stochastic model based: Topics by Science.gov

Sample records for stochastic model based

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.
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.
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).
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
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.
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
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...
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.
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
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.
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.
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
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.
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 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.
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 simulation by image quilting of process-based geological models

NASA Astrophysics Data System (ADS)

Hoffimann, Júlio; Scheidt, Céline; Barfod, Adrian; Caers, Jef

2017-09-01

Process-based modeling offers a way to represent realistic geological heterogeneity in subsurface models. The main limitation lies in conditioning such models to data. Multiple-point geostatistics can use these process-based models as training images and address the data conditioning problem. In this work, we further develop image quilting as a method for 3D stochastic simulation capable of mimicking the realism of process-based geological models with minimal modeling effort (i.e. parameter tuning) and at the same time condition them to a variety of data. In particular, we develop a new probabilistic data aggregation method for image quilting that bypasses traditional ad-hoc weighting of auxiliary variables. In addition, we propose a novel criterion for template design in image quilting that generalizes the entropy plot for continuous training images. The criterion is based on the new concept of voxel reuse-a stochastic and quilting-aware function of the training image. We compare our proposed method with other established simulation methods on a set of process-based training images of varying complexity, including a real-case example of stochastic simulation of the buried-valley groundwater system in Denmark.
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.
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.
Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

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

2016-12-01

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

PubMed Central

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

2016-01-01

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

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can be successfully applied to process-based models of high complexity. The methodology is particularly suitable for heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models.

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.
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
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.
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...
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.
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
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.
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 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.
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
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)
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.
On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgrid

NASA Astrophysics Data System (ADS)

Velarde, P.; Valverde, L.; Maestre, J. M.; Ocampo-Martinez, C.; Bordons, C.

2017-03-01

In this paper, a performance comparison among three well-known stochastic model predictive control approaches, namely, multi-scenario, tree-based, and chance-constrained model predictive control is presented. To this end, three predictive controllers have been designed and implemented in a real renewable-hydrogen-based microgrid. The experimental set-up includes a PEM electrolyzer, lead-acid batteries, and a PEM fuel cell as main equipment. The real experimental results show significant differences from the plant components, mainly in terms of use of energy, for each implemented technique. Effectiveness, performance, advantages, and disadvantages of these techniques are extensively discussed and analyzed to give some valid criteria when selecting an appropriate stochastic predictive controller.
Development of a voltage-dependent current noise algorithm for conductance-based stochastic modelling of auditory nerve fibres.

PubMed

Badenhorst, Werner; Hanekom, Tania; Hanekom, Johan J

2016-12-01

This study presents the development of an alternative noise current term and novel voltage-dependent current noise algorithm for conductance-based stochastic auditory nerve fibre (ANF) models. ANFs are known to have significant variance in threshold stimulus which affects temporal characteristics such as latency. This variance is primarily caused by the stochastic behaviour or microscopic fluctuations of the node of Ranvier's voltage-dependent sodium channels of which the intensity is a function of membrane voltage. Though easy to implement and low in computational cost, existing current noise models have two deficiencies: it is independent of membrane voltage, and it is unable to inherently determine the noise intensity required to produce in vivo measured discharge probability functions. The proposed algorithm overcomes these deficiencies while maintaining its low computational cost and ease of implementation compared to other conductance and Markovian-based stochastic models. The algorithm is applied to a Hodgkin-Huxley-based compartmental cat ANF model and validated via comparison of the threshold probability and latency distributions to measured cat ANF data. Simulation results show the algorithm's adherence to in vivo stochastic fibre characteristics such as an exponential relationship between the membrane noise and transmembrane voltage, a negative linear relationship between the log of the relative spread of the discharge probability and the log of the fibre diameter and a decrease in latency with an increase in stimulus intensity.
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.
Research on user behavior authentication model based on stochastic Petri nets

NASA Astrophysics Data System (ADS)

Zhang, Chengyuan; Xu, Haishui

2017-08-01

A behavioural authentication model based on stochastic Petri net is proposed to meet the randomness, uncertainty and concurrency characteristics of user behaviour. The use of random models in the location, changes, arc and logo to describe the characteristics of a variety of authentication and game relationships, so as to effectively implement the graphical user behaviour authentication model analysis method, according to the corresponding proof to verify the model is valuable.
Linking agent-based models and stochastic models of financial markets

PubMed Central

Feng, Ling; Li, Baowen; Podobnik, Boris; Preis, Tobias; Stanley, H. Eugene

2012-01-01

It is well-known that financial asset returns exhibit fat-tailed distributions and long-term memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agent-based simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agent-based model to quantitatively demonstrate that “fat” tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of long-term memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the long-term memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting. PMID:22586086
Linking agent-based models and stochastic models of financial markets.

PubMed

Feng, Ling; Li, Baowen; Podobnik, Boris; Preis, Tobias; Stanley, H Eugene

2012-05-29

It is well-known that financial asset returns exhibit fat-tailed distributions and long-term memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agent-based simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agent-based model to quantitatively demonstrate that "fat" tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of long-term memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the long-term memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting.
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.
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.

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.
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.
Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

DOE PAGES

Butler, Troy; Graham, L.; Estep, D.; ...

2015-02-03

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 in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in amore » 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. Finally, 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.« 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.
Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling

NASA Astrophysics Data System (ADS)

Yang, Huanhuan; Gunzburger, Max

2017-06-01

Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic optimization algorithm is posed based on the conditional value-at-risk measure so that an ideal acoustic liner impedance is determined that is robust in the presence of uncertainties. A parallel reduced-order modeling framework is developed that dramatically improves the computational efficiency of the stochastic optimization solver for a realistic nacelle geometry. The reduced stochastic optimization solver takes less than 500 seconds to execute. In addition, well-posedness and finite element error analyses of the state system and optimization problem are provided.
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
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.
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
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
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...
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.
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.
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.
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.
Stochastic Human Exposure and Dose Simulation for Air Toxics

EPA Science Inventory

The Stochastic Human Exposure and Dose Simulation model for Air Toxics (SHEDS-AirToxics) is a multimedia, multipathway population-based exposure and dose model for air toxics developed by the US EPA's National Exposure Research Laboratory (NERL). SHEDS-AirToxics uses a probabili...
Extinction in neutrally stable stochastic Lotka-Volterra models

NASA Astrophysics Data System (ADS)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
Extinction in neutrally stable stochastic Lotka-Volterra models.

PubMed

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Tsunami evacuation plans for future megathrust earthquakes in Padang, Indonesia, considering stochastic earthquake scenarios

NASA Astrophysics Data System (ADS)

Muhammad, Ario; Goda, Katsuichiro; Alexander, Nicholas A.; Kongko, Widjo; Muhari, Abdul

2017-12-01

This study develops tsunami evacuation plans in Padang, Indonesia, using a stochastic tsunami simulation method. The stochastic results are based on multiple earthquake scenarios for different magnitudes (Mw 8.5, 8.75, and 9.0) that reflect asperity characteristics of the 1797 historical event in the same region. The generation of the earthquake scenarios involves probabilistic models of earthquake source parameters and stochastic synthesis of earthquake slip distributions. In total, 300 source models are generated to produce comprehensive tsunami evacuation plans in Padang. The tsunami hazard assessment results show that Padang may face significant tsunamis causing the maximum tsunami inundation height and depth of 15 and 10 m, respectively. A comprehensive tsunami evacuation plan - including horizontal evacuation area maps, assessment of temporary shelters considering the impact due to ground shaking and tsunami, and integrated horizontal-vertical evacuation time maps - has been developed based on the stochastic tsunami simulation results. The developed evacuation plans highlight that comprehensive mitigation policies can be produced from the stochastic tsunami simulation for future tsunamigenic events.
Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.
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.
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.
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 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
Efficient physics-based tracking of heart surface motion for beating heart surgery robotic systems.

PubMed

Bogatyrenko, Evgeniya; Pompey, Pascal; Hanebeck, Uwe D

2011-05-01

Tracking of beating heart motion in a robotic surgery system is required for complex cardiovascular interventions. A heart surface motion tracking method is developed, including a stochastic physics-based heart surface model and an efficient reconstruction algorithm. The algorithm uses the constraints provided by the model that exploits the physical characteristics of the heart. The main advantage of the model is that it is more realistic than most standard heart models. Additionally, no explicit matching between the measurements and the model is required. The application of meshless methods significantly reduces the complexity of physics-based tracking. Based on the stochastic physical model of the heart surface, this approach considers the motion of the intervention area and is robust to occlusions and reflections. The tracking algorithm is evaluated in simulations and experiments on an artificial heart. Providing higher accuracy than the standard model-based methods, it successfully copes with occlusions and provides high performance even when all measurements are not available. Combining the physical and stochastic description of the heart surface motion ensures physically correct and accurate prediction. Automatic initialization of the physics-based cardiac motion tracking enables system evaluation in a clinical environment.
3D aquifer characterization using stochastic streamline calibration

NASA Astrophysics Data System (ADS)

