the stochastic source‐based model has larger bias at lower frequencies (<0.5  Hz) and cannot reproduce the varying frequency content in the time domain. The spatial distribution of GMRotI50 residuals shows that there is no obvious pattern with distance in the simulation bias, but there is some azimuthal variability. The comparison between synthetics and GMPEs shows similar fall‐off with distance for all three models, comparable PGA and PSA amplitudes for the physics‐based and stochastic site‐based models, and systematic lower amplitudes for the stochastic source‐based model at lower frequencies (<0.5  Hz).

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

PubMed

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

DOE PAGES

Moon, Jae; Manuel, Lance; Churchfield, Matthew; ...

2017-12-28

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

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

Moon, Jae; Manuel, Lance; Churchfield, Matthew

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

NASA Astrophysics Data System (ADS)

Spettl, A.; Wimmer, R.; Werz, T.; Heinze, M.; Odenbach, S.; Krill, C. E., III; Schmidt, V.

2015-09-01

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al-Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Inflow forecasting model construction with stochastic time series for coordinated dam operation

NASA Astrophysics Data System (ADS)

Kim, T.; Jung, Y.; Kim, H.; Heo, J. H.

2014-12-01

Dam inflow forecasting is one of the most important tasks in dam operation for an effective water resources management and control. In general, dam inflow forecasting with stochastic time series model is possible to apply when the data is stationary because most of stochastic process based on stationarity. However, recent hydrological data cannot be satisfied the stationarity anymore because of climate change. Therefore a stochastic time series model, which can consider seasonality and trend in the data series, named SARIMAX(Seasonal Autoregressive Integrated Average with eXternal variable) model were constructed in this study. This SARIMAX model could increase the performance of stochastic time series model by considering the nonstationarity components and external variable such as precipitation. For application, the models were constructed for four coordinated dams on Han river in South Korea with monthly time series data. As a result, the models of each dam have similar performance and it would be possible to use the model for coordinated dam operation.Acknowledgement This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-NH-12-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Influence of stochastic sea ice parametrization on climate and the role of atmosphere–sea ice–ocean interaction

PubMed Central

Juricke, Stephan; Jung, Thomas

2014-01-01

The influence of a stochastic sea ice strength parametrization on the mean climate is investigated in a coupled atmosphere–sea ice–ocean model. The results are compared with an uncoupled simulation with a prescribed atmosphere. It is found that the stochastic sea ice parametrization causes an effective weakening of the sea ice. In the uncoupled model this leads to an Arctic sea ice volume increase of about 10–20% after an accumulation period of approximately 20–30 years. In the coupled model, no such increase is found. Rather, the stochastic perturbations lead to a spatial redistribution of the Arctic sea ice thickness field. A mechanism involving a slightly negative atmospheric feedback is proposed that can explain the different responses in the coupled and uncoupled system. Changes in integrated Antarctic sea ice quantities caused by the stochastic parametrization are generally small, as memory is lost during the melting season because of an almost complete loss of sea ice. However, stochastic sea ice perturbations affect regional sea ice characteristics in the Southern Hemisphere, both in the uncoupled and coupled model. Remote impacts of the stochastic sea ice parametrization on the mean climate of non-polar regions were found to be small. PMID:24842027

Some mechanistic requirements for major transitions.

PubMed

Schuster, Peter

2016-08-19

Major transitions in nature and human society are accompanied by a substantial change towards higher complexity in the core of the evolving system. New features are established, novel hierarchies emerge, new regulatory mechanisms are required and so on. An obvious way to achieve higher complexity is integration of autonomous elements into new organized systems whereby the previously independent units give up their autonomy at least in part. In this contribution, we reconsider the more than 40 years old hypercycle model and analyse it by the tools of stochastic chemical kinetics. An open system is implemented in the form of a flow reactor. The formation of new dynamically organized units through integration of competitors is identified with transcritical bifurcations. In the stochastic model, the fully organized state is quasi-stationary whereas the unorganized state corresponds to a population with natural selection. The stability of the organized state depends strongly on the number of individual subspecies, n, that have to be integrated: two and three classes of individuals, [Formula: see text] and [Formula: see text], readily form quasi-stationary states. The four-membered deterministic dynamical system, [Formula: see text], is stable but in the stochastic approach self-enhancing fluctuations drive it into extinction. In systems with five and more classes of individuals, [Formula: see text], the state of cooperation is unstable and the solutions of the deterministic ODEs exhibit large amplitude oscillations. In the stochastic system self-enhancing fluctuations lead to extinction as observed with [Formula: see text] Interestingly, cooperative systems in nature are commonly two-membered as shown by numerous examples of binary symbiosis. A few cases of symbiosis of three partners, called three-way symbiosis, have been found and were analysed within the past decade. Four-way symbiosis is rather rare but was reported to occur in fungus-growing ants. The model reported here can be used to illustrate the interplay between competition and cooperation whereby we obtain a hint on the role that resources play in major transitions. Abundance of resources seems to be an indispensable prerequisite of radical innovation that apparently needs substantial investments. Economists often claim that scarcity is driving innovation. Our model sheds some light on this apparent contradiction. In a nutshell, the answer is: scarcity drives optimization and increase in efficiency but abundance is required for radical novelty and the development of new features.This article is part of the themed issue 'The major synthetic evolutionary transitions'. © 2016 The Author(s).

Chemical event chain model of coupled genetic oscillators.

PubMed

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

NASA Astrophysics Data System (ADS)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Stochastic modelling of intermittency.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2010-01-13

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series. This journal is © 2010 The Royal Society

Low Frequency Predictive Skill Despite Structural Instability and Model Error

DTIC Science & Technology

2014-09-30

Majda, based on earlier theoretical work. 1. Dynamic Stochastic Superresolution of sparseley observed turbulent systems M. Branicki (Post doc...of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by...resolving subgridscale turbulence through Dynamic Stochastic Superresolution utilizing aliased grids is a potential breakthrough for practical online

Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2016-11-01

In this paper, we consider a stochastic non-autonomous SISV epidemic model. For the non-autonomous periodic system, firstly, we get the threshold of the system which determines whether the epidemic occurs or not. Then in the case of persistence, we show that there exists at least one nontrivial positive periodic solution of the stochastic system.

Predicting the Stochastic Properties of the Shallow Subsurface for Improved Geophysical Modeling

NASA Astrophysics Data System (ADS)

Stroujkova, A.; Vynne, J.; Bonner, J.; Lewkowicz, J.

2005-12-01

Strong ground motion data from numerous explosive field experiments and from moderate to large earthquakes show significant variations in amplitude and waveform shape with respect to both azimuth and range. Attempts to model these variations using deterministic models have often been unsuccessful. It has been hypothesized that a stochastic description of the geological medium is a more realistic approach. To estimate the stochastic properties of the shallow subsurface, we use Measurement While Drilling (MWD) data, which are routinely collected by mines in order to facilitate design of blast patterns. The parameters, such as rotation speed of the drill, torque, and penetration rate, are used to compute the rock's Specific Energy (SE), which is then related to a blastability index. We use values of SE measured at two different mines and calibrated to laboratory measurements of rock properties to determine correlation lengths of the subsurface rocks in 2D, needed to obtain 2D and 3D stochastic models. The stochastic models are then combined with the deterministic models and used to compute synthetic seismic waveforms.

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

NASA Astrophysics Data System (ADS)

Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.

2018-02-01

A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.

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.

Phthalocyanine-BODIPY dye: synthesis, characterization, and utilization for pattern recognition of CYFRA 21-1 in whole blood samples.

PubMed

Stefan-van Staden, Raluca-Ioana; Comnea-Stancu, Ionela Raluca; Yanık, Hülya; Göksel, Meltem; Alexandru, Anghel; Durmuş, Mahmut

2017-10-01

Phthalocyanine-BODIPY dye (BODIPY = boron dipyrromethene) was synthesized, fully characterized, and used for molecular recognition of CYFRA 21-1, a lung cancer biomarker, from whole blood samples. Thin films of three magnesium oxides ((MgO) n , where n = 8, 9, or 10)) were deposited on a paper substrate, and they were immersed in a solution of phthalocyanine-BODIPY dye (1.17 × 10 -3  mol/L) for the design of stochastic sensors. Limits of determination of picograms per milliliter magnitude order were recorded for the proposed stochastic sensors. CYFRA 21-1 was reliably identified and determined with recoveries higher than 95% and RSD lower than 1% in whole blood samples.

Analysis of the Space Propulsion System Problem Using RAVEN

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

diego mandelli; curtis smith; cristian rabiti

This paper presents the solution of the space propulsion problem using a PRA code currently under development at Idaho National Laboratory (INL). RAVEN (Reactor Analysis and Virtual control ENviroment) is a multi-purpose Probabilistic Risk Assessment (PRA) software framework that allows dispatching different functionalities. It is designed to derive and actuate the control logic required to simulate the plant control system and operator actions (guided procedures) and to perform both Monte- Carlo sampling of random distributed events and Event Tree based analysis. In order to facilitate the input/output handling, a Graphical User Interface (GUI) and a post-processing data-mining module are available.more » RAVEN allows also to interface with several numerical codes such as RELAP5 and RELAP-7 and ad-hoc system simulators. For the space propulsion system problem, an ad-hoc simulator has been developed and written in python language and then interfaced to RAVEN. Such simulator fully models both deterministic (e.g., system dynamics and interactions between system components) and stochastic behaviors (i.e., failures of components/systems such as distribution lines and thrusters). Stochastic analysis is performed using random sampling based methodologies (i.e., Monte-Carlo). Such analysis is accomplished to determine both the reliability of the space propulsion system and to propagate the uncertainties associated to a specific set of parameters. As also indicated in the scope of the benchmark problem, the results generated by the stochastic analysis are used to generate risk-informed insights such as conditions under witch different strategy can be followed.« less

Spike timing precision of neuronal circuits.

PubMed

Kilinc, Deniz; Demir, Alper

2018-06-01

Spike timing is believed to be a key factor in sensory information encoding and computations performed by the neurons and neuronal circuits. However, the considerable noise and variability, arising from the inherently stochastic mechanisms that exist in the neurons and the synapses, degrade spike timing precision. Computational modeling can help decipher the mechanisms utilized by the neuronal circuits in order to regulate timing precision. In this paper, we utilize semi-analytical techniques, which were adapted from previously developed methods for electronic circuits, for the stochastic characterization of neuronal circuits. These techniques, which are orders of magnitude faster than traditional Monte Carlo type simulations, can be used to directly compute the spike timing jitter variance, power spectral densities, correlation functions, and other stochastic characterizations of neuronal circuit operation. We consider three distinct neuronal circuit motifs: Feedback inhibition, synaptic integration, and synaptic coupling. First, we show that both the spike timing precision and the energy efficiency of a spiking neuron are improved with feedback inhibition. We unveil the underlying mechanism through which this is achieved. Then, we demonstrate that a neuron can improve on the timing precision of its synaptic inputs, coming from multiple sources, via synaptic integration: The phase of the output spikes of the integrator neuron has the same variance as that of the sample average of the phases of its inputs. Finally, we reveal that weak synaptic coupling among neurons, in a fully connected network, enables them to behave like a single neuron with a larger membrane area, resulting in an improvement in the timing precision through cooperation.