Jang, Minchul

2007-03-01

In this study, a new inverse approach, stochastic streamline calibration is proposed. Using both a streamline concept and a stochastic technique, stochastic streamline calibration optimizes an identified field to fit in given observation data in a exceptionally fast and stable fashion. In the stochastic streamline calibration, streamlines are adopted as basic elements not only for describing fluid flow but also for identifying the permeability distribution. Based on the streamline-based inversion by Agarwal et al. [Agarwal B, Blunt MJ. Streamline-based method with full-physics forward simulation for history matching performance data of a North sea field. SPE J 2003;8(2):171-80], Wang and Kovscek [Wang Y, Kovscek AR. Streamline approach for history matching production data. SPE J 2000;5(4):353-62], permeability is modified rather along streamlines than at the individual gridblocks. Permeabilities in the gridblocks which a streamline passes are adjusted by being multiplied by some factor such that we can match flow and transport properties of the streamline. This enables the inverse process to achieve fast convergence. In addition, equipped with a stochastic module, the proposed technique supportively calibrates the identified field in a stochastic manner, while incorporating spatial information into the field. This prevents the inverse process from being stuck in local minima and helps search for a globally optimized solution. Simulation results indicate that stochastic streamline calibration identifies an unknown permeability exceptionally quickly. More notably, the identified permeability distribution reflected realistic geological features, which had not been achieved in the original work by Agarwal et al. with the limitations of the large modifications along streamlines for matching production data only. The constructed model by stochastic streamline calibration forecasted transport of plume which was similar to that of a reference model. By this, we can expect the proposed approach to be applied to the construction of an aquifer model and forecasting of the aquifer performances of interest.
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.
Assessment of BTEX-induced health risk under multiple uncertainties at a petroleum-contaminated site: An integrated fuzzy stochastic approach

NASA Astrophysics Data System (ADS)

Zhang, Xiaodong; Huang, Guo H.

2011-12-01

Groundwater pollution has gathered more and more attention in the past decades. Conducting an assessment of groundwater contamination risk is desired to provide sound bases for supporting risk-based management decisions. Therefore, the objective of this study is to develop an integrated fuzzy stochastic approach to evaluate risks of BTEX-contaminated groundwater under multiple uncertainties. It consists of an integrated interval fuzzy subsurface modeling system (IIFMS) and an integrated fuzzy second-order stochastic risk assessment (IFSOSRA) model. The IIFMS is developed based on factorial design, interval analysis, and fuzzy sets approach to predict contaminant concentrations under hybrid uncertainties. Two input parameters (longitudinal dispersivity and porosity) are considered to be uncertain with known fuzzy membership functions, and intrinsic permeability is considered to be an interval number with unknown distribution information. A factorial design is conducted to evaluate interactive effects of the three uncertain factors on the modeling outputs through the developed IIFMS. The IFSOSRA model can systematically quantify variability and uncertainty, as well as their hybrids, presented as fuzzy, stochastic and second-order stochastic parameters in health risk assessment. The developed approach haw been applied to the management of a real-world petroleum-contaminated site within a western Canada context. The results indicate that multiple uncertainties, under a combination of information with various data-quality levels, can be effectively addressed to provide supports in identifying proper remedial efforts. A unique contribution of this research is the development of an integrated fuzzy stochastic approach for handling various forms of uncertainties associated with simulation and risk assessment efforts.
Prediction of mortality rates using a model with stochastic parameters

NASA Astrophysics Data System (ADS)

Tan, Chon Sern; Pooi, Ah Hin

2016-10-01

Prediction of future mortality rates is crucial to insurance companies because they face longevity risks while providing retirement benefits to a population whose life expectancy is increasing. In the past literature, a time series model based on multivariate power-normal distribution has been applied on mortality data from the United States for the years 1933 till 2000 to forecast the future mortality rates for the years 2001 till 2010. In this paper, a more dynamic approach based on the multivariate time series will be proposed where the model uses stochastic parameters that vary with time. The resulting prediction intervals obtained using the model with stochastic parameters perform better because apart from having good ability in covering the observed future mortality rates, they also tend to have distinctly shorter interval lengths.
HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Brownston, Lee

2012-01-01

Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.
Impact of correlated magnetic noise on the detection of stochastic gravitational waves: Estimation based on a simple analytical model

NASA Astrophysics Data System (ADS)

Himemoto, Yoshiaki; Taruya, Atsushi

2017-07-01

After the first direct detection of gravitational waves (GW), detection of the stochastic background of GWs is an important next step, and the first GW event suggests that it is within the reach of the second-generation ground-based GW detectors. Such a GW signal is typically tiny and can be detected by cross-correlating the data from two spatially separated detectors if the detector noise is uncorrelated. It has been advocated, however, that the global magnetic fields in the Earth-ionosphere cavity produce the environmental disturbances at low-frequency bands, known as Schumann resonances, which potentially couple with GW detectors. In this paper, we present a simple analytical model to estimate its impact on the detection of stochastic GWs. The model crucially depends on the geometry of the detector pair through the directional coupling, and we investigate the basic properties of the correlated magnetic noise based on the analytic expressions. The model reproduces the major trend of the recently measured global correlation between the GW detectors via magnetometer. The estimated values of the impact of correlated noise also match those obtained from the measurement. Finally, we give an implication to the detection of stochastic GWs including upcoming detectors, KAGRA and LIGO India. The model suggests that LIGO Hanford-Virgo and Virgo-KAGRA pairs are possibly less sensitive to the correlated noise and can achieve a better sensitivity to the stochastic GW signal in the most pessimistic case.
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.
Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy

USDA-ARS?s Scientific Manuscript database

When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...
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.

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.
Disease mapping based on stochastic SIR-SI model for Dengue and Chikungunya in Malaysia

NASA Astrophysics Data System (ADS)

Samat, N. A.; Ma'arof, S. H. Mohd Imam

2014-12-01

This paper describes and demonstrates a method for relative risk estimation which is based on the stochastic SIR-SI vector-borne infectious disease transmission model specifically for Dengue and Chikungunya diseases in Malaysia. Firstly, the common compartmental model for vector-borne infectious disease transmission called the SIR-SI model (susceptible-infective-recovered for human populations; susceptible-infective for vector populations) is presented. This is followed by the explanations on the stochastic SIR-SI model which involve the Bayesian description. This stochastic model then is used in the relative risk formulation in order to obtain the posterior relative risk estimation. Then, this relative estimation model is demonstrated using Dengue and Chikungunya data of Malaysia. The viruses of these diseases are transmitted by the same type of female vector mosquito named Aedes Aegypti and Aedes Albopictus. Finally, the findings of the analysis of relative risk estimation for both Dengue and Chikungunya diseases are presented, compared and displayed in graphs and maps. The distribution from risk maps show the high and low risk area of Dengue and Chikungunya diseases occurrence. This map can be used as a tool for the prevention and control strategies for both diseases.
Disease mapping based on stochastic SIR-SI model for Dengue and Chikungunya in Malaysia

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

Samat, N. A.; Ma'arof, S. H. Mohd Imam

This paper describes and demonstrates a method for relative risk estimation which is based on the stochastic SIR-SI vector-borne infectious disease transmission model specifically for Dengue and Chikungunya diseases in Malaysia. Firstly, the common compartmental model for vector-borne infectious disease transmission called the SIR-SI model (susceptible-infective-recovered for human populations; susceptible-infective for vector populations) is presented. This is followed by the explanations on the stochastic SIR-SI model which involve the Bayesian description. This stochastic model then is used in the relative risk formulation in order to obtain the posterior relative risk estimation. Then, this relative estimation model is demonstrated using Denguemore » and Chikungunya data of Malaysia. The viruses of these diseases are transmitted by the same type of female vector mosquito named Aedes Aegypti and Aedes Albopictus. Finally, the findings of the analysis of relative risk estimation for both Dengue and Chikungunya diseases are presented, compared and displayed in graphs and maps. The distribution from risk maps show the high and low risk area of Dengue and Chikungunya diseases occurrence. This map can be used as a tool for the prevention and control strategies for both diseases.« less
Stochastic output error vibration-based damage detection and assessment in structures under earthquake excitation

NASA Astrophysics Data System (ADS)

Sakellariou, J. S.; Fassois, S. D.

2006-11-01

A stochastic output error (OE) vibration-based methodology for damage detection and assessment (localization and quantification) in structures under earthquake excitation is introduced. The methodology is intended for assessing the state of a structure following potential damage occurrence by exploiting vibration signal measurements produced by low-level earthquake excitations. It is based upon (a) stochastic OE model identification, (b) statistical hypothesis testing procedures for damage detection, and (c) a geometric method (GM) for damage assessment. The methodology's advantages include the effective use of the non-stationary and limited duration earthquake excitation, the handling of stochastic uncertainties, the tackling of the damage localization and quantification subproblems, the use of "small" size, simple and partial (in both the spatial and frequency bandwidth senses) identified OE-type models, and the use of a minimal number of measured vibration signals. Its feasibility and effectiveness are assessed via Monte Carlo experiments employing a simple simulation model of a 6 storey building. It is demonstrated that damage levels of 5% and 20% reduction in a storey's stiffness characteristics may be properly detected and assessed using noise-corrupted vibration signals.
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.
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.
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.
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
Development and validation of a generic finite element vehicle buck model for the analysis of driver rib fractures in real life nearside oblique frontal crashes.