A Correlation-based Framework for Evaluating Postural Control Stochastic Dynamics

PubMed Central

Hernandez, Manuel E.; Snider, Joseph; Stevenson, Cory; Cauwenberghs, Gert; Poizner, Howard

2016-01-01

The inability to maintain balance during varying postural control conditions can lead to falls, a significant cause of mortality and serious injury among older adults. However, our understanding of the underlying dynamical and stochastic processes in human postural control have not been fully explored. To further our understanding of the underlying dynamical processes, we examine a novel conceptual framework for studying human postural control using the center of pressure (COP) velocity autocorrelation function (COP-VAF) and compare its results to Stabilogram Diffusion Analysis (SDA). Eleven healthy young participants were studied under quiet unipedal or bipedal standing conditions with eyes either opened or closed. COP trajectories were analyzed using both the traditional posturographic measure SDA and the proposed COP-VAF. It is shown that the COP-VAF leads to repeatable, physiologically meaningful measures that distinguish postural control differences in unipedal versus bipedal stance trials with and without vision in healthy individuals. More specifically, both a unipedal stance and lack of visual feedback increased initial values of the COP-VAF, magnitude of the first minimum, and diffusion coefficient, particularly in contrast to bipedal stance trials with open eyes. Use of a stochastic postural control model, based on an Ornstein-Uhlenbeck process that accounts for natural weight-shifts, suggests an increase in spring constant and decreased damping coefficient when fitted to experimental data. This work suggests that we can further extend our understanding of the underlying mechanisms behind postural control in quiet stance under varying stance conditions using the COP-VAF and provides a tool for quantifying future neurorehabilitative interventions. PMID:26011886

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

NASA Astrophysics Data System (ADS)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Pattern Transitions in Bacterial Oscillating System under Nanofluidic Confinement

NASA Astrophysics Data System (ADS)

Shen, Jie-Pan; Chou, Chia-Fu

2011-03-01

Successful binary fission in E. coli relies on remarkable oscillatory behavior of the MinCDE protein system to determine the exact division site. The most favorable models to explain this fascinating spatiotemporal regulation on dynamic MinDE pattern formation in cells are based on reaction-diffusion scenario. Although not fully understood, geometric factors caused by bacterial morphology play a crucial role in MinDE dynamics. In the present study, bacteria were cultured, confined and reshaped in various micro/nanofluidic devices, to mimic either curvature changes of cell peripherals. Fluorescence imaging was utilized to detail the mode transitions in multiple MinDE patterns. The understanding of the physics in multiple pattern formations is further complemented via in silico modeling. The study synergizes the join merits of in vivo, in vitro and in silico approaches, to grasp the insight of stochastic dynamics inherited from the noisy mesoscopic biophysics. We acknowledge support from the Foresight Project, Academia Sinica.

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.

PubMed

Vlachas, Pantelis R; Byeon, Wonmin; Wan, Zhong Y; Sapsis, Themistoklis P; Koumoutsakos, Petros

2018-05-01

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model

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

Griebel, M., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de; Rüttgers, A., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de

The multiscale FENE model is applied to a 3D square-square contraction flow problem. For this purpose, the stochastic Brownian configuration field method (BCF) has been coupled with our fully parallelized three-dimensional Navier-Stokes solver NaSt3DGPF. The robustness of the BCF method enables the numerical simulation of high Deborah number flows for which most macroscopic methods suffer from stability issues. The results of our simulations are compared with that of experimental measurements from literature and show a very good agreement. In particular, flow phenomena such as a strong vortex enhancement, streamline divergence and a flow inversion for highly elastic flows are reproduced.more » Due to their computational complexity, our simulations require massively parallel computations. Using a domain decomposition approach with MPI, the implementation achieves excellent scale-up results for up to 128 processors.« less

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Stochastic receding horizon control: application to an octopedal robot

NASA Astrophysics Data System (ADS)

Shah, Shridhar K.; Tanner, Herbert G.

2013-06-01

Miniature autonomous systems are being developed under ARL's Micro Autonomous Systems and Technology (MAST). These systems can only be fitted with a small-size processor, and their motion behavior is inherently uncertain due to manufacturing and platform-ground interactions. One way to capture this uncertainty is through a stochastic model. This paper deals with stochastic motion control design and implementation for MAST- specific eight-legged miniature crawling robots, which have been kinematically modeled as systems exhibiting the behavior of a Dubin's car with stochastic noise. The control design takes the form of stochastic receding horizon control, and is implemented on a Gumstix Overo Fire COM with 720 MHz processor and 512 MB RAM, weighing 5.5 g. The experimental results show the effectiveness of this control law for miniature autonomous systems perturbed by stochastic noise.

The nature of turbulence in a triangular lattice gas automaton

NASA Astrophysics Data System (ADS)

Duong-Van, Minh; Feit, M. D.; Keller, P.; Pound, M.

1986-12-01

Power spectra calculated from the coarse-graining of a simple lattice gas automaton, and those of time averaging other stochastic times series that we have investigated, have exponents in the range -1.6 to -2, consistent with observation of fully developed turbulence. This power spectrum is a natural consequence of coarse-graining; the exponent -2 represents the continuum limit.

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.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

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

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology

NASA Astrophysics Data System (ADS)

Fridström, R.; Chapman, B. E.; Almagri, A. F.; Frassinetti, L.; Brunsell, P. R.; Nishizawa, T.; Sarff, J. S.

2018-06-01

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ˜ tenfold variation in the fluctuation amplitude, the viscosity increases ˜100 -fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Simulating biological processes: stochastic physics from whole cells to colonies.

PubMed

Earnest, Tyler M; Cole, John A; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Simulating biological processes: stochastic physics from whole cells to colonies

NASA Astrophysics Data System (ADS)

Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Model-assisted probability of detection of flaws in aluminum blocks using polynomial chaos expansions

NASA Astrophysics Data System (ADS)

Du, Xiaosong; Leifsson, Leifur; Grandin, Robert; Meeker, William; Roberts, Ronald; Song, Jiming

2018-04-01

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination with model-assisted POD (MAPOD) methods. With the development of advanced physics-based methods, such as ultrasonic NDT testing, the empirical information, needed for POD methods, can be reduced. However, performing accurate numerical simulations can be prohibitively time-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through the physics-based simulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using non-intrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary least-squares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw in an aluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation model for this case, which is the UTSim2 model.

Data Assimilation and Propagation of Uncertainty in Multiscale Cardiovascular Simulation

NASA Astrophysics Data System (ADS)

Schiavazzi, Daniele; Marsden, Alison

2015-11-01

Cardiovascular modeling is the application of computational tools to predict hemodynamics. State-of-the-art techniques couple a 3D incompressible Navier-Stokes solver with a boundary circulation model and can predict local and peripheral hemodynamics, analyze the post-operative performance of surgical designs and complement clinical data collection minimizing invasive and risky measurement practices. The ability of these tools to make useful predictions is directly related to their accuracy in representing measured physiologies. Tuning of model parameters is therefore a topic of paramount importance and should include clinical data uncertainty, revealing how this uncertainty will affect the predictions. We propose a fully Bayesian, multi-level approach to data assimilation of uncertain clinical data in multiscale circulation models. To reduce the computational cost, we use a stable, condensed approximation of the 3D model build by linear sparse regression of the pressure/flow rate relationship at the outlets. Finally, we consider the problem of non-invasively propagating the uncertainty in model parameters to the resulting hemodynamics and compare Monte Carlo simulation with Stochastic Collocation approaches based on Polynomial or Multi-resolution Chaos expansions.

Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.

PubMed

Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel

2018-03-01

In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

PubMed

Zimmer, Christoph

2016-01-01

Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

Stochastic Parameterization: Toward a New View of Weather and Climate Models

DOE PAGES

Berner, Judith; Achatz, Ulrich; Batté, Lauriane; ...

2017-03-31

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

Stochastic Parameterization: Toward a New View of Weather and Climate Models

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

Berner, Judith; Achatz, Ulrich; Batté, Lauriane

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Stochastic simulation of human pulmonary blood flow and transit time frequency distribution based on anatomic and elasticity data.

PubMed

Huang, Wei; Shi, Jun; Yen, R T

2012-12-01

The objective of our study was to develop a computing program for computing the transit time frequency distributions of red blood cell in human pulmonary circulation, based on our anatomic and elasticity data of blood vessels in human lung. A stochastic simulation model was introduced to simulate blood flow in human pulmonary circulation. In the stochastic simulation model, the connectivity data of pulmonary blood vessels in human lung was converted into a probability matrix. Based on this model, the transit time of red blood cell in human pulmonary circulation and the output blood pressure were studied. Additionally, the stochastic simulation model can be used to predict the changes of blood flow in human pulmonary circulation with the advantage of the lower computing cost and the higher flexibility. In conclusion, a stochastic simulation approach was introduced to simulate the blood flow in the hierarchical structure of a pulmonary circulation system, and to calculate the transit time distributions and the blood pressure outputs.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Moroz, I.; Palmer, T.

2015-12-01

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic ensemble forecasts, and a number of different techniques have been proposed for this purpose. Stochastic convection parameterization schemes use random numbers to represent the difference between a deterministic parameterization scheme and the true atmosphere, accounting for the unresolved sub grid-scale variability associated with convective clouds. An alternative approach varies the values of poorly constrained physical parameters in the model to represent the uncertainty in these parameters. This study presents new perturbed parameter schemes for use in the European Centre for Medium Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parametrisation scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are changed between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, Stochastically Perturbed Parametrisation Tendencies (SPPT), and to a model which does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parametrisation in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skilful representations of model uncertainty due to convection parametrisation. Reference: H. M. Christensen, I. M. Moroz, and T. N. Palmer, 2015: Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization. J. Atmos. Sci., 72, 2525-2544.

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui

2018-06-01

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness.

Representing and computing regular languages on massively parallel networks

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

Miller, M.I.; O'Sullivan, J.A.; Boysam, B.

1991-01-01

This paper proposes a general method for incorporating rule-based constraints corresponding to regular languages into stochastic inference problems, thereby allowing for a unified representation of stochastic and syntactic pattern constraints. The authors' approach first established the formal connection of rules to Chomsky grammars, and generalizes the original work of Shannon on the encoding of rule-based channel sequences to Markov chains of maximum entropy. This maximum entropy probabilistic view leads to Gibb's representations with potentials which have their number of minima growing at precisely the exponential rate that the language of deterministically constrained sequences grow. These representations are coupled to stochasticmore » diffusion algorithms, which sample the language-constrained sequences by visiting the energy minima according to the underlying Gibbs' probability law. The coupling to stochastic search methods yields the all-important practical result that fully parallel stochastic cellular automata may be derived to generate samples from the rule-based constraint sets. The production rules and neighborhood state structure of the language of sequences directly determines the necessary connection structures of the required parallel computing surface. Representations of this type have been mapped to the DAP-510 massively-parallel processor consisting of 1024 mesh-connected bit-serial processing elements for performing automated segmentation of electron-micrograph images.« less

Amerciamysis bahia Stochastic Matrix Population Model for Laboratory Populations

EPA Science Inventory

The population model described here is a stochastic, density-independent matrix model for integrating the effects of toxicants on survival and reproduction of the marine invertebrate, Americamysis bahia. The model was constructed using Microsoft® Excel 2003. The focus of the mode...

Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2017-08-01

The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Threshold for extinction and survival in stochastic tumor immune system

NASA Astrophysics Data System (ADS)

Li, Dongxi; Cheng, Fangjuan

2017-10-01

This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.

Digital hardware implementation of a stochastic two-dimensional neuron model.

PubMed

Grassia, F; Kohno, T; Levi, T

2016-11-01

This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments. Copyright © 2017 Elsevier Ltd. All rights reserved.

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

NASA Astrophysics Data System (ADS)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

Identification and stochastic control of helicopter dynamic modes

NASA Technical Reports Server (NTRS)

Molusis, J. A.; Bar-Shalom, Y.

1983-01-01

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

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.

GillesPy: A Python Package for Stochastic Model Building and Simulation.

PubMed

Abel, John H; Drawert, Brian; Hellander, Andreas; Petzold, Linda R

2016-09-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.

GillesPy: A Python Package for Stochastic Model Building and Simulation

PubMed Central

Abel, John H.; Drawert, Brian; Hellander, Andreas; Petzold, Linda R.

2017-01-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community. PMID:28630888

Dynamics of a stochastic cell-to-cell HIV-1 model with distributed delay

NASA Astrophysics Data System (ADS)

Ji, Chunyan; Liu, Qun; Jiang, Daqing

2018-02-01

In this paper, we consider a stochastic cell-to-cell HIV-1 model with distributed delay. Firstly, we show that there is a global positive solution of this model before exploring its long-time behavior. Then sufficient conditions for extinction of the disease are established. Moreover, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Finally, we provide some numerical examples to illustrate theoretical results.

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.

Dynamics of stochastic SEIS epidemic model with varying population size

NASA Astrophysics Data System (ADS)

Liu, Jiamin; Wei, Fengying

2016-12-01

We introduce the stochasticity into a deterministic model which has state variables susceptible-exposed-infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô's formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

Study on the threshold of a stochastic SIR epidemic model and its extensions

NASA Astrophysics Data System (ADS)

Zhao, Dianli

2016-09-01

This paper provides a simple but effective method for estimating the threshold of a class of the stochastic epidemic models by use of the nonnegative semimartingale convergence theorem. Firstly, the threshold R0SIR is obtained for the stochastic SIR model with a saturated incidence rate, whose value is below 1 or above 1 will completely determine the disease to go extinct or prevail for any size of the white noise. Besides, when R0SIR > 1 , the system is proved to be convergent in time mean. Then, the threshold of the stochastic SIVS models with or without saturated incidence rate are also established by the same method. Comparing with the previously-known literatures, the related results are improved, and the method is simpler than before.

Smoothing spline ANOVA frailty model for recurrent event data.

PubMed

Du, Pang; Jiang, Yihua; Wang, Yuedong

2011-12-01

Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data. © 2011, The International Biometric Society.

No tension between assembly models of super massive black hole binaries and pulsar observations.

PubMed

Middleton, Hannah; Chen, Siyuan; Del Pozzo, Walter; Sesana, Alberto; Vecchio, Alberto

2018-02-08

Pulsar timing arrays are presently the only means to search for the gravitational wave stochastic background from super massive black hole binary populations, considered to be within the grasp of current or near-future observations. The stringent upper limit from the Parkes Pulsar Timing Array has been interpreted as excluding (>90% confidence) the current paradigm of binary assembly through galaxy mergers and hardening via stellar interaction, suggesting evolution is accelerated or stalled. Using Bayesian hierarchical modelling we consider implications of this upper limit for a range of astrophysical scenarios, without invoking stalling, nor more exotic physical processes. All scenarios are fully consistent with the upper limit, but (weak) bounds on population parameters can be inferred. Recent upward revisions of the black hole-galaxy bulge mass relation are disfavoured at 1.6σ against lighter models. Once sensitivity improves by an order of magnitude, a non-detection will disfavour the most optimistic scenarios at 3.9σ.

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.

Stochastic Ordering Using the Latent Trait and the Sum Score in Polytomous IRT Models.

ERIC Educational Resources Information Center

Hemker, Bas T.; Sijtsma, Klaas; Molenaar, Ivo W.; Junker, Brian W.

1997-01-01

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)

Stochastic analysis of future vehicle populations

DOT National Transportation Integrated Search

1979-05-01

The purpose of this study was to build a stochastic model of future vehicle populations. Such a model can be used to investigate the uncertainties inherent in Future Vehicle Populations. The model, which is called the Future Automobile Population Sto...

Evidence-based Controls for Epidemics Using Spatio-temporal Stochastic Model as a Bayesian Framwork

USDA-ARS?s Scientific Manuscript database

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models con...

On the impact of a refined stochastic model for airborne LiDAR measurements

NASA Astrophysics Data System (ADS)

Bolkas, Dimitrios; Fotopoulos, Georgia; Glennie, Craig

2016-09-01

Accurate topographic information is critical for a number of applications in science and engineering. In recent years, airborne light detection and ranging (LiDAR) has become a standard tool for acquiring high quality topographic information. The assessment of airborne LiDAR derived DEMs is typically based on (i) independent ground control points and (ii) forward error propagation utilizing the LiDAR geo-referencing equation. The latter approach is dependent on the stochastic model information of the LiDAR observation components. In this paper, the well-known statistical tool of variance component estimation (VCE) is implemented for a dataset in Houston, Texas, in order to refine the initial stochastic information. Simulations demonstrate the impact of stochastic-model refinement for two practical applications, namely coastal inundation mapping and surface displacement estimation. Results highlight scenarios where erroneous stochastic information is detrimental. Furthermore, the refined stochastic information provides insights on the effect of each LiDAR measurement in the airborne LiDAR error budget. The latter is important for targeting future advancements in order to improve point cloud accuracy.

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation

PubMed Central

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO2) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms. PMID:29670508

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation.

PubMed

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO 2 ) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Treesearch

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

PubMed Central

Walpole, J.; Chappell, J.C.; Cluceru, J.G.; Mac Gabhann, F.; Bautch, V.L.; Peirce, S. M.

2015-01-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods. PMID:26158406

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks.

PubMed

Walpole, J; Chappell, J C; Cluceru, J G; Mac Gabhann, F; Bautch, V L; Peirce, S M

2015-09-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies

NASA Astrophysics Data System (ADS)

Williams, Paul; Howe, Nicola; Gregory, Jonathan; Smith, Robin; Joshi, Manoj

2017-04-01

In climate simulations, the impacts of the subgrid scales on the resolved scales are conventionally represented using deterministic closure schemes, which assume that the impacts are uniquely determined by the resolved scales. Stochastic parameterization relaxes this assumption, by sampling the subgrid variability in a computationally inexpensive manner. This study shows that the simulated climatological state of the ocean is improved in many respects by implementing a simple stochastic parameterization of ocean eddies into a coupled atmosphere-ocean general circulation model. Simulations from a high-resolution, eddy-permitting ocean model are used to calculate the eddy statistics needed to inject realistic stochastic noise into a low-resolution, non-eddy-permitting version of the same model. A suite of four stochastic experiments is then run to test the sensitivity of the simulated climate to the noise definition by varying the noise amplitude and decorrelation time within reasonable limits. The addition of zero-mean noise to the ocean temperature tendency is found to have a nonzero effect on the mean climate. Specifically, in terms of the ocean temperature and salinity fields both at the surface and at depth, the noise reduces many of the biases in the low-resolution model and causes it to more closely resemble the high-resolution model. The variability of the strength of the global ocean thermohaline circulation is also improved. It is concluded that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost. Therefore, stochastic parameterizations of ocean eddies have the potential to significantly improve climate simulations. Reference Williams PD, Howe NJ, Gregory JM, Smith RS, and Joshi MM (2016) Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies. Journal of Climate, 29, 8763-8781. http://dx.doi.org/10.1175/JCLI-D-15-0746.1

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

Petri Net and Probabilistic Model Checking Based Approach for the Modelling, Simulation and Verification of Internet Worm Propagation

PubMed Central

Razzaq, Misbah; Ahmad, Jamil

2015-01-01

Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR) model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) (SEIDQR(S/I)) along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework. PMID:26713449

Petri Net and Probabilistic Model Checking Based Approach for the Modelling, Simulation and Verification of Internet Worm Propagation.

PubMed

Razzaq, Misbah; Ahmad, Jamil

2015-01-01

Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR) model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) (SEIDQR(S/I)) along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework.

Assessing sequential data assimilation techniques for integrating GRACE data into a hydrological model

NASA Astrophysics Data System (ADS)

Khaki, M.; Hoteit, I.; Kuhn, M.; Awange, J.; Forootan, E.; van Dijk, A. I. J. M.; Schumacher, M.; Pattiaratchi, C.

2017-09-01

The time-variable terrestrial water storage (TWS) products from the Gravity Recovery And Climate Experiment (GRACE) have been increasingly used in recent years to improve the simulation of hydrological models by applying data assimilation techniques. In this study, for the first time, we assess the performance of the most popular data assimilation sequential techniques for integrating GRACE TWS into the World-Wide Water Resources Assessment (W3RA) model. We implement and test stochastic and deterministic ensemble-based Kalman filters (EnKF), as well as Particle filters (PF) using two different resampling approaches of Multinomial Resampling and Systematic Resampling. These choices provide various opportunities for weighting observations and model simulations during the assimilation and also accounting for error distributions. Particularly, the deterministic EnKF is tested to avoid perturbing observations before assimilation (that is the case in an ordinary EnKF). Gaussian-based random updates in the EnKF approaches likely do not fully represent the statistical properties of the model simulations and TWS observations. Therefore, the fully non-Gaussian PF is also applied to estimate more realistic updates. Monthly GRACE TWS are assimilated into W3RA covering the entire Australia. To evaluate the filters performances and analyze their impact on model simulations, their estimates are validated by independent in-situ measurements. Our results indicate that all implemented filters improve the estimation of water storage simulations of W3RA. The best results are obtained using two versions of deterministic EnKF, i.e. the Square Root Analysis (SQRA) scheme and the Ensemble Square Root Filter (EnSRF), respectively, improving the model groundwater estimations errors by 34% and 31% compared to a model run without assimilation. Applying the PF along with Systematic Resampling successfully decreases the model estimation error by 23%.

Price sensitive demand with random sales price - a newsboy problem

NASA Astrophysics Data System (ADS)

Sankar Sana, Shib

2012-03-01

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks.