PubMed

Iraeus, Johan; Lindquist, Mats

2016-10-01

Frontal crashes still account for approximately half of all fatalities in passenger cars, despite several decades of crash-related research. For serious injuries in this crash mode, several authors have listed the thorax as the most important. Computer simulation provides an effective tool to study crashes and evaluate injury mechanisms, and using stochastic input data, whole populations of crashes can be studied. The aim of this study was to develop a generic buck model and to validate this model on a population of real-life frontal crashes in terms of the risk of rib fracture. The study was conducted in four phases. In the first phase, real-life validation data were derived by analyzing NASS/CDS data to find the relationship between injury risk and crash parameters. In addition, available statistical distributions for the parameters were collected. In the second phase, a generic parameterized finite element (FE) model of a vehicle interior was developed based on laser scans from the A2MAC1 database. In the third phase, model parameters that could not be found in the literature were estimated using reverse engineering based on NCAP tests. Finally, in the fourth phase, the stochastic FE model was used to simulate a population of real-life crashes, and the result was compared to the validation data from phase one. The stochastic FE simulation model overestimates the risk of rib fracture, more for young occupants and less for senior occupants. However, if the effect of underestimation of rib fractures in the NASS/CDS material is accounted for using statistical simulations, the risk of rib fracture based on the stochastic FE model matches the risk based on the NASS/CDS data for senior occupants. The current version of the stochastic model can be used to evaluate new safety measures using a population of frontal crashes for senior occupants. Copyright © 2016 Elsevier Ltd. All rights reserved.
Modeling precipitation-runoff relationships to determine water yield from a ponderosa pine forest watershed

Treesearch

Assefa S. Desta

2006-01-01

A stochastic precipitation-runoff modeling is used to estimate a cold and warm-seasons water yield from a ponderosa pine forested watershed in the north-central Arizona. The model consists of two parts namely, simulation of the temporal and spatial distribution of precipitation using a stochastic, event-based approach and estimation of water yield from the watershed...
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.
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.
Variance decomposition in stochastic simulators.

PubMed

Le Maître, O P; Knio, O M; Moraes, A

2015-06-28

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators

NASA Astrophysics Data System (ADS)

Le Maître, O. P.; Knio, O. M.; Moraes, A.

2015-06-01

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Exploring Ackermann and LQR stability control of stochastic state-space model of hexacopter equipped with robotic arm

NASA Astrophysics Data System (ADS)

Ibrahim, I. N.; Akkad, M. A. Al; Abramov, I. V.

2018-05-01

This paper discusses the control of Unmanned Aerial Vehicles (UAVs) for active interaction and manipulation of objects. The manipulator motion with an unknown payload was analysed concerning force and moment disturbances, which influence the mass distribution, and the centre of gravity (CG). Therefore, a general dynamics mathematical model of a hexacopter was formulated where a stochastic state-space model was extracted in order to build anti-disturbance controllers. Based on the compound pendulum method, the disturbances model that simulates the robotic arm with a payload was inserted into the stochastic model. This study investigates two types of controllers in order to study the stability of a hexacopter. A controller based on Ackermann’s method and the other - on the linear quadratic regulator (LQR) approach - were presented. The latter constitutes a challenge for UAV control performance especially with the presence of uncertainties and disturbances.
Recent topographic evolution and erosion of the deglaciated Washington Cascades inferred from a stochastic landscape evolution model

NASA Astrophysics Data System (ADS)

Moon, Seulgi; Shelef, Eitan; Hilley, George E.

2015-05-01

In this study, we model postglacial surface processes and examine the evolution of the topography and denudation rates within the deglaciated Washington Cascades to understand the controls on and time scales of landscape response to changes in the surface process regime after deglaciation. The postglacial adjustment of this landscape is modeled using a geomorphic-transport-law-based numerical model that includes processes of river incision, hillslope diffusion, and stochastic landslides. The surface lowering due to landslides is parameterized using a physically based slope stability model coupled to a stochastic model of the generation of landslides. The model parameters of river incision and stochastic landslides are calibrated based on the rates and distribution of thousand-year-time scale denudation rates measured from cosmogenic 10Be isotopes. The probability distributions of those model parameters calculated based on a Bayesian inversion scheme show comparable ranges from previous studies in similar rock types and climatic conditions. The magnitude of landslide denudation rates is determined by failure density (similar to landslide frequency), whereas precipitation and slopes affect the spatial variation in landslide denudation rates. Simulation results show that postglacial denudation rates decay over time and take longer than 100 kyr to reach time-invariant rates. Over time, the landslides in the model consume the steep slopes characteristic of deglaciated landscapes. This response time scale is on the order of or longer than glacial/interglacial cycles, suggesting that frequent climatic perturbations during the Quaternary may produce a significant and prolonged impact on denudation and topography.
Genetic Algorithm Based Framework for Automation of Stochastic Modeling of Multi-Season Streamflows

NASA Astrophysics Data System (ADS)

Srivastav, R. K.; Srinivasan, K.; Sudheer, K.

2009-05-01

Synthetic streamflow data generation involves the synthesis of likely streamflow patterns that are statistically indistinguishable from the observed streamflow data. The various kinds of stochastic models adopted for multi-season streamflow generation in hydrology are: i) parametric models which hypothesize the form of the periodic dependence structure and the distributional form a priori (examples are PAR, PARMA); disaggregation models that aim to preserve the correlation structure at the periodic level and the aggregated annual level; ii) Nonparametric models (examples are bootstrap/kernel based methods), which characterize the laws of chance, describing the stream flow process, without recourse to prior assumptions as to the form or structure of these laws; (k-nearest neighbor (k-NN), matched block bootstrap (MABB)); non-parametric disaggregation model. iii) Hybrid models which blend both parametric and non-parametric models advantageously to model the streamflows effectively. Despite many of these developments that have taken place in the field of stochastic modeling of streamflows over the last four decades, accurate prediction of the storage and the critical drought characteristics has been posing a persistent challenge to the stochastic modeler. This is partly because, usually, the stochastic streamflow model parameters are estimated by minimizing a statistically based objective function (such as maximum likelihood (MLE) or least squares (LS) estimation) and subsequently the efficacy of the models is being validated based on the accuracy of prediction of the estimates of the water-use characteristics, which requires large number of trial simulations and inspection of many plots and tables. Still accurate prediction of the storage and the critical drought characteristics may not be ensured. In this study a multi-objective optimization framework is proposed to find the optimal hybrid model (blend of a simple parametric model, PAR(1) model and matched block bootstrap (MABB) ) based on the explicit objective functions of minimizing the relative bias and relative root mean square error in estimating the storage capacity of the reservoir. The optimal parameter set of the hybrid model is obtained based on the search over a multi- dimensional parameter space (involving simultaneous exploration of the parametric (PAR(1)) as well as the non-parametric (MABB) components). This is achieved using the efficient evolutionary search based optimization tool namely, non-dominated sorting genetic algorithm - II (NSGA-II). This approach helps in reducing the drudgery involved in the process of manual selection of the hybrid model, in addition to predicting the basic summary statistics dependence structure, marginal distribution and water-use characteristics accurately. The proposed optimization framework is used to model the multi-season streamflows of River Beaver and River Weber of USA. In case of both the rivers, the proposed GA-based hybrid model yields a much better prediction of the storage capacity (where simultaneous exploration of both parametric and non-parametric components is done) when compared with the MLE-based hybrid models (where the hybrid model selection is done in two stages, thus probably resulting in a sub-optimal model). This framework can be further extended to include different linear/non-linear hybrid stochastic models at other temporal and spatial scales as well.
A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE PAGES

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

2016-11-21

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

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

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

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

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.
Synthetic Sediments and Stochastic Groundwater Hydrology

NASA Astrophysics Data System (ADS)

Wilson, J. L.

2002-12-01

For over twenty years the groundwater community has pursued the somewhat elusive goal of describing the effects of aquifer heterogeneity on subsurface flow and chemical transport. While small perturbation stochastic moment methods have significantly advanced theoretical understanding, why is it that stochastic applications use instead simulations of flow and transport through multiple realizations of synthetic geology? Allan Gutjahr was a principle proponent of the Fast Fourier Transform method for the synthetic generation of aquifer properties and recently explored new, more geologically sound, synthetic methods based on multi-scale Markov random fields. Focusing on sedimentary aquifers, how has the state-of-the-art of synthetic generation changed and what new developments can be expected, for example, to deal with issues like conceptual model uncertainty, the differences between measurement and modeling scales, and subgrid scale variability? What will it take to get stochastic methods, whether based on moments, multiple realizations, or some other approach, into widespread application?
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.
Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

NASA Astrophysics Data System (ADS)

Rana, Navdeep; Ghosh, Pushpita; Perlekar, Prasad

2017-11-01

We study spreading of a nonmotile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility, and the inherent demographic noise. Population fluctuations are inherent in an agent-based model, whereas for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with nonlinear diffusivity lead to a transition from a diffusion limited aggregation type of morphology to an Eden-like morphology on decreasing the initial nutrient concentration.
ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.
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
Compressible cavitation with stochastic field method

NASA Astrophysics Data System (ADS)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear 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 Lagrange 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 Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.
On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

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

Konstantinidis, A. A., E-mail: akonsta@civil.auth.gr; Zhang, X., E-mail: zhangxu26@126.com; Aifantis, E. C., E-mail: mom@mom.gen.auth.gr

2015-02-17

A formulation for addressing heterogeneous material deformation is proposed. It is based on the use of a stochasticity-enhanced gradient plasticity model implemented through a cellular automaton. The specific application is on Mo-micropillar compression, for which the irregularities of the strain bursts observed have been experimentally measured and theoretically interpreted through Tsallis' q-statistics.
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.
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
A stochastic model for eye movements during fixation on a stationary target.