PubMed

Adalsteinsson, David; McMillen, David; Elston, Timothy C

2004-03-08

Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solves the appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Simple and Hierarchical Models for Stochastic Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

1993-01-01

Test misgrading is treated as a stochastic process. The expected number of misgradings, inter-occurrence time of misgradings, and waiting time for the "n"th misgrading are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Examples of model construction are given. (SLD)

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

EPA Science Inventory

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Application of an NLME-Stochastic Deconvolution Approach to Level A IVIVC Modeling.

PubMed

Kakhi, Maziar; Suarez-Sharp, Sandra; Shepard, Terry; Chittenden, Jason

2017-07-01

Stochastic deconvolution is a parameter estimation method that calculates drug absorption using a nonlinear mixed-effects model in which the random effects associated with absorption represent a Wiener process. The present work compares (1) stochastic deconvolution and (2) numerical deconvolution, using clinical pharmacokinetic (PK) data generated for an in vitro-in vivo correlation (IVIVC) study of extended release (ER) formulations of a Biopharmaceutics Classification System class III drug substance. The preliminary analysis found that numerical and stochastic deconvolution yielded superimposable fraction absorbed (F abs ) versus time profiles when supplied with exactly the same externally determined unit impulse response parameters. In a separate analysis, a full population-PK/stochastic deconvolution was applied to the clinical PK data. Scenarios were considered in which immediate release (IR) data were either retained or excluded to inform parameter estimation. The resulting F abs profiles were then used to model level A IVIVCs. All the considered stochastic deconvolution scenarios, and numerical deconvolution, yielded on average similar results with respect to the IVIVC validation. These results could be achieved with stochastic deconvolution without recourse to IR data. Unlike numerical deconvolution, this also implies that in crossover studies where certain individuals do not receive an IR treatment, their ER data alone can still be included as part of the IVIVC analysis. Published by Elsevier Inc.

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

NASA Astrophysics Data System (ADS)

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

2018-06-01

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.

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.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

PubMed Central

Zimmer, Christoph

2016-01-01

Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802

Lagrangian acceleration statistics in a turbulent channel flow

NASA Astrophysics Data System (ADS)

Stelzenmuller, Nickolas; Polanco, Juan Ignacio; Vignal, Laure; Vinkovic, Ivana; Mordant, Nicolas

2017-05-01

Lagrangian acceleration statistics in a fully developed turbulent channel flow at Reτ=1440 are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced Lagrangian stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.

ESS++: a C++ objected-oriented algorithm for Bayesian stochastic search model exploration

PubMed Central

Bottolo, Leonardo; Langley, Sarah R.; Petretto, Enrico; Tiret, Laurence; Tregouet, David; Richardson, Sylvia

2011-01-01

Summary: ESS++ is a C++ implementation of a fully Bayesian variable selection approach for single and multiple response linear regression. ESS++ works well both when the number of observations is larger than the number of predictors and in the ‘large p, small n’ case. In the current version, ESS++ can handle several hundred observations, thousands of predictors and a few responses simultaneously. The core engine of ESS++ for the selection of relevant predictors is based on Evolutionary Monte Carlo. Our implementation is open source, allowing community-based alterations and improvements. Availability: C++ source code and documentation including compilation instructions are available under GNU licence at http://bgx.org.uk/software/ESS.html. Contact: l.bottolo@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:21233165

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.

Parameter discovery in stochastic biological models using simulated annealing and statistical model checking.

PubMed

Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J

2014-01-01

Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.

Stochastic volatility models and Kelvin waves

NASA Astrophysics Data System (ADS)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Didactic discussion of stochastic resonance effects and weak signals

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

Adair, R.K.

1996-12-01

A simple, paradigmatic, model is used to illustrate some general properties of effects subsumed under the label stochastic resonance. In particular, analyses of the transparent model show that (1) a small amount of noise added to a much larger signal can greatly increase the response to the signal, but (2) a weak signal added to much larger noise will not generate a substantial added response. The conclusions drawn from the model illustrate the general result that stochastic resonance effects do not provide an avenue for signals that are much smaller than noise to affect biology. A further analysis demonstrates themore » effects of small signals in the shifting of biologically important chemical equilibria under conditions where stochastic resonance effects are significant.« less

Inference for dynamics of continuous variables: the extended Plefka expansion with hidden nodes

NASA Astrophysics Data System (ADS)

Bravi, B.; Sollich, P.

2017-06-01

We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks underlying many cellular and metabolic processes are important realizations of such a scenario as typically one is interested in reconstructing the time evolution of unobserved chemical concentrations starting from the experimentally more accessible ones. We present an application to this problem of a novel dynamical mean field approximation, the extended Plefka expansion, which is based on a path integral description of the stochastic dynamics. As a paradigmatic model we study the stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings. The resulting joint distribution is known to be Gaussian and this allows us to fully characterize the posterior statistics of the hidden nodes. In particular the equal-time hidden-to-hidden variance—conditioned on observations—gives the expected error at each node when the hidden time courses are predicted based on the observations. We assess the accuracy of the extended Plefka expansion in predicting these single node variances as well as error correlations over time, focussing on the role of the system size and the number of observed nodes.

On Local Homogeneity and Stochastically Ordered Mixed Rasch Models

ERIC Educational Resources Information Center

Kreiner, Svend; Hansen, Mogens; Hansen, Carsten Rosenberg

2006-01-01

Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total…

The critical domain size of stochastic population models.

PubMed

Reimer, Jody R; Bonsall, Michael B; Maini, Philip K

2017-02-01

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.

Stochastic Approximation Methods for Latent Regression Item Response Models

ERIC Educational Resources Information Center

von Davier, Matthias; Sinharay, Sandip

2010-01-01

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…

Stochastic models for regulatory networks of the genetic toggle switch.

PubMed

Tian, Tianhai; Burrage, Kevin

2006-05-30

Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic models for regulatory networks of the genetic toggle switch

PubMed Central

Tian, Tianhai; Burrage, Kevin

2006-01-01

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks. PMID:16714385

Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells.

PubMed

Garijo, N; Manzano, R; Osta, R; Perez, M A

2012-12-07

Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stochastic modeling of soundtrack for efficient segmentation and indexing of video

NASA Astrophysics Data System (ADS)

Naphade, Milind R.; Huang, Thomas S.

1999-12-01

Tools for efficient and intelligent management of digital content are essential for digital video data management. An extremely challenging research area in this context is that of multimedia analysis and understanding. The capabilities of audio analysis in particular for video data management are yet to be fully exploited. We present a novel scheme for indexing and segmentation of video by analyzing the audio track. This analysis is then applied to the segmentation and indexing of movies. We build models for some interesting events in the motion picture soundtrack. The models built include music, human speech and silence. We propose the use of hidden Markov models to model the dynamics of the soundtrack and detect audio-events. Using these models we segment and index the soundtrack. A practical problem in motion picture soundtracks is that the audio in the track is of a composite nature. This corresponds to the mixing of sounds from different sources. Speech in foreground and music in background are common examples. The coexistence of multiple individual audio sources forces us to model such events explicitly. Experiments reveal that explicit modeling gives better result than modeling individual audio events separately.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator.

PubMed

González Ochoa, Héctor O; Perales, Gualberto Solís; Epstein, Irving R; Femat, Ricardo

2018-05-01

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator

NASA Astrophysics Data System (ADS)

González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo

2018-05-01

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

Reynolds, Andy

2002-11-01

It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

An inexact mixed risk-aversion two-stage stochastic programming model for water resources management under uncertainty.

PubMed

Li, W; Wang, B; Xie, Y L; Huang, G H; Liu, L

2015-02-01

Uncertainties exist in the water resources system, while traditional two-stage stochastic programming is risk-neutral and compares the random variables (e.g., total benefit) to identify the best decisions. To deal with the risk issues, a risk-aversion inexact two-stage stochastic programming model is developed for water resources management under uncertainty. The model was a hybrid methodology of interval-parameter programming, conditional value-at-risk measure, and a general two-stage stochastic programming framework. The method extends on the traditional two-stage stochastic programming method by enabling uncertainties presented as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. It could not only provide information on the benefits of the allocation plan to the decision makers but also measure the extreme expected loss on the second-stage penalty cost. The developed model was applied to a hypothetical case of water resources management. Results showed that that could help managers generate feasible and balanced risk-aversion allocation plans, and analyze the trade-offs between system stability and economy.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Food web structure and interaction strength pave the way for vulnerability to extinction.

PubMed

Karlsson, Patrik; Jonsson, Tomas; Jonsson, Annie

2007-11-07

This paper focuses on how food web structure and interactions among species affects the vulnerability, due to environmental variability, to extinction of species at different positions in model food webs. Vulnerability is here not measured by a traditional extinction threshold but is instead inspired by the IUCN criteria for endangered species: an observed rapid decline in population abundance. Using model webs influenced by stochasticity with zero autocorrelation, we investigate the ecological determinants of species vulnerability, i.e. the trophic interactions between species and food web structure and how these interact with the risk of sudden drops in abundance of species. We find that (i) producers fulfil the criterion of vulnerable species more frequently than other species, (ii) food web structure is related to vulnerability, and (iii) the vulnerability of species is greater when involved in a strong trophic interaction than when not. We note that our result on the relationship between extinction risk and trophic position of species contradict previous suggestions and argue that the main reason for the discrepancy probably is due to the fact that we study the vulnerability to environmental stochasticity and not extinction risk due to overexploitation, habitat destruction or interactions with introduced species. Thus, we suggest that the vulnerability of species to environmental stochasticity may be differently related to trophic position than the vulnerability of species to other factors. Earlier research on species extinctions has looked for intrinsic traits of species that correlate with increased vulnerability to extinction. However, to fully understand the extinction process we must also consider that species interactions may affect vulnerability and that not all extinctions are the result of long, gradual reductions in species abundances. Under environmental stochasticity (which importance frequently is assumed to increase as a result of climate change) and direct and indirect interactions with other species some extinctions may occur rapidly and apparently unexpectedly. To identify the first declines of population abundances that may escalate and lead to extinctions as early as possible, we need to recognize which species are at greatest risk of entering such dangerous routes and under what circumstances. This new perspective may contribute to our understanding of the processes leading to extinction of populations and eventually species. This is especially urgent in the light of the current biodiversity crisis where a large fraction of the world's biodiversity is threatened.

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.

A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs.

PubMed

Liang, Yanfeng; Greenhalgh, David; Mao, Xuerong

2016-01-01

We introduce stochasticity into the deterministic differential equation model for the spread of HIV amongst people who inject drugs (PWIDs) studied by Greenhalgh and Hay (1997). This was based on the original model constructed by Kaplan (1989) which analyses the behaviour of HIV/AIDS amongst a population of PWIDs. We derive a stochastic differential equation (SDE) for the fraction of PWIDs who are infected with HIV at time. The stochasticity is introduced using the well-known standard technique of parameter perturbation. We first prove that the resulting SDE for the fraction of infected PWIDs has a unique solution in (0, 1) provided that some infected PWIDs are initially present and next construct the conditions required for extinction and persistence. Furthermore, we show that there exists a stationary distribution for the persistence case. Simulations using realistic parameter values are then constructed to illustrate and support our theoretical results. Our results provide new insight into the spread of HIV amongst PWIDs. The results show that the introduction of stochastic noise into a model for the spread of HIV amongst PWIDs can cause the disease to die out in scenarios where deterministic models predict disease persistence.

A study about the existence of the leverage effect in stochastic volatility models

NASA Astrophysics Data System (ADS)

Florescu, Ionuţ; Pãsãricã, Cristian Gabriel

2009-02-01

The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage effect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility increases and vice versa. Consequently, it is important to demonstrate that any formulated model for the asset price is capable of generating this effect observed in practice. Furthermore, we need to understand the conditions on the parameters present in the model that guarantee the apparition of the leverage effect. In this paper we analyze two general specifications of stochastic volatility models and their capability of generating the perceived leverage effect. We derive conditions for the apparition of leverage effect in both of these stochastic volatility models. We exemplify using stochastic volatility models used in practice and we explicitly state the conditions for the existence of the leverage effect in these examples.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race.

PubMed

Warnke, Tom; Reinhardt, Oliver; Klabunde, Anna; Willekens, Frans; Uhrmacher, Adelinde M

2017-10-01

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

Performance of stochastic approaches for forecasting river water quality.

PubMed

Ahmad, S; Khan, I H; Parida, B P

2001-12-01

This study analysed water quality data collected from the river Ganges in India from 1981 to 1990 for forecasting using stochastic models. Initially the box and whisker plots and Kendall's tau test were used to identify the trends during the study period. For detecting the possible intervention in the data the time series plots and cusum charts were used. The three approaches of stochastic modelling which account for the effect of seasonality in different ways. i.e. multiplicative autoregressive integrated moving average (ARIMA) model. deseasonalised model and Thomas-Fiering model were used to model the observed pattern in water quality. The multiplicative ARIMA model having both nonseasonal and seasonal components were, in general, identified as appropriate models. In the deseasonalised modelling approach, the lower order ARIMA models were found appropriate for the stochastic component. The set of Thomas-Fiering models were formed for each month for all water quality parameters. These models were then used to forecast the future values. The error estimates of forecasts from the three approaches were compared to identify the most suitable approach for the reliable forecast. The deseasonalised modelling approach was recommended for forecasting of water quality parameters of a river.

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

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.

Reflected stochastic differential equation models for constrained animal movement

USGS Publications Warehouse

Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.

2017-01-01

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.

Development and validation of a stochastic model for potential growth of Listeria monocytogenes in naturally contaminated lightly preserved seafood.

PubMed

Mejlholm, Ole; Bøknæs, Niels; Dalgaard, Paw

2015-02-01

A new stochastic model for the simultaneous growth of Listeria monocytogenes and lactic acid bacteria (LAB) was developed and validated on data from naturally contaminated samples of cold-smoked Greenland halibut (CSGH) and cold-smoked salmon (CSS). During industrial processing these samples were added acetic and/or lactic acids. The stochastic model was developed from an existing deterministic model including the effect of 12 environmental parameters and microbial interaction (O. Mejlholm and P. Dalgaard, Food Microbiology, submitted for publication). Observed maximum population density (MPD) values of L. monocytogenes in naturally contaminated samples of CSGH and CSS were accurately predicted by the stochastic model based on measured variability in product characteristics and storage conditions. Results comparable to those from the stochastic model were obtained, when product characteristics of the least and most preserved sample of CSGH and CSS were used as input for the existing deterministic model. For both modelling approaches, it was shown that lag time and the effect of microbial interaction needs to be included to accurately predict MPD values of L. monocytogenes. Addition of organic acids to CSGH and CSS was confirmed as a suitable mitigation strategy against the risk of growth by L. monocytogenes as both types of products were in compliance with the EU regulation on ready-to-eat foods. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Hybrid Stochastic-Neuro-Fuzzy Model-Based System for In-Flight Gas Turbine Engine Diagnostics

DTIC Science & Technology

2001-04-05

Margin (ADM) and (ii) Fault Detection Margin (FDM). Key Words: ANFIS, Engine Health Monitoring , Gas Path Analysis, and Stochastic Analysis Adaptive Network...The paper illustrates the application of a hybrid Stochastic- Fuzzy -Inference Model-Based System (StoFIS) to fault diagnostics and prognostics for both...operational history monitored on-line by the engine health management (EHM) system. To capture the complex functional relationships between different

Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models

NASA Astrophysics Data System (ADS)

Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.

2018-02-01

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Inducing Tropical Cyclones to Undergo Brownian Motion

NASA Astrophysics Data System (ADS)

Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.

2014-12-01

Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.

Stochastic spectral projection of electrochemical thermal model for lithium-ion cell state estimation

NASA Astrophysics Data System (ADS)

Tagade, Piyush; Hariharan, Krishnan S.; Kolake, Subramanya Mayya; Song, Taewon; Oh, Dukjin

2017-03-01

A novel approach for integrating a pseudo-two dimensional electrochemical thermal (P2D-ECT) model and data assimilation algorithm is presented for lithium-ion cell state estimation. This approach refrains from making any simplifications in the P2D-ECT model while making it amenable for online state estimation. Though deterministic, uncertainty in the initial states induces stochasticity in the P2D-ECT model. This stochasticity is resolved by spectrally projecting the stochastic P2D-ECT model on a set of orthogonal multivariate Hermite polynomials. Volume averaging in the stochastic dimensions is proposed for efficient numerical solution of the resultant model. A state estimation framework is developed using a transformation of the orthogonal basis to assimilate the measurables with this system of equations. Effectiveness of the proposed method is first demonstrated by assimilating the cell voltage and temperature data generated using a synthetic test bed. This validated method is used with the experimentally observed cell voltage and temperature data for state estimation at different operating conditions and drive cycle protocols. The results show increased prediction accuracy when the data is assimilated every 30s. High accuracy of the estimated states is exploited to infer temperature dependent behavior of the lithium-ion cell.

Stochastic simulation of the spray formation assisted by a high pressure

NASA Astrophysics Data System (ADS)

Gorokhovski, M.; Chtab-Desportes, A.; Voloshina, I.; Askarova, A.

2010-03-01

The stochastic model of spray formation in the vicinity of the injector and in the far-field has been described and assessed by comparison with measurements in Diesel-like conditions. In the proposed mesh-free approach, the 3D configuration of continuous liquid core is simulated stochastically by ensemble of spatial trajectories of the specifically introduced stochastic particles. The parameters of the stochastic process are presumed from the physics of primary atomization. The spray formation model consists in computation of spatial distribution of the probability of finding the non-fragmented liquid jet in the near-to-injector region. This model is combined with KIVA II computation of atomizing Diesel spray in two-ways. First, simultaneously with the gas phase RANS computation, the ensemble of stochastic particles is tracking and the probability field of their positions is calculated, which is used for sampling of initial locations of primary blobs. Second, the velocity increment of the gas due to the liquid injection is computed from the mean volume fraction of the simulated liquid core. Two novelties are proposed in the secondary atomization modeling. The first one is due to unsteadiness of the injection velocity. When the injection velocity increment in time is decreasing, the supplementary breakup may be induced. Therefore the critical Weber number is based on such increment. Second, a new stochastic model of the secondary atomization is proposed, in which the intermittent turbulent stretching is taken into account as the main mechanism. The measurements reported by Arcoumanis et al. (time-history of the mean axial centre-line velocity of droplet, and of the centre-line Sauter Mean Diameter), are compared with computations.

Option pricing, stochastic volatility, singular dynamics and constrained path integrals

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Hojman, Sergio A.

2014-01-01

Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter ρ which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases ρ=±1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values ρ=±1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac’s method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral.

Generalised filtering and stochastic DCM for fMRI.

PubMed

Li, Baojuan; Daunizeau, Jean; Stephan, Klaas E; Penny, Will; Hu, Dewen; Friston, Karl

2011-09-15

This paper is about the fitting or inversion of dynamic causal models (DCMs) of fMRI time series. It tries to establish the validity of stochastic DCMs that accommodate random fluctuations in hidden neuronal and physiological states. We compare and contrast deterministic and stochastic DCMs, which do and do not ignore random fluctuations or noise on hidden states. We then compare stochastic DCMs, which do and do not ignore conditional dependence between hidden states and model parameters (generalised filtering and dynamic expectation maximisation, respectively). We first characterise state-noise by comparing the log evidence of models with different a priori assumptions about its amplitude, form and smoothness. Face validity of the inversion scheme is then established using data simulated with and without state-noise to ensure that DCM can identify the parameters and model that generated the data. Finally, we address construct validity using real data from an fMRI study of internet addiction. Our analyses suggest the following. (i) The inversion of stochastic causal models is feasible, given typical fMRI data. (ii) State-noise has nontrivial amplitude and smoothness. (iii) Stochastic DCM has face validity, in the sense that Bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity. (iv) Relaxing conditional independence assumptions can have greater construct validity, in terms of revealing group differences not disclosed by variational schemes. Finally, we note that the ability to model endogenous or random fluctuations on hidden neuronal (and physiological) states provides a new and possibly more plausible perspective on how regionally specific signals in fMRI are generated. Copyright © 2011. Published by Elsevier Inc.

Stochastic Models of Quality Control on Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

Stochastic models are developed in this article to examine the rate of test misgrading in educational and psychological measurement. The estimation of inadvertent grading errors can serve as a basis for quality control in measurement. Limitations of traditional Poisson models have been reviewed to highlight the need to introduce new models using…

The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence.

PubMed

Niu, Yuanling; Wang, Yue; Zhou, Da

2015-12-07

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In the previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples. Copyright © 2015 Elsevier Ltd. All rights reserved.

Approaches for modeling within subject variability in pharmacometric count data analysis: dynamic inter-occasion variability and stochastic differential equations.

PubMed

Deng, Chenhui; Plan, Elodie L; Karlsson, Mats O

2016-06-01

Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

Stochastic hybrid systems for studying biochemical processes.

PubMed

Singh, Abhyudai; Hespanha, João P

2010-11-13

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

Stochastic Robust Mathematical Programming Model for Power System Optimization

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

Liu, Cong; Changhyeok, Lee; Haoyong, Chen

2016-01-01

This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.

Statement Verification: A Stochastic Model of Judgment and Response.