NASA Technical Reports Server (NTRS)

Vasudevan, R.; Phatak, A. V.; Smith, J. D.

1971-01-01

A stochastic model describing small eye movements occurring during steady fixation on a stationary target is presented. Based on eye movement data for steady gaze, the model has a hierarchical structure; the principal level represents the random motion of the image point within a local area of fixation, while the higher level mimics the jump processes involved in transitions from one local area to another. Target image motion within a local area is described by a Langevin-like stochastic differential equation taking into consideration the microsaccadic jumps pictured as being due to point processes and the high frequency muscle tremor, represented as a white noise. The transform of the probability density function for local area motion is obtained, leading to explicit expressions for their means and moments. Evaluation of these moments based on the model is comparable with experimental results.
Stochastic Earthquake Rupture Modeling Using Nonparametric Co-Regionalization

NASA Astrophysics Data System (ADS)

Lee, Kyungbook; Song, Seok Goo

2017-09-01

Accurate predictions of the intensity and variability of ground motions are essential in simulation-based seismic hazard assessment. Advanced simulation-based ground motion prediction methods have been proposed to complement the empirical approach, which suffers from the lack of observed ground motion data, especially in the near-source region for large events. It is important to quantify the variability of the earthquake rupture process for future events and to produce a number of rupture scenario models to capture the variability in simulation-based ground motion predictions. In this study, we improved the previously developed stochastic earthquake rupture modeling method by applying the nonparametric co-regionalization, which was proposed in geostatistics, to the correlation models estimated from dynamically derived earthquake rupture models. The nonparametric approach adopted in this study is computationally efficient and, therefore, enables us to simulate numerous rupture scenarios, including large events ( M > 7.0). It also gives us an opportunity to check the shape of true input correlation models in stochastic modeling after being deformed for permissibility. We expect that this type of modeling will improve our ability to simulate a wide range of rupture scenario models and thereby predict ground motions and perform seismic hazard assessment more accurately.
Construction of dynamic stochastic simulation models using knowledge-based techniques

NASA Technical Reports Server (NTRS)

Williams, M. Douglas; Shiva, Sajjan G.

1990-01-01

Over the past three decades, computer-based simulation models have proven themselves to be cost-effective alternatives to the more structured deterministic methods of systems analysis. During this time, many techniques, tools and languages for constructing computer-based simulation models have been developed. More recently, advances in knowledge-based system technology have led many researchers to note the similarities between knowledge-based programming and simulation technologies and to investigate the potential application of knowledge-based programming techniques to simulation modeling. The integration of conventional simulation techniques with knowledge-based programming techniques is discussed to provide a development environment for constructing knowledge-based simulation models. A comparison of the techniques used in the construction of dynamic stochastic simulation models and those used in the construction of knowledge-based systems provides the requirements for the environment. This leads to the design and implementation of a knowledge-based simulation development environment. These techniques were used in the construction of several knowledge-based simulation models including the Advanced Launch System Model (ALSYM).
Evolutionary Game Theory in Growing Populations

NASA Astrophysics Data System (ADS)

Melbinger, Anna; Cremer, Jonas; Frey, Erwin

2010-10-01

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.
Reliability based fatigue design and maintenance procedures

NASA Technical Reports Server (NTRS)

Hanagud, S.

1977-01-01

A stochastic model has been developed to describe a probability for fatigue process by assuming a varying hazard rate. This stochastic model can be used to obtain the desired probability of a crack of certain length at a given location after a certain number of cycles or time. Quantitative estimation of the developed model was also discussed. Application of the model to develop a procedure for reliability-based cost-effective fail-safe structural design is presented. This design procedure includes the reliability improvement due to inspection and repair. Methods of obtaining optimum inspection and maintenance schemes are treated.
Dynamical crossover in a stochastic model of cell fate decision

NASA Astrophysics Data System (ADS)

Yamaguchi, Hiroki; Kawaguchi, Kyogo; Sagawa, Takahiro

2017-07-01

We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e., proliferation or differentiation) depending on local cell density. Based on this model, we propose a scenario for multicellular organisms to maintain the density of cells (i.e., homeostasis) through finite-ranged cell-cell interactions. Furthermore, we numerically show that the distribution of the number of descendant cells changes over time, thus unifying the previously proposed two models regarding homeostasis: the critical birth death process and the voter model. Our results provide a general platform for the study of stochastic cell fate decision in terms of nonequilibrium statistical mechanics.
An inexact log-normal distribution-based stochastic chance-constrained model for agricultural water quality management

NASA Astrophysics Data System (ADS)

Wang, Yu; Fan, Jie; Xu, Ye; Sun, Wei; Chen, Dong

2018-05-01

In this study, an inexact log-normal-based stochastic chance-constrained programming model was developed for solving the non-point source pollution issues caused by agricultural activities. Compared to the general stochastic chance-constrained programming model, the main advantage of the proposed model is that it allows random variables to be expressed as a log-normal distribution, rather than a general normal distribution. Possible deviations in solutions caused by irrational parameter assumptions were avoided. The agricultural system management in the Erhai Lake watershed was used as a case study, where critical system factors, including rainfall and runoff amounts, show characteristics of a log-normal distribution. Several interval solutions were obtained under different constraint-satisfaction levels, which were useful in evaluating the trade-off between system economy and reliability. The applied results show that the proposed model could help decision makers to design optimal production patterns under complex uncertainties. The successful application of this model is expected to provide a good example for agricultural management in many other watersheds.
Finite state projection based bounds to compare chemical master equation models using single-cell data

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

Fox, Zachary; Neuert, Gregor; Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232

2016-08-21

Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort.more » In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.« less

Contributions of the stochastic shape wake model to predictions of aerodynamic loads and power under single wake conditions

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

Doubrawa, P.; Barthelmie, R. J.; Wang, H.

The contribution of wake meandering and shape asymmetry to load and power estimates is quantified by comparing aeroelastic simulations initialized with different inflow conditions: an axisymmetric base wake, an unsteady stochastic shape wake, and a large-eddy simulation with rotating actuator-line turbine representation. Time series of blade-root and tower base bending moments are analyzed. We find that meandering has a large contribution to the fluctuation of the loads. Moreover, considering the wake edge intermittence via the stochastic shape model improves the simulation of load and power fluctuations and of the fatigue damage equivalent loads. Furthermore, these results indicate that the stochasticmore » shape wake simulator is a valuable addition to simplified wake models when seeking to obtain higher-fidelity computationally inexpensive predictions of loads and power.« less
Contributions of the stochastic shape wake model to predictions of aerodynamic loads and power under single wake conditions

DOE PAGES

Doubrawa, P.; Barthelmie, R. J.; Wang, H.; ...

2016-10-03

The contribution of wake meandering and shape asymmetry to load and power estimates is quantified by comparing aeroelastic simulations initialized with different inflow conditions: an axisymmetric base wake, an unsteady stochastic shape wake, and a large-eddy simulation with rotating actuator-line turbine representation. Time series of blade-root and tower base bending moments are analyzed. We find that meandering has a large contribution to the fluctuation of the loads. Moreover, considering the wake edge intermittence via the stochastic shape model improves the simulation of load and power fluctuations and of the fatigue damage equivalent loads. Furthermore, these results indicate that the stochasticmore » shape wake simulator is a valuable addition to simplified wake models when seeking to obtain higher-fidelity computationally inexpensive predictions of loads and power.« less
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.
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.
Memristor-based neural networks: Synaptic versus neuronal stochasticity

NASA Astrophysics Data System (ADS)

Naous, Rawan; AlShedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled Nabil

2016-11-01

In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.
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.
MOSES: A Matlab-based open-source stochastic epidemic simulator.