ERIC Educational Resources Information Center

Wallsten, Thomas S.; Gonzalez-Vallejo, Claudia

1994-01-01

A stochastic judgment model (SJM) is presented as a framework for addressing issues in statement verification and probability judgment. Results of 5 experiments with 264 undergraduates support the validity of the model and provide new information that is interpreted in terms of the SJM. (SLD)

A stochastic method for stand-alone photovoltaic system sizing

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

Cabral, Claudia Valeria Tavora; Filho, Delly Oliveira; Martins, Jose Helvecio

Photovoltaic systems utilize solar energy to generate electrical energy to meet load demands. Optimal sizing of these systems includes the characterization of solar radiation. Solar radiation at the Earth's surface has random characteristics and has been the focus of various academic studies. The objective of this study was to stochastically analyze parameters involved in the sizing of photovoltaic generators and develop a methodology for sizing of stand-alone photovoltaic systems. Energy storage for isolated systems and solar radiation were analyzed stochastically due to their random behavior. For the development of the methodology proposed stochastic analysis were studied including the Markov chainmore » and beta probability density function. The obtained results were compared with those for sizing of stand-alone using from the Sandia method (deterministic), in which the stochastic model presented more reliable values. Both models present advantages and disadvantages; however, the stochastic one is more complex and provides more reliable and realistic results. (author)« less

Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model

NASA Astrophysics Data System (ADS)

Dtchetgnia Djeundam, S. R.; Yamapi, R.; Kofane, T. C.; Aziz-Alaoui, M. A.

2013-09-01

We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.

Ion heat transport in improved confinement MST plasmas

NASA Astrophysics Data System (ADS)

Xing, Zichuan; Nornberg, Mark; den Hartog, Daniel J.; Kumar, Santhosh; Anderson, Jay K.

2016-10-01

Ion power balance in improved confinement (PPCD) plasmas in MST is dominated by electron collisional heating balanced by charge exchange transport. Neoclassical effects on ions in the RFP are inherently small and PPCD plasmas have reduced turbulence and stochasticity. Thus PPCD plasmas provide a good starting point for a transport model developed to account for collisional equilibration between species, classical conductive energy transport, and energy loss due to charge exchange collisions. This model also allows a possible noncollisional anomalous term to be isolated for study, and correlations between residual magnetic fluctuations during PPCD plasmas and anomalous heating and transport will be investigated. Recent modeling with DEGAS2 Monte Carlo neutral simulation suggests higher core neutral temperature than previously estimated with more simplistic assumptions. However, the working model does not fully account for the electron density increase in the core during PPCD, which is higher than expected from classical particle transport, and neutral and impurity ionization. Other possible mechanisms are considered and analyzed, including more complex impurity charge-state balance and pinch effects. Work supported by the US DOE. DEGAS2 is provided by PPPL.

SPH simulations of WBC adhesion to the endothelium: the role of haemodynamics and endothelial binding kinetics.

PubMed

Gholami, Babak; Comerford, Andrew; Ellero, Marco

2015-11-01

A multiscale Lagrangian particle solver introduced in our previous work is extended to model physiologically realistic near-wall cell dynamics. Three-dimensional simulation of particle trajectories is combined with realistic receptor-ligand adhesion behaviour to cover full cell interactions in the vicinity of the endothelium. The selected stochastic adhesion model, which is based on a Monte Carlo acceptance-rejection method, fits in our Lagrangian framework and does not compromise performance. Additionally, appropriate inflow/outflow boundary conditions are implemented for our SPH solver to enable realistic pulsatile flow simulation. The model is tested against in-vitro data from a 3D geometry with a stenosis and sudden expansion. In both steady and pulsatile flow conditions, results show close agreement with the experimental ones. Furthermore we demonstrate, in agreement with experimental observations, that haemodynamics alone does not account for adhesion of white blood cells, in this case U937 monocytic human cells. Our findings suggest that the current framework is fully capable of modelling cell dynamics in large arteries in a realistic and efficient manner.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME.

PubMed

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2016-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters: Theory and application to microfilaments

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

Li, Tong; Gu, YuanTong, E-mail: yuantong.gu@qut.edu.au

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grainedmore » level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.« less

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

PubMed

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Approximation methods of European option pricing in multiscale stochastic volatility model

NASA Astrophysics Data System (ADS)

Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.

Optimal Stochastic Modeling and Control of Flexible Structures

DTIC Science & Technology

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Multivariate moment closure techniques for stochastic kinetic models

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

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

The Impact of STTP on the GEFS Forecast of Week-2 and Beyond in the Presence of Stochastic Physics

NASA Astrophysics Data System (ADS)

Hou, D.

2015-12-01

The Stochastic Total Tendency Perturbation (STTP) scheme was designed to represent the model related uncertainties not considered in the numerical model itself and the physics based stochastic schemes. It has been applied in NCEP's Global Ensemble Forecast System (GEFS) since 2010, showing significant positive impacts on the forecast with improved spread-error ratio and probabilistic forecast skills. The scheme is robust and it went well with the resolution increases and model improvements in 2012 and 2015 with minimum changes. Recently, a set of stochastic physics schemes are coded in the Global Forecast System model and tested in the GEFS package. With these schemes turned on and STTP off, the forecast performance is comparable or even superior to the operational GEFS, in which STTP is the only contributor to the model related uncertainties. This is true especially in week one. However, over the second week and beyond, both the experimental and the operational GEFS has insufficient spread, especially over the warmer seasons. This is a major challenge when the GEFS is extended to sub-seasonal (week 4-6) time scales. The impact of STTP on the GEFS forecast in the presence of stochastic physics is investigated by turning both the stochastic physics schemes and STTP on and carefully tuning their amplitudes. Analysis will be focused on the forecast of extended range, especially week 2. Its impacts on week 3-4 will also be addressed.

Parameterization of norfolk sandy loam properties for stochastic modeling of light in-wheel motor UGV

USDA-ARS?s Scientific Manuscript database

To accurately develop a mathematical model for an In-Wheel Motor Unmanned Ground Vehicle (IWM UGV) on soft terrain, parameterization of terrain properties is essential to stochastically model tire-terrain interaction for each wheel independently. Operating in off-road conditions requires paying clos...

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.

Stochastic model for fatigue crack size and cost effective design decisions. [for aerospace structures

NASA Technical Reports Server (NTRS)

Hanagud, S.; Uppaluri, B.

1975-01-01

This paper describes a methodology for making cost effective fatigue design decisions. The methodology is based on a probabilistic model for the stochastic process of fatigue crack growth with time. The development of a particular model for the stochastic process is also discussed in the paper. The model is based on the assumption of continuous time and discrete space of crack lengths. Statistical decision theory and the developed probabilistic model are used to develop the procedure for making fatigue design decisions on the basis of minimum expected cost or risk function and reliability bounds. Selections of initial flaw size distribution, NDT, repair threshold crack lengths, and inspection intervals are discussed.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation.

PubMed

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-09-08

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines.

PubMed

Neftci, Emre O; Pedroni, Bruno U; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

PubMed Central

Neftci, Emre O.; Pedroni, Bruno U.; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware. PMID:27445650

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Time-varying Concurrent Risk of Extreme Droughts and Heatwaves in California

NASA Astrophysics Data System (ADS)

Sarhadi, A.; Diffenbaugh, N. S.; Ausin, M. C.

2016-12-01

Anthropogenic global warming has changed the nature and the risk of extreme climate phenomena such as droughts and heatwaves. The concurrent of these nature-changing climatic extremes may result in intensifying undesirable consequences in terms of human health and destructive effects in water resources. The present study assesses the risk of concurrent extreme droughts and heatwaves under dynamic nonstationary conditions arising from climate change in California. For doing so, a generalized fully Bayesian time-varying multivariate risk framework is proposed evolving through time under dynamic human-induced environment. In this methodology, an extreme, Bayesian, dynamic copula (Gumbel) is developed to model the time-varying dependence structure between the two different climate extremes. The time-varying extreme marginals are previously modeled using a Generalized Extreme Value (GEV) distribution. Bayesian Markov Chain Monte Carlo (MCMC) inference is integrated to estimate parameters of the nonstationary marginals and copula using a Gibbs sampling method. Modelled marginals and copula are then used to develop a fully Bayesian, time-varying joint return period concept for the estimation of concurrent risk. Here we argue that climate change has increased the chance of concurrent droughts and heatwaves over decades in California. It is also demonstrated that a time-varying multivariate perspective should be incorporated to assess realistic concurrent risk of the extremes for water resources planning and management in a changing climate in this area. The proposed generalized methodology can be applied for other stochastic nature-changing compound climate extremes that are under the influence of climate change.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

NASA Astrophysics Data System (ADS)

Zakynthinaki, M. S.; Stirling, J. R.

2007-01-01

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

Development of a Stochastically-driven, Forward Predictive Performance Model for PEMFCs

NASA Astrophysics Data System (ADS)

Harvey, David Benjamin Paul

A one-dimensional multi-scale coupled, transient, and mechanistic performance model for a PEMFC membrane electrode assembly has been developed. The model explicitly includes each of the 5 layers within a membrane electrode assembly and solves for the transport of charge, heat, mass, species, dissolved water, and liquid water. Key features of the model include the use of a multi-step implementation of the HOR reaction on the anode, agglomerate catalyst sub-models for both the anode and cathode catalyst layers, a unique approach that links the composition of the catalyst layer to key properties within the agglomerate model and the implementation of a stochastic input-based approach for component material properties. The model employs a new methodology for validation using statistically varying input parameters and statistically-based experimental performance data; this model represents the first stochastic input driven unit cell performance model. The stochastic input driven performance model was used to identify optimal ionomer content within the cathode catalyst layer, demonstrate the role of material variation in potential low performing MEA materials, provide explanation for the performance of low-Pt loaded MEAs, and investigate the validity of transient-sweep experimental diagnostic methods.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Implications of random variation in the Stand Prognosis Model

Treesearch

David A. Hamilton

1991-01-01

Although the Stand Prognosis Model has several stochastic components, features have been included in the model in an attempt to minimize run-to-run variation attributable to these stochastic components. This has led many users to assume that comparisons of management alternatives could be made based on a single run of the model for each alternative. Recent analyses...

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 Approximation Methods for Latent Regression Item Response Models. Research Report. ETS RR-09-09

ERIC Educational Resources Information Center

von Davier, Matthias; Sinharay, Sandip

2009-01-01

This paper presents an application of a stochastic approximation EM-algorithm using a Metropolis-Hastings sampler to estimate the parameters of an item response latent regression model. Latent regression models are extensions of item response theory (IRT) to a 2-level latent variable model in which covariates serve as predictors of the…

Automated Flight Routing Using Stochastic Dynamic Programming

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

PubMed

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity/diversity analysis and drug discovery protocols.

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.

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.

A Two-Step Method to Select Major Surge-Producing Extratropical Cyclones from a 10,000-Year Stochastic Catalog

NASA Astrophysics Data System (ADS)

Keshtpoor, M.; Carnacina, I.; Yablonsky, R. M.

2016-12-01

Extratropical cyclones (ETCs) are the primary driver of storm surge events along the UK and northwest mainland Europe coastlines. In an effort to evaluate the storm surge risk in coastal communities in this region, a stochastic catalog is developed by perturbing the historical storm seeds of European ETCs to account for 10,000 years of possible ETCs. Numerical simulation of the storm surge generated by the full 10,000-year stochastic catalog, however, is computationally expensive and may take several months to complete with available computational resources. A new statistical regression model is developed to select the major surge-generating events from the stochastic ETC catalog. This regression model is based on the maximum storm surge, obtained via numerical simulations using a calibrated version of the Delft3D-FM hydrodynamic model with a relatively coarse mesh, of 1750 historical ETC events that occurred over the past 38 years in Europe. These numerically-simulated surge values were regressed to the local sea level pressure and the U and V components of the wind field at the location of 196 tide gauge stations near the UK and northwest mainland Europe coastal areas. The regression model suggests that storm surge values in the area of interest are highly correlated to the U- and V-component of wind speed, as well as the sea level pressure. Based on these correlations, the regression model was then used to select surge-generating storms from the 10,000-year stochastic catalog. Results suggest that roughly 105,000 events out of 480,000 stochastic storms are surge-generating events and need to be considered for numerical simulation using a hydrodynamic model. The selected stochastic storms were then simulated in Delft3D-FM, and the final refinement of the storm population was performed based on return period analysis of the 1750 historical event simulations at each of the 196 tide gauges in preparation for Delft3D-FM fine mesh simulations.

Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-11-01

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0 ≤ 1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0 > 1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

A stochastic multi-agent optimization model for energy infrastructure planning under uncertainty and competition.

DOT National Transportation Integrated Search

2017-07-04

This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...

Large Deviations for Stochastic Models of Two-Dimensional Second Grade Fluids

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

Zhai, Jianliang, E-mail: zhaijl@ustc.edu.cn; Zhang, Tusheng, E-mail: Tusheng.Zhang@manchester.ac.uk

2017-06-15

In this paper, we establish a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by Budhiraja and Dupuis (Probab Math Statist 20:39–61, 2000) plays an important role.

Cash transportation vehicle routing and scheduling under stochastic travel times

NASA Astrophysics Data System (ADS)

Yan, Shangyao; Wang, Sin-Siang; Chang, Yu-Hsuan

2014-03-01

Stochastic disturbances occurring in real-world operations could have a significant influence on the planned routing and scheduling results of cash transportation vehicles. In this study, a time-space network flow technique is utilized to construct a cash transportation vehicle routing and scheduling model incorporating stochastic travel times. In addition, to help security carriers to formulate more flexible routes and schedules, a concept of the similarity of time and space for vehicle routing and scheduling is incorporated into the model. The test results show that the model could be useful for security carriers in actual practice.

Gryphon: A Hybrid Agent-Based Modeling and Simulation Platform for Infectious Diseases

NASA Astrophysics Data System (ADS)

Yu, Bin; Wang, Jijun; McGowan, Michael; Vaidyanathan, Ganesh; Younger, Kristofer

In this paper we present Gryphon, a hybrid agent-based stochastic modeling and simulation platform developed for characterizing the geographic spread of infectious diseases and the effects of interventions. We study both local and non-local transmission dynamics of stochastic simulations based on the published parameters and data for SARS. The results suggest that the expected numbers of infections and the timeline of control strategies predicted by our stochastic model are in reasonably good agreement with previous studies. These preliminary results indicate that Gryphon is able to characterize other future infectious diseases and identify endangered regions in advance.

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.

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction

PubMed Central

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity. PMID:29467642

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction.

PubMed

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh-Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

The Social Cost of Stochastic and Irreversible Climate Change

NASA Astrophysics Data System (ADS)

Cai, Y.; Judd, K. L.; Lontzek, T.

2013-12-01

Many scientists are worried about climate change triggering abrupt and irreversible events leading to significant and long-lasting damages. For example, a rapid release of methane from permafrost may lead to amplified global warming, and global warming may increase the frequency and severity of heavy rainfall or typhoon, destroying large cities and killing numerous people. Some elements of the climate system which might exhibit such a triggering effect are called tipping elements. There is great uncertainty about the impact of anthropogenic carbon and tipping elements on future economic wellbeing. Any rational policy choice must consider the great uncertainty about the magnitude and timing of global warming's impact on economic productivity. While the likelihood of tipping points may be a function of contemporaneous temperature, their effects are long lasting and might be independent of future temperatures. It is assumed that some of these tipping points might occur even in this century, but also that their duration and post-tipping impact are uncertain. A faithful representation of the possibility of tipping points for the calculation of social cost of carbon would require a fully stochastic formulation of irreversibility, and accounting for the deep layer of uncertainties regarding the duration of the tipping process and also its economic impact. We use DSICE, a DSGE extension of the DICE2007 model of William Nordhaus, which incorporates beliefs about the uncertain economic impact of possible climate tipping events and uses empirically plausible parameterizations of Epstein-Zin preferences to represent attitudes towards risk. We find that the uncertainty associated with anthropogenic climate change imply carbon taxes much higher than implied by deterministic models. This analysis indicates that the absence of uncertainty in DICE2007 and similar IAM models may result in substantial understatement of the potential benefits of policies to reduce GHG emissions.

Aircraft Structural Mass Property Prediction Using Conceptual-Level Structural Analysis

NASA Technical Reports Server (NTRS)

Sexstone, Matthew G.

1998-01-01

This paper describes a methodology that extends the use of the Equivalent LAminated Plate Solution (ELAPS) structural analysis code from conceptual-level aircraft structural analysis to conceptual-level aircraft mass property analysis. Mass property analysis in aircraft structures has historically depended upon parametric weight equations at the conceptual design level and Finite Element Analysis (FEA) at the detailed design level. ELAPS allows for the modeling of detailed geometry, metallic and composite materials, and non-structural mass coupled with analytical structural sizing to produce high-fidelity mass property analyses representing fully configured vehicles early in the design process. This capability is especially valuable for unusual configuration and advanced concept development where existing parametric weight equations are inapplicable and FEA is too time consuming for conceptual design. This paper contrasts the use of ELAPS relative to empirical weight equations and FEA. ELAPS modeling techniques are described and the ELAPS-based mass property analysis process is detailed. Examples of mass property stochastic calculations produced during a recent systems study are provided. This study involved the analysis of three remotely piloted aircraft required to carry scientific payloads to very high altitudes at subsonic speeds. Due to the extreme nature of this high-altitude flight regime, few existing vehicle designs are available for use in performance and weight prediction. ELAPS was employed within a concurrent engineering analysis process that simultaneously produces aerodynamic, structural, and static aeroelastic results for input to aircraft performance analyses. The ELAPS models produced for each concept were also used to provide stochastic analyses of wing structural mass properties. The results of this effort indicate that ELAPS is an efficient means to conduct multidisciplinary trade studies at the conceptual design level.

Aircraft Structural Mass Property Prediction Using Conceptual-Level Structural Analysis

NASA Technical Reports Server (NTRS)

Sexstone, Matthew G.

1998-01-01

This paper describes a methodology that extends the use of the Equivalent LAminated Plate Solution (ELAPS) structural analysis code from conceptual-level aircraft structural analysis to conceptual-level aircraft mass property analysis. Mass property analysis in aircraft structures has historically depended upon parametric weight equations at the conceptual design level and Finite Element Analysis (FEA) at the detailed design level ELAPS allows for the modeling of detailed geometry, metallic and composite materials, and non-structural mass coupled with analytical structural sizing to produce high-fidelity mass property analyses representing fully configured vehicles early in the design process. This capability is especially valuable for unusual configuration and advanced concept development where existing parametric weight equations are inapplicable and FEA is too time consuming for conceptual design. This paper contrasts the use of ELAPS relative to empirical weight equations and FEA. ELAPS modeling techniques are described and the ELAPS-based mass property analysis process is detailed Examples of mass property stochastic calculations produced during a recent systems study are provided This study involved the analysis of three remotely piloted aircraft required to carry scientific payloads to very high altitudes at subsonic speeds. Due to the extreme nature of this high-altitude flight regime,few existing vehicle designs are available for use in performance and weight prediction. ELAPS was employed within a concurrent engineering analysis process that simultaneously produces aerodynamic, structural, and static aeroelastic results for input to aircraft performance analyses. The ELAPS models produced for each concept were also used to provide stochastic analyses of wing structural mass properties. The results of this effort indicate that ELAPS is an efficient means to conduct multidisciplinary trade studies at the conceptual design level.

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.

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

Pavlou, A. T.; Betzler, B. R.; Burke, T. P.

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3)more » a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)« less

Analysis of the stochastic excitability in the flow chemical reactor

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

Bashkirtseva, Irina

2015-11-30

A dynamic model of the thermochemical process in the flow reactor is considered. We study an influence of the random disturbances on the stationary regime of this model. A phenomenon of noise-induced excitability is demonstrated. For the analysis of this phenomenon, a constructive technique based on the stochastic sensitivity functions and confidence domains is applied. It is shown how elaborated technique can be used for the probabilistic analysis of the generation of mixed-mode stochastic oscillations in the flow chemical reactor.

Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation

PubMed Central

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-01-01

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein. PMID:16965175

Analysis of the stochastic excitability in the flow chemical reactor

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina

2015-11-01

A dynamic model of the thermochemical process in the flow reactor is considered. We study an influence of the random disturbances on the stationary regime of this model. A phenomenon of noise-induced excitability is demonstrated. For the analysis of this phenomenon, a constructive technique based on the stochastic sensitivity functions and confidence domains is applied. It is shown how elaborated technique can be used for the probabilistic analysis of the generation of mixed-mode stochastic oscillations in the flow chemical reactor.

Flexible and scalable methods for quantifying stochastic variability in the era of massive time-domain astronomical data sets

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

Kelly, Brandon C.; Becker, Andrew C.; Sobolewska, Malgosia

2014-06-10

We present the use of continuous-time autoregressive moving average (CARMA) models as a method for estimating the variability features of a light curve, and in particular its power spectral density (PSD). CARMA models fully account for irregular sampling and measurement errors, making them valuable for quantifying variability, forecasting and interpolating light curves, and variability-based classification. We show that the PSD of a CARMA model can be expressed as a sum of Lorentzian functions, which makes them extremely flexible and able to model a broad range of PSDs. We present the likelihood function for light curves sampled from CARMA processes, placingmore » them on a statistically rigorous foundation, and we present a Bayesian method to infer the probability distribution of the PSD given the measured light curve. Because calculation of the likelihood function scales linearly with the number of data points, CARMA modeling scales to current and future massive time-domain data sets. We conclude by applying our CARMA modeling approach to light curves for an X-ray binary, two active galactic nuclei, a long-period variable star, and an RR Lyrae star in order to illustrate their use, applicability, and interpretation.« less

A damage analysis for brittle materials using stochastic micro-structural information

NASA Astrophysics Data System (ADS)

Lin, Shih-Po; Chen, Jiun-Shyan; Liang, Shixue

2016-03-01

In this work, a micro-crack informed stochastic damage analysis is performed to consider the failures of material with stochastic microstructure. The derivation of the damage evolution law is based on the Helmholtz free energy equivalence between cracked microstructure and homogenized continuum. The damage model is constructed under the stochastic representative volume element (SRVE) framework. The characteristics of SRVE used in the construction of the stochastic damage model have been investigated based on the principle of the minimum potential energy. The mesh dependency issue has been addressed by introducing a scaling law into the damage evolution equation. The proposed methods are then validated through the comparison between numerical simulations and experimental observations of a high strength concrete. It is observed that the standard deviation of porosity in the microstructures has stronger effect on the damage states and the peak stresses than its effect on the Young's and shear moduli in the macro-scale responses.