PubMed

Varol, Huseyin Atakan

2016-08-01

This paper presents an open-source stochastic epidemic simulator. Discrete Time Markov Chain based simulator is implemented in Matlab. The simulator capable of simulating SEQIJR (susceptible, exposed, quarantined, infected, isolated and recovered) model can be reduced to simpler models by setting some of the parameters (transition probabilities) to zero. Similarly, it can be extended to more complicated models by editing the source code. It is designed to be used for testing different control algorithms to contain epidemics. The simulator is also designed to be compatible with a network based epidemic simulator and can be used in the network based scheme for the simulation of a node. Simulations show the capability of reproducing different epidemic model behaviors successfully in a computationally efficient manner.
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.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertholon, François; Harant, Olivier; Bourlon, Bertrand

This article introduces a joined Bayesian estimation of gas samples issued from a gas chromatography column (GC) coupled with a NEMS sensor based on Giddings Eyring microscopic molecular stochastic model. The posterior distribution is sampled using a Monte Carlo Markov Chain and Gibbs sampling. Parameters are estimated using the posterior mean. This estimation scheme is finally applied on simulated and real datasets using this molecular stochastic forward model.
Variance decomposition in stochastic simulators

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

Le Maître, O. P., E-mail: olm@limsi.fr; Knio, O. M., E-mail: knio@duke.edu; Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance.more » Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.« less
Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes

NASA Astrophysics Data System (ADS)

Liyanagedera, Chamika M.; Sengupta, Abhronil; Jaiswal, Akhilesh; Roy, Kaushik

2017-12-01

Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway to achieving "brainlike" compact and energy-efficient cognitive intelligence. The computational model attempt to exploit the intrinsic device stochasticity of nanoelectronic synaptic or neural components to perform learning or inference. However, there has been limited analysis on the scaling effect of stochastic spin devices and its impact on the operation of such stochastic networks at the system level. This work attempts to explore the design space and analyze the performance of nanomagnet-based stochastic neuromorphic computing architectures for magnets with different barrier heights. We illustrate how the underlying network architecture must be modified to account for the random telegraphic switching behavior displayed by magnets with low barrier heights as they are scaled into the superparamagnetic regime. We perform a device-to-system-level analysis on a deep neural-network architecture for a digit-recognition problem on the MNIST data set.
Sensor trustworthiness in uncertain time varying stochastic environments

NASA Astrophysics Data System (ADS)

Verma, Ajay; Fernandes, Ronald; Vadakkeveedu, Kalyan

2011-06-01

Persistent surveillance applications require unattended sensors deployed in remote regions to track and monitor some physical stimulant of interest that can be modeled as output of time varying stochastic process. However, the accuracy or the trustworthiness of the information received through a remote and unattended sensor and sensor network cannot be readily assumed, since sensors may get disabled, corrupted, or even compromised, resulting in unreliable information. The aim of this paper is to develop information theory based metric to determine sensor trustworthiness from the sensor data in an uncertain and time varying stochastic environment. In this paper we show an information theory based determination of sensor data trustworthiness using an adaptive stochastic reference sensor model that tracks the sensor performance for the time varying physical feature, and provides a baseline model that is used to compare and analyze the observed sensor output. We present an approach in which relative entropy is used for reference model adaptation and determination of divergence of the sensor signal from the estimated reference baseline. We show that that KL-divergence is a useful metric that can be successfully used in determination of sensor failures or sensor malice of various types.
Rupture Propagation for Stochastic Fault Models

NASA Astrophysics Data System (ADS)

Favreau, P.; Lavallee, D.; Archuleta, R.

2003-12-01

The inversion of strong motion data of large earhquakes give the spatial distribution of pre-stress on the ruptured faults and it can be partially reproduced by stochastic models, but a fundamental question remains: how rupture propagates, constrained by the presence of spatial heterogeneity? For this purpose we investigate how the underlying random variables, that control the pre-stress spatial variability, condition the propagation of the rupture. Two stochastic models of prestress distributions are considered, respectively based on Cauchy and Gaussian random variables. The parameters of the two stochastic models have values corresponding to the slip distribution of the 1979 Imperial Valley earthquake. We use a finite difference code to simulate the spontaneous propagation of shear rupture on a flat fault in a 3D continuum elastic body. The friction law is the slip dependent friction law. The simulations show that the propagation of the rupture front is more complex, incoherent or snake-like for a prestress distribution based on Cauchy random variables. This may be related to the presence of a higher number of asperities in this case. These simulations suggest that directivity is stronger in the Cauchy scenario, compared to the smoother rupture of the Gauss scenario.
Method of sound synthesis

DOEpatents

Miner, Nadine E.; Caudell, Thomas P.

2004-06-08

A sound synthesis method for modeling and synthesizing dynamic, parameterized sounds. The sound synthesis method yields perceptually convincing sounds and provides flexibility through model parameterization. By manipulating model parameters, a variety of related, but perceptually different sounds can be generated. The result is subtle changes in sounds, in addition to synthesis of a variety of sounds, all from a small set of models. The sound models can change dynamically according to changes in the simulation environment. The method is applicable to both stochastic (impulse-based) and non-stochastic (pitched) sounds.
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.
Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

PubMed Central

Gong, Haijun; Guo, Yusong; Linstedt, Adam

2017-01-01

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi—a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model—each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor SNARE proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size. PMID:20365406
Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

PubMed Central

Liu, Fei; Heiner, Monika; Yang, Ming

2016-01-01

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information. PMID:26910830
The Stochastic Multicloud Model as part of an operational convection parameterisation in a comprehensive GCM

NASA Astrophysics Data System (ADS)

Peters, Karsten; Jakob, Christian; Möbis, Benjamin

2015-04-01

An adequate representation of convective processes in numerical models of the atmospheric circulation (general circulation models, GCMs) remains one of the grand challenges in atmospheric science. In particular, the models struggle with correctly representing the spatial distribution and high variability of tropical convection. It is thought that this model deficiency partly results from formulating current convection parameterisation schemes in a purely deterministic manner. Here, we use observations of tropical convection to inform the design of a novel convection parameterisation with stochastic elements. The novel scheme is built around the Stochastic MultiCloud Model (SMCM, Khouider et al 2010). We present the progress made in utilising SMCM-based estimates of updraft area fractions at cloud base as part of the deep convection scheme of a GCM. The updraft area fractions are used to yield one part of the cloud base mass-flux used in the closure assumption of convective mass-flux schemes. The closure thus receives a stochastic component, potentially improving modeled convective variability and coherence. For initial investigations, we apply the above methodology to the operational convective parameterisation of the ECHAM6 GCM. We perform 5-year AMIP simulations, i.e. with prescribed observed SSTs. We find that with the SMCM, convection is weaker and more coherent and continuous from timestep to timestep compared to the standard model. Total global precipitation is reduced in the SMCM run, but this reduces i) the overall error compared to observed global precipitation (GPCP) and ii) middle tropical tropospheric temperature biases compared to ERA-Interim. Hovmoeller diagrams indicate a slightly higher degree of convective organisation compared to the base case and Wheeler-Kiladis frequency wavenumber diagrams indicate slightly more spectral power in the MJO range.
Stochastic modelling of temperatures affecting the in situ performance of a solar-assisted heat pump: The multivariate approach and physical interpretation

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

Loveday, D.L.; Craggs, C.

Box-Jenkins-based multivariate stochastic modeling is carried out using data recorded from a domestic heating system. The system comprises an air-source heat pump sited in the roof space of a house, solar assistance being provided by the conventional tile roof acting as a radiation absorber. Multivariate models are presented which illustrate the time-dependent relationships between three air temperatures - at external ambient, at entry to, and at exit from, the heat pump evaporator. Using a deterministic modeling approach, physical interpretations are placed on the results of the multivariate technique. It is concluded that the multivariate Box-Jenkins approach is a suitable techniquemore » for building thermal analysis. Application to multivariate Box-Jenkins approach is a suitable technique for building thermal analysis. Application to multivariate model-based control is discussed, with particular reference to building energy management systems. It is further concluded that stochastic modeling of data drawn from a short monitoring period offers a means of retrofitting an advanced model-based control system in existing buildings, which could be used to optimize energy savings. An approach to system simulation is suggested.« less

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)
Stochastic optimization algorithms for barrier dividend strategies

NASA Astrophysics Data System (ADS)

Yin, G.; Song, Q. S.; Yang, H.

2009-01-01

This work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy. A new approach based on stochastic optimization methods is developed. Compared with the existing results in the literature, more general surplus processes are considered. Precise models of the surplus need not be known; only noise-corrupted observations of the dividends are used. Using barrier-type strategies, a class of stochastic optimization algorithms are developed. Convergence of the algorithm is analyzed; rate of convergence is also provided. Numerical results are reported to demonstrate the performance of the algorithm.
Essays on variational approximation techniques for stochastic optimization problems

NASA Astrophysics Data System (ADS)

Deride Silva, Julio A.

This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence of estimators, and a problem for creating probabilistic scenarios on renewable energies estimation. In Chapter 7 we re-visited one of the "folk theorems" in statistics, where a family of Bayes estimators under 0-1 loss functions is claimed to converge to the maximum a posteriori estimator. This assertion is studied under the scope of the hypo-convergence theory, and the density functions are included in the class of upper semicontinuous functions. We conclude this chapter with an example in which the convergence does not hold true, and we provided sufficient conditions that guarantee convergence. The last chapter, Chapter 8, addresses the important topic of creating probabilistic scenarios for solar power generation. Scenarios are a fundamental input for the stochastic optimization problem of energy dispatch, especially when incorporating renewables. We proposed a model designed to capture the constraints induced by physical characteristics of the variables based on the application of an epi-spline density estimation along with a copula estimation, in order to account for partial correlations between variables.
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 dual theory of price and value in a meso-scale economic model with stochastic profit rate

NASA Astrophysics Data System (ADS)

Greenblatt, R. E.

2014-12-01

The problem of commodity price determination in a market-based, capitalist economy has a long and contentious history. Neoclassical microeconomic theories are based typically on marginal utility assumptions, while classical macroeconomic theories tend to be value-based. In the current work, I study a simplified meso-scale model of a commodity capitalist economy. The production/exchange model is represented by a network whose nodes are firms, workers, capitalists, and markets, and whose directed edges represent physical or monetary flows. A pair of multivariate linear equations with stochastic input parameters represent physical (supply/demand) and monetary (income/expense) balance. The input parameters yield a non-degenerate profit rate distribution across firms. Labor time and price are found to be eigenvector solutions to the respective balance equations. A simple relation is derived relating the expected value of commodity price to commodity labor content. Results of Monte Carlo simulations are consistent with the stochastic price/labor content relation.
Multi-fidelity Gaussian process regression for prediction of random fields

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

Parussini, L.; Venturi, D., E-mail: venturi@ucsc.edu; Perdikaris, P.

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgersmore » equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.« less
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.
Rényi entropy measure of noise-aided information transmission in a binary channel.

PubMed

Chapeau-Blondeau, François; Rousseau, David; Delahaies, Agnès

2010-05-01

This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise-aided binary image transmission.
Stochastic kinetic mean field model

NASA Astrophysics Data System (ADS)

Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.

2016-07-01

This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.
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.
A stochastic bioenergetics model based approach to translating large river flow and temperature in to fish population responses: The pallid sturgeon example

USGS Publications Warehouse

Wildhaber, Mark L.; Dey, Rima; Wikle, Christopher K.; Moran, Edward H.; Anderson, Christopher J.; Franz, Kristie J.

2015-01-01

In managing fish populations, especially at-risk species, realistic mathematical models are needed to help predict population response to potential management actions in the context of environmental conditions and changing climate while effectively incorporating the stochastic nature of real world conditions. We provide a key component of such a model for the endangered pallid sturgeon (Scaphirhynchus albus) in the form of an individual-based bioenergetics model influenced not only by temperature but also by flow. This component is based on modification of a known individual-based bioenergetics model through incorporation of: the observed ontogenetic shift in pallid sturgeon diet from marcroinvertebrates to fish; the energetic costs of swimming under flowing-water conditions; and stochasticity. We provide an assessment of how differences in environmental conditions could potentially alter pallid sturgeon growth estimates, using observed temperature and velocity from channelized portions of the Lower Missouri River mainstem. We do this using separate relationships between the proportion of maximum consumption and fork length and swimming cost standard error estimates for fish captured above and below the Kansas River in the Lower Missouri River. Critical to our matching observed growth in the field with predicted growth based on observed environmental conditions was a two-step shift in diet from macroinvertebrates to fish.
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.
Perception Accuracy of Affiliative Relationships in Elementary School Children and Young Adolescents

PubMed Central

Daniel, João R.; Silva, Rita R.; Santos, António J.; Cardoso, Jordana; Coelho, Leandra; Freitas, Miguel; Ribeiro, Olívia

2017-01-01

There has been a rapid growth of studies focused on selection and socialization processes of peer groups, mostly due to the development of stochastic actor-based models to analyze longitudinal social network data. One of the core assumptions of these models is that individuals have an accurate knowledge of the dyadic relationships within their network (i.e., who is and is not connected to whom). Recent cross-sectional findings suggest that elementary school children are very inaccurate in perceiving their classmates’ dyadic relationships. These findings question the validity of stochastic actor-based models to study the developmental dynamics of children and carry implications for future research as well as for the interpretation of past findings. The goal of the present study was thus to further explore the adequacy of the accuracy assumption, analysing data from three longitudinal samples of different age groups (elementary school children and adolescents). Our results support the validity of stochastic actor-based models to study the network of adolescents and suggest that the violation of the accuracy assumption for elementary school children is not as severe as previously thought. PMID:29163310
Compartmental and Spatial Rule-Based Modeling with Virtual Cell.

PubMed

Blinov, Michael L; Schaff, James C; Vasilescu, Dan; Moraru, Ion I; Bloom, Judy E; Loew, Leslie M

2017-10-03

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Stochastic inference with spiking neurons in the high-conductance state

NASA Astrophysics Data System (ADS)

Petrovici, Mihai A.; Bill, Johannes; Bytschok, Ilja; Schemmel, Johannes; Meier, Karlheinz

2016-10-01

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.
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.
Interpretation of scrape-off layer profile evolution and first-wall ion flux statistics on JET using a stochastic framework based on fillamentary motion

NASA Astrophysics Data System (ADS)

Walkden, N. R.; Wynn, A.; Militello, F.; Lipschultz, B.; Matthews, G.; Guillemaut, C.; Harrison, J.; Moulton, D.; Contributors, JET

2017-08-01

This paper presents the use of a novel modelling technique based around intermittent transport due to filament motion, to interpret experimental profile and fluctuation data in the scrape-off layer (SOL) of JET during the onset and evolution of a density profile shoulder. A baseline case is established, prior to shoulder formation, and the stochastic model is shown to be capable of simultaneously matching the time averaged profile measurement as well as the PDF shape and autocorrelation function from the ion-saturation current time series at the outer wall. Aspects of the stochastic model are then varied with the aim of producing a profile shoulder with statistical measurements consistent with experiment. This is achieved through a strong localised reduction in the density sink acting on the filaments within the model. The required reduction of the density sink occurs over a highly localised region with the timescale of the density sink increased by a factor of 25. This alone is found to be insufficient to model the expansion and flattening of the shoulder region as the density increases, which requires additional changes within the stochastic model. An example is found which includes both a reduction in the density sink and filament acceleration and provides a consistent match to the experimental data as the shoulder expands, though the uniqueness of this solution can not be guaranteed. Within the context of the stochastic model, this implies that the localised reduction in the density sink can trigger shoulder formation, but additional physics is required to explain the subsequent evolution of the profile.
Stochastic mechanical model of vocal folds for producing jitter and for identifying pathologies through real voices.

PubMed

Cataldo, E; Soize, C

2018-06-06

Jitter, in voice production applications, is a random phenomenon characterized by the deviation of the glottal cycle length with respect to a mean value. Its study can help in identifying pathologies related to the vocal folds according to the values obtained through the different ways to measure it. This paper aims to propose a stochastic model, considering three control parameters, to generate jitter based on a deterministic one-mass model for the dynamics of the vocal folds and to identify parameters from the stochastic model taking into account real voice signals experimentally obtained. To solve the corresponding stochastic inverse problem, the cost function used is based on the distance between probability density functions of the random variables associated with the fundamental frequencies obtained by the experimental voices and the simulated ones, and also on the distance between features extracted from the voice signals, simulated and experimental, to calculate jitter. The results obtained show that the model proposed is valid and some samples of voices are synthesized considering the identified parameters for normal and pathological cases. The strategy adopted is also a novelty and mainly because a solution was obtained. In addition to the use of three parameters to construct the model of jitter, it is the discussion of a parameter related to the bandwidth of the power spectral density function of the stochastic process to measure the quality of the signal generated. A study about the influence of all the main parameters is also performed. The identification of the parameters of the model considering pathological cases is maybe of all novelties introduced by the paper the most interesting. Copyright © 2018 Elsevier Ltd. All rights reserved.

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME

PubMed Central

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2017-01-01

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. PMID:28190948
Collective behavior of coupled nonuniform stochastic oscillators

NASA Astrophysics Data System (ADS)

Assis, Vladimir R. V.; Copelli, Mauro

2012-02-01

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α‧<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.
Stochastic optimal operation of reservoirs based on copula functions

NASA Astrophysics Data System (ADS)

Lei, Xiao-hui; Tan, Qiao-feng; Wang, Xu; Wang, Hao; Wen, Xin; Wang, Chao; Zhang, Jing-wen

2018-02-01

Stochastic dynamic programming (SDP) has been widely used to derive operating policies for reservoirs considering streamflow uncertainties. In SDP, there is a need to calculate the transition probability matrix more accurately and efficiently in order to improve the economic benefit of reservoir operation. In this study, we proposed a stochastic optimization model for hydropower generation reservoirs, in which 1) the transition probability matrix was calculated based on copula functions; and 2) the value function of the last period was calculated by stepwise iteration. Firstly, the marginal distribution of stochastic inflow in each period was built and the joint distributions of adjacent periods were obtained using the three members of the Archimedean copulas, based on which the conditional probability formula was derived. Then, the value in the last period was calculated by a simple recursive equation with the proposed stepwise iteration method and the value function was fitted with a linear regression model. These improvements were incorporated into the classic SDP and applied to the case study in Ertan reservoir, China. The results show that the transition probability matrix can be more easily and accurately obtained by the proposed copula function based method than conventional methods based on the observed or synthetic streamflow series, and the reservoir operation benefit can also be increased.
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.
Inadequacy representation of flamelet-based RANS model for turbulent non-premixed flame

NASA Astrophysics Data System (ADS)

Lee, Myoungkyu; Oliver, Todd; Moser, Robert

2017-11-01

Stochastic representations for model inadequacy in RANS-based models of non-premixed jet flames are developed and explored. Flamelet-based RANS models are attractive for engineering applications relative to higher-fidelity methods because of their low computational costs. However, the various assumptions inherent in such models introduce errors that can significantly affect the accuracy of computed quantities of interest. In this work, we develop an approach to represent the model inadequacy of the flamelet-based RANS model. In particular, we pose a physics-based, stochastic PDE for the triple correlation of the mixture fraction. This additional uncertain state variable is then used to construct perturbations of the PDF for the instantaneous mixture fraction, which is used to obtain an uncertain perturbation of the flame temperature. A hydrogen-air non-premixed jet flame is used to demonstrate the representation of the inadequacy of the flamelet-based RANS model. This work was supported by DARPA-EQUiPS(Enabling Quantification of Uncertainty in Physical Systems) program.
Representing Micro-Macro Linkages by Actor-Based Dynamic Network Models

ERIC Educational Resources Information Center

Snijders, Tom A. B.; Steglich, Christian E. G.