Evolutionary stability concepts in a stochastic environment

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

NASA Technical Reports Server (NTRS)

Goad, Clyde C.; Chadwell, C. David

1993-01-01

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Strategy to discover diverse optimal molecules in the small molecule universe.

PubMed

Rupakheti, Chetan; Virshup, Aaron; Yang, Weitao; Beratan, David N

2015-03-23

The small molecule universe (SMU) is defined as a set of over 10(60) synthetically feasible organic molecules with molecular weight less than ∼500 Da. Exhaustive enumerations and evaluation of all SMU molecules for the purpose of discovering favorable structures is impossible. We take a stochastic approach and extend the ACSESS framework ( Virshup et al. J. Am. Chem. Soc. 2013 , 135 , 7296 - 7303 ) to develop diversity oriented molecular libraries that can generate a set of compounds that is representative of the small molecule universe and that also biases the library toward favorable physical property values. We show that the approach is efficient compared to exhaustive enumeration and to existing evolutionary algorithms for generating such libraries by testing in the NKp fitness landscape model and in the fully enumerated GDB-9 chemical universe containing 3 × 10(5) molecules.

Strategy To Discover Diverse Optimal Molecules in the Small Molecule Universe

PubMed Central

2015-01-01

The small molecule universe (SMU) is defined as a set of over 1060 synthetically feasible organic molecules with molecular weight less than ∼500 Da. Exhaustive enumerations and evaluation of all SMU molecules for the purpose of discovering favorable structures is impossible. We take a stochastic approach and extend the ACSESS framework (Virshup et al. J. Am. Chem. Soc.2013, 135, 7296–730323548177) to develop diversity oriented molecular libraries that can generate a set of compounds that is representative of the small molecule universe and that also biases the library toward favorable physical property values. We show that the approach is efficient compared to exhaustive enumeration and to existing evolutionary algorithms for generating such libraries by testing in the NKp fitness landscape model and in the fully enumerated GDB-9 chemical universe containing 3 × 105 molecules. PMID:25594586

Coexistence and specialization of pathogen strains on contact networks.

PubMed

Eames, Ken T D; Keeling, Matt J

2006-08-01

The coexistence of different pathogen strains has implications for pathogen variability and disease control and has been explained in a number of different ways. We use contact networks, which represent interactions between individuals through which infection could be transmitted, to investigate strain coexistence. For sexually transmitted diseases the structure of contact networks has received detailed study and has been shown to be a vital determinant of the epidemiological dynamics. By using analytical pairwise models and stochastic simulations, we demonstrate that network structure also has a profound influence on the interaction between pathogen strains. In particular, when the population is serially monogamous, fully cross-reactive strains can coexist, with different strains dominating in network regions with different characteristics. Furthermore, we observe specialization of different strains in different risk groups within the network, suggesting the existence of diverging evolutionary pressures.

An Anatomically Constrained, Stochastic Model of Eye Movement Control in Reading

ERIC Educational Resources Information Center

McDonald, Scott A.; Carpenter, R. H. S.; Shillcock, Richard C.

2005-01-01

This article presents SERIF, a new model of eye movement control in reading that integrates an established stochastic model of saccade latencies (LATER; R. H. S. Carpenter, 1981) with a fundamental anatomical constraint on reading: the vertically split fovea and the initial projection of information in either visual field to the contralateral…

Comparison of holstein and jersey milk production with a new stochastic animal reproduction model

USDA-ARS?s Scientific Manuscript database

Holsteins and Jerseys are the most popular breeds in the US dairy industry. We built a stochastic, Monte Carlo life events simulation model in Python to test if Jersey cattle’s higher conception rate offsets their lower milk production. The model simulates individual cows and their life events such ...

Development and Evaluation of a New Air Exchange Rate Algorithm for the Stochastic Human Exposure and Dose Simulation Model

EPA Science Inventory

between-home and between-city variability in residential pollutant infiltration. This is likely a result of differences in home ventilation, or air exchange rates (AER). The Stochastic Human Exposure and Dose Simulation (SHEDS) model is a population exposure model that uses a pro...

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

Health safety nets can break cycles of poverty and disease: a stochastic ecological model.

PubMed

Plucinski, Mateusz M; Ngonghala, Calistus N; Bonds, Matthew H

2011-12-07

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a 'safety net', defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

NASA Astrophysics Data System (ADS)

Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

Stochastic simulation of multiscale complex systems with PISKaS: A rule-based approach.

PubMed

Perez-Acle, Tomas; Fuenzalida, Ignacio; Martin, Alberto J M; Santibañez, Rodrigo; Avaria, Rodrigo; Bernardin, Alejandro; Bustos, Alvaro M; Garrido, Daniel; Dushoff, Jonathan; Liu, James H

2018-03-29

Computational simulation is a widely employed methodology to study the dynamic behavior of complex systems. Although common approaches are based either on ordinary differential equations or stochastic differential equations, these techniques make several assumptions which, when it comes to biological processes, could often lead to unrealistic models. Among others, model approaches based on differential equations entangle kinetics and causality, failing when complexity increases, separating knowledge from models, and assuming that the average behavior of the population encompasses any individual deviation. To overcome these limitations, simulations based on the Stochastic Simulation Algorithm (SSA) appear as a suitable approach to model complex biological systems. In this work, we review three different models executed in PISKaS: a rule-based framework to produce multiscale stochastic simulations of complex systems. These models span multiple time and spatial scales ranging from gene regulation up to Game Theory. In the first example, we describe a model of the core regulatory network of gene expression in Escherichia coli highlighting the continuous model improvement capacities of PISKaS. The second example describes a hypothetical outbreak of the Ebola virus occurring in a compartmentalized environment resembling cities and highways. Finally, in the last example, we illustrate a stochastic model for the prisoner's dilemma; a common approach from social sciences describing complex interactions involving trust within human populations. As whole, these models demonstrate the capabilities of PISKaS providing fertile scenarios where to explore the dynamics of complex systems. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Stochastically-forced Decadal Variability in Australian Rainfall

NASA Astrophysics Data System (ADS)

Taschetto, A.

2015-12-01

Iconic Australian dry and wet periods were driven by anomalous conditions in the tropical oceans, such as the worst short-term drought in the southeast in 1982 associated with the strong El Niño and the widespread "Big Wet" in 1974 linked with a La Niña event. The association with oceanic conditions makes droughts predictable to some extent. However, prediction can be difficult when there is no clear external forcing such as El Niños. Can dry spells be triggered and maintained with no ocean memory? In this study, we investigate the potential role of internal multi-century atmospheric variability in controlling the frequency, duration and intensity of long-term dry and wet spells over Australia. Two multi-century-scale simulations were performed with the NCAR CESM: (1) a fully-coupled simulation (CPLD) and (2) an atmospheric simulation forced by a seasonal SST climatology derived from the coupled experiment (ACGM). Results reveal that droughts and wet spells can indeed be generated by internal variability of the atmosphere. Those internally generated events are less severe than those forced by oceanic variability, however the duration of dry and wet spells longer than 3 years is comparable with and without the ocean memory. Large-scale ocean modes of variability seem to play an important role in producing continental-scale rainfall impacts over Australia. While the Pacific Decadal Oscillation plays an important role in generating droughts in the fully coupled model, perturbations of monsoonal winds seem to be the main trigger of dry spells in the AGCM case. Droughts in the mid-latitude regions such as Tasmania can be driven by perturbations in the Southern Annular Mode, not necessarily linked to oceanic conditions even in the fully-coupled model. The mechanisms behind internally-driven mega-droughts and mega-wets will be discussed.

PDF modeling of turbulent flows on unstructured grids

NASA Astrophysics Data System (ADS)

Bakosi, Jozsef

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. Because the technique solves a transport equation for the PDF of the velocity and scalars, a mathematically exact treatment of advection, viscous effects and arbitrarily complex chemical reactions is possible; these processes are treated without closure assumptions. A set of algorithms is proposed to provide an efficient solution of the PDF transport equation modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain and to track particles. All three aspects regarding the grid make use of the finite element method. Compared to hybrid methods, the current methodology is stand-alone, therefore it is consistent both numerically and at the level of turbulence closure without the use of consistency conditions. Since both the turbulent velocity and scalar concentration fields are represented in a stochastic way, the method allows for a direct and close interaction between these fields, which is beneficial in computing accurate scalar statistics. Boundary conditions implemented along solid bodies are of the free-slip and no-slip type without the need for ghost elements. Boundary layers at no-slip boundaries are either fully resolved down to the viscous sublayer, explicitly modeling the high anisotropy and inhomogeneity of the low-Reynolds-number wall region without damping or wall-functions or specified via logarithmic wall-functions. As in moment closures and large eddy simulation, these wall-treatments provide the usual trade-off between resolution and computational cost as required by the given application. Particular attention is focused on modeling the dispersion of passive scalars in inhomogeneous turbulent flows. Two different micromixing models are investigated that incorporate the effect of small scale mixing on the transported scalar: the widely used interaction by exchange with the mean and the interaction by exchange with the conditional mean model. An adaptive algorithm to compute the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. The development also concentrates on a generally applicable micromixing timescale for complex flow domains. Several newly developed algorithms are described in detail that facilitate a stable numerical solution in arbitrarily complex flow geometries, including a stabilized mean-pressure projection scheme, the estimation of conditional and unconditional Eulerian statistics and their derivatives from stochastic particle fields employing finite element shapefunctions, particle tracking through unstructured grids, an efficient particle redistribution procedure and techniques related to efficient random number generation. The algorithm is validated and tested by computing three different turbulent flows: the fully developed turbulent channel flow, a street canyon (or cavity) flow and the turbulent wake behind a circular cylinder at a sub-critical Reynolds number. The solver has been parallelized and optimized for shared memory and multi-core architectures using the OpenMP standard. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed and presented in detail. The methodology shows great promise in the simulation of high-Reynolds-number incompressible inert or reactive turbulent flows in realistic configurations.

Gene regulation and noise reduction by coupling of stochastic processes

NASA Astrophysics Data System (ADS)

Ramos, Alexandre F.; Hornos, José Eduardo M.; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Gene regulation and noise reduction by coupling of stochastic processes

PubMed Central

Hornos, José Eduardo M.; Reinitz, John

2015-01-01

Here we characterize the low noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the the two gene states depends on protein number. This fact has a very important implication: there exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction. PMID:25768447

Gene regulation and noise reduction by coupling of stochastic processes.

PubMed

Ramos, Alexandre F; Hornos, José Eduardo M; Reinitz, John

2015-02-01

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.