2015-01-01

Stochastic actor-based models for network dynamics have the primary aim of statistical inference about processes of network change, but may be regarded as a kind of agent-based models. Similar to many other agent-based models, they are based on local rules for actor behavior. Different from many other agent-based models, by including elements of…
Adaptive two-regime method: Application to front propagation

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

Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Flegg, Mark, E-mail: mark.flegg@monash.edu

2014-03-28

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in termsmore » of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.« less
A new stochastic model considering satellite clock interpolation errors in precise point positioning

NASA Astrophysics Data System (ADS)

Wang, Shengli; Yang, Fanlin; Gao, Wang; Yan, Lizi; Ge, Yulong

2018-03-01

Precise clock products are typically interpolated based on the sampling interval of the observational data when they are used for in precise point positioning. However, due to the occurrence of white noise in atomic clocks, a residual component of such noise will inevitable reside within the observations when clock errors are interpolated, and such noise will affect the resolution of the positioning results. In this paper, which is based on a twenty-one-week analysis of the atomic clock noise characteristics of numerous satellites, a new stochastic observation model that considers satellite clock interpolation errors is proposed. First, the systematic error of each satellite in the IGR clock product was extracted using a wavelet de-noising method to obtain the empirical characteristics of atomic clock noise within each clock product. Then, based on those empirical characteristics, a stochastic observation model was structured that considered the satellite clock interpolation errors. Subsequently, the IGR and IGS clock products at different time intervals were used for experimental validation. A verification using 179 stations worldwide from the IGS showed that, compared with the conventional model, the convergence times using the stochastic model proposed in this study were respectively shortened by 4.8% and 4.0% when the IGR and IGS 300-s-interval clock products were used and by 19.1% and 19.4% when the 900-s-interval clock products were used. Furthermore, the disturbances during the initial phase of the calculation were also effectively improved.
Circular analysis in complex stochastic systems

PubMed Central

Valleriani, Angelo

2015-01-01

Ruling out observations can lead to wrong models. This danger occurs unwillingly when one selects observations, experiments, simulations or time-series based on their outcome. In stochastic processes, conditioning on the future outcome biases all local transition probabilities and makes them consistent with the selected outcome. This circular self-consistency leads to models that are inconsistent with physical reality. It is also the reason why models built solely on macroscopic observations are prone to this fallacy. PMID:26656656
Algorithm refinement for stochastic partial differential equations: II. Correlated systems

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

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less
Detecting Abnormal Vehicular Dynamics at Intersections Based on an Unsupervised Learning Approach and a Stochastic Model

PubMed Central

Jiménez-Hernández, Hugo; González-Barbosa, Jose-Joel; Garcia-Ramírez, Teresa

2010-01-01

This investigation demonstrates an unsupervised approach for modeling traffic flow and detecting abnormal vehicle behaviors at intersections. In the first stage, the approach reveals and records the different states of the system. These states are the result of coding and grouping the historical motion of vehicles as long binary strings. In the second stage, using sequences of the recorded states, a stochastic graph model based on a Markovian approach is built. A behavior is labeled abnormal when current motion pattern cannot be recognized as any state of the system or a particular sequence of states cannot be parsed with the stochastic model. The approach is tested with several sequences of images acquired from a vehicular intersection where the traffic flow and duration used in connection with the traffic lights are continuously changed throughout the day. Finally, the low complexity and the flexibility of the approach make it reliable for use in real time systems. PMID:22163616
Detecting abnormal vehicular dynamics at intersections based on an unsupervised learning approach and a stochastic model.

PubMed

Jiménez-Hernández, Hugo; González-Barbosa, Jose-Joel; Garcia-Ramírez, Teresa

2010-01-01

This investigation demonstrates an unsupervised approach for modeling traffic flow and detecting abnormal vehicle behaviors at intersections. In the first stage, the approach reveals and records the different states of the system. These states are the result of coding and grouping the historical motion of vehicles as long binary strings. In the second stage, using sequences of the recorded states, a stochastic graph model based on a Markovian approach is built. A behavior is labeled abnormal when current motion pattern cannot be recognized as any state of the system or a particular sequence of states cannot be parsed with the stochastic model. The approach is tested with several sequences of images acquired from a vehicular intersection where the traffic flow and duration used in connection with the traffic lights are continuously changed throughout the day. Finally, the low complexity and the flexibility of the approach make it reliable for use in real time systems.
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
Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.
Incorporating variability in simulations of seasonally forced phenology using integral projection models

DOE PAGES

Goodsman, Devin W.; Aukema, Brian H.; McDowell, Nate G.; ...

2017-11-26

Phenology models are becoming increasingly important tools to accurately predict how climate change will impact the life histories of organisms. We propose a class of integral projection phenology models derived from stochastic individual-based models of insect development and demography. Our derivation, which is based on the rate summation concept, produces integral projection models that capture the effect of phenotypic rate variability on insect phenology, but which are typically more computationally frugal than equivalent individual-based phenology models. We demonstrate our approach using a temperature-dependent model of the demography of the mountain pine beetle (Dendroctonus ponderosae Hopkins), an insect that kills maturemore » pine trees. This work illustrates how a wide range of stochastic phenology models can be reformulated as integral projection models. Due to their computational efficiency, these integral projection models are suitable for deployment in large-scale simulations, such as studies of altered pest distributions under climate change.« less
Incorporating variability in simulations of seasonally forced phenology using integral projection models

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

Goodsman, Devin W.; Aukema, Brian H.; McDowell, Nate G.

Phenology models are becoming increasingly important tools to accurately predict how climate change will impact the life histories of organisms. We propose a class of integral projection phenology models derived from stochastic individual-based models of insect development and demography. Our derivation, which is based on the rate summation concept, produces integral projection models that capture the effect of phenotypic rate variability on insect phenology, but which are typically more computationally frugal than equivalent individual-based phenology models. We demonstrate our approach using a temperature-dependent model of the demography of the mountain pine beetle (Dendroctonus ponderosae Hopkins), an insect that kills maturemore » pine trees. This work illustrates how a wide range of stochastic phenology models can be reformulated as integral projection models. Due to their computational efficiency, these integral projection models are suitable for deployment in large-scale simulations, such as studies of altered pest distributions under climate change.« less
ON NONSTATIONARY STOCHASTIC MODELS FOR EARTHQUAKES.

USGS Publications Warehouse

Safak, Erdal; Boore, David M.

1986-01-01

A seismological stochastic model for earthquake ground-motion description is presented. Seismological models are based on the physical properties of the source and the medium and have significant advantages over the widely used empirical models. The model discussed here provides a convenient form for estimating structural response by using random vibration theory. A commonly used random process for ground acceleration, filtered white-noise multiplied by an envelope function, introduces some errors in response calculations for structures whose periods are longer than the faulting duration. An alternate random process, filtered shot-noise process, eliminates these errors.
A Novel Biobjective Risk-Based Model for Stochastic Air Traffic Network Flow Optimization Problem.

PubMed

Cai, Kaiquan; Jia, Yaoguang; Zhu, Yanbo; Xiao, Mingming

2015-01-01

Network-wide air traffic flow management (ATFM) is an effective way to alleviate demand-capacity imbalances globally and thereafter reduce airspace congestion and flight delays. The conventional ATFM models assume the capacities of airports or airspace sectors are all predetermined. However, the capacity uncertainties due to the dynamics of convective weather may make the deterministic ATFM measures impractical. This paper investigates the stochastic air traffic network flow optimization (SATNFO) problem, which is formulated as a weighted biobjective 0-1 integer programming model. In order to evaluate the effect of capacity uncertainties on ATFM, the operational risk is modeled via probabilistic risk assessment and introduced as an extra objective in SATNFO problem. Computation experiments using real-world air traffic network data associated with simulated weather data show that presented model has far less constraints compared to stochastic model with nonanticipative constraints, which means our proposed model reduces the computation complexity.
Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics.

PubMed

Marquez-Lago, Tatiana T; Burrage, Kevin

2007-09-14

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.

Consentaneous Agent-Based and Stochastic Model of the Financial Markets

PubMed Central

Gontis, Vygintas; Kononovicius, Aleksejus

2014-01-01

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation. PMID:25029364
Use of suprathreshold stochastic resonance in cochlear implant coding

NASA Astrophysics Data System (ADS)

Allingham, David; Stocks, Nigel G.; Morse, Robert P.

2003-05-01

In this article we discuss the possible use of a novel form of stochastic resonance, termed suprathreshold stochastic resonance (SSR), to improve signal encoding/transmission in cochlear implants. A model, based on the leaky-integrate-and-fire (LIF) neuron, has been developed from physiological data and use to model information flow in a population of cochlear nerve fibers. It is demonstrated that information flow can, in principle, be enhanced by the SSR effect. Furthermore, SSR was found to enhance information transmission for signal parameters that are commonly encountered in cochlear implants. This, therefore, gives hope that SSR may be implemented in cochlear implants to improve speech comprehension.
A comparison of two- and three-dimensional stochastic models of regional solute movement

USGS Publications Warehouse

Shapiro, A.M.; Cvetkovic, V.D.

1990-01-01

Recent models of solute movement in porous media that are based on a stochastic description of the porous medium properties have been dedicated primarily to a three-dimensional interpretation of solute movement. In many practical problems, however, it is more convenient and consistent with measuring techniques to consider flow and solute transport as an areal, two-dimensional phenomenon. The physics of solute movement, however, is dependent on the three-dimensional heterogeneity in the formation. A comparison of two- and three-dimensional stochastic interpretations of solute movement in a porous medium having a statistically isotropic hydraulic conductivity field is investigated. To provide an equitable comparison between the two- and three-dimensional analyses, the stochastic properties of the transmissivity are defined in terms of the stochastic properties of the hydraulic conductivity. The variance of the transmissivity is shown to be significantly reduced in comparison to that of the hydraulic conductivity, and the transmissivity is spatially correlated over larger distances. These factors influence the two-dimensional interpretations of solute movement by underestimating the longitudinal and transverse growth of the solute plume in comparison to its description as a three-dimensional phenomenon. Although this analysis is based on small perturbation approximations and the special case of a statistically isotropic hydraulic conductivity field, it casts doubt on the use of a stochastic interpretation of the transmissivity in describing regional scale movement. However, by assuming the transmissivity to be the vertical integration of the hydraulic conductivity field at a given position, the stochastic properties of the hydraulic conductivity can be estimated from the stochastic properties of the transmissivity and applied to obtain a more accurate interpretation of solute movement. ?? 1990 Kluwer Academic Publishers.
Stochastic global identification of a bio-inspired self-sensing composite UAV wing via wind tunnel experiments

NASA Astrophysics Data System (ADS)

Kopsaftopoulos, Fotios; Nardari, Raphael; Li, Yu-Hung; Wang, Pengchuan; Chang, Fu-Kuo

2016-04-01

In this work, the system design, integration, and wind tunnel experimental evaluation are presented for a bioinspired self-sensing intelligent composite unmanned aerial vehicle (UAV) wing. A total of 148 micro-sensors, including piezoelectric, strain, and temperature sensors, in the form of stretchable sensor networks are embedded in the layup of a composite wing in order to enable its self-sensing capabilities. Novel stochastic system identification techniques based on time series models and statistical parameter estimation are employed in order to accurately interpret the sensing data and extract real-time information on the coupled air flow-structural dynamics. Special emphasis is given to the wind tunnel experimental assessment under various flight conditions defined by multiple airspeeds and angles of attack. A novel modeling approach based on the recently introduced Vector-dependent Functionally Pooled (VFP) model structure is employed for the stochastic identification of the "global" coupled airflow-structural dynamics of the wing and their correlation with dynamic utter and stall. The obtained results demonstrate the successful system-level integration and effectiveness of the stochastic identification approach, thus opening new perspectives for the state sensing and awareness capabilities of the next generation of "fly-by-fee" UAVs.
Stochastic and Geometric Reasoning for Indoor Building Models with Electric Installations - Bridging the Gap Between GIS and Bim

NASA Astrophysics Data System (ADS)

Dehbi, Y.; Haunert, J.-H.; Plümer, L.

2017-10-01

3D city and building models according to CityGML encode the geometry, represent the structure and model semantically relevant building parts such as doors, windows and balconies. Building information models support the building design, construction and the facility management. In contrast to CityGML, they include also objects which cannot be observed from the outside. The three dimensional indoor models characterize a missing link between both worlds. Their derivation, however, is expensive. The semantic automatic interpretation of 3D point clouds of indoor environments is a methodically demanding task. The data acquisition is costly and difficult. The laser scanners and image-based methods require the access to every room. Based on an approach which does not require an additional geometry acquisition of building indoors, we propose an attempt for filling the gaps between 3D building models and building information models. Based on sparse observations such as the building footprint and room areas, 3D indoor models are generated using combinatorial and stochastic reasoning. The derived models are expanded by a-priori not observable structures such as electric installation. Gaussian mixtures, linear and bi-linear constraints are used to represent the background knowledge and structural regularities. The derivation of hypothesised models is performed by stochastic reasoning using graphical models, Gauss-Markov models and MAP-estimators.
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.
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE PAGES

Hagos, Samson; Feng, Zhe; Plant, Robert S.; ...

2018-02-20

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

NASA Astrophysics Data System (ADS)

Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

2018-02-01

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less
The nature of combustion noise: Stochastic or chaotic?

NASA Astrophysics Data System (ADS)

Gupta, Vikrant; Lee, Min Chul; Li, Larry K. B.

2016-11-01

Combustion noise, which refers to irregular low-amplitude pressure oscillations, is conventionally thought to be stochastic. It has therefore been modeled using a stochastic term in the analysis of thermoacoustic systems. Recently, however, there has been a renewed interest in the validity of that stochastic assumption, with tests based on nonlinear dynamical theory giving seemingly contradictory results: some show combustion noise to be stochastic while others show it to be chaotic. In this study, we show that this contradiction arises because those tests cannot distinguish between noise amplification and chaos. We further show that although there are many similarities between noise amplification and chaos, there are also some subtle differences. It is these subtle differences, not the results of those tests, that should be the focus of analyses aimed at determining the true nature of combustion noise. Recognizing this is an important step towards improved understanding and modeling of combustion noise for the study of thermoacoustic instabilities. This work was supported by the Research Grants Council of Hong Kong (Project No. 16235716 and 26202815).
Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Slepukhina, Evdokia

A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh-Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed.
Modeling stochastic frontier based on vine copulas

NASA Astrophysics Data System (ADS)

Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito

2017-11-01

This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.
Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors

NASA Astrophysics Data System (ADS)

Mehanna Ismail, Mohammed Ali

The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the implementation of time splitting, variable stochastic fluid particle mass control, and a second order time accurate (predictor-corrector) scheme used for solving the stochastic differential equations governing the particles evolution. The model compared well against experimental data found in the literature for two different configurations: bluff body and swirl stabilized combustors. The generalized stochastic reactor is a newly developed model. This model relies on the generalization of the concept of the classical stochastic reactor theory in the sense that it accounts for both finite micro- and macro-mixing processes. (Abstract shortened by UMI.)
Mesoscopic and continuum modelling of angiogenesis

PubMed Central

Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

2016-01-01

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. PMID:24615007
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.
Stochastic resonance based on modulation instability in spatiotemporal chaos.

PubMed

Han, Jing; Liu, Hongjun; Huang, Nan; Wang, Zhaolu

2017-04-03

A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.
Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2017-10-01

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to 3 / 2, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.
Effluent trading in river systems through stochastic decision-making process: a case study.

PubMed

Zolfagharipoor, Mohammad Amin; Ahmadi, Azadeh

2017-09-01

The objective of this paper is to provide an efficient framework for effluent trading in river systems. The proposed framework consists of two pessimistic and optimistic decision-making models to increase the executability of river water quality trading programs. The models used for this purpose are (1) stochastic fallback bargaining (SFB) to reach an agreement among wastewater dischargers and (2) stochastic multi-criteria decision-making (SMCDM) to determine the optimal treatment strategy. The Monte-Carlo simulation method is used to incorporate the uncertainty into analysis. This uncertainty arises from stochastic nature and the errors in the calculation of wastewater treatment costs. The results of river water quality simulation model are used as the inputs of models. The proposed models are used in a case study on the Zarjoub River in northern Iran to determine the best solution for the pollution load allocation. The best treatment alternatives selected by each model are imported, as the initial pollution discharge permits, into an optimization model developed for trading of pollution discharge permits among pollutant sources. The results show that the SFB-based water pollution trading approach reduces the costs by US$ 14,834 while providing a relative consensus among pollutant sources. Meanwhile, the SMCDM-based water pollution trading approach reduces the costs by US$ 218,852, but it is less acceptable by pollutant sources. Therefore, it appears that giving due attention to stability, or in other words acceptability of pollution trading programs for all pollutant sources, is an essential element of their success.
Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

PubMed

Nishiura, Hiroshi

2011-02-16

Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.
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.

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

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

Samin, Adib J.

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.
A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

NASA Astrophysics Data System (ADS)

Samin, Adib J.

2016-05-01

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.
Inferring microbial interaction networks from metagenomic data using SgLV-EKF algorithm.

PubMed

Alshawaqfeh, Mustafa; Serpedin, Erchin; Younes, Ahmad Bani

2017-03-27

Inferring the microbial interaction networks (MINs) and modeling their dynamics are critical in understanding the mechanisms of the bacterial ecosystem and designing antibiotic and/or probiotic therapies. Recently, several approaches were proposed to infer MINs using the generalized Lotka-Volterra (gLV) model. Main drawbacks of these models include the fact that these models only consider the measurement noise without taking into consideration the uncertainties in the underlying dynamics. Furthermore, inferring the MIN is characterized by the limited number of observations and nonlinearity in the regulatory mechanisms. Therefore, novel estimation techniques are needed to address these challenges. This work proposes SgLV-EKF: a stochastic gLV model that adopts the extended Kalman filter (EKF) algorithm to model the MIN dynamics. In particular, SgLV-EKF employs a stochastic modeling of the MIN by adding a noise term to the dynamical model to compensate for modeling uncertainties. This stochastic modeling is more realistic than the conventional gLV model which assumes that the MIN dynamics are perfectly governed by the gLV equations. After specifying the stochastic model structure, we propose the EKF to estimate the MIN. SgLV-EKF was compared with two similarity-based algorithms, one algorithm from the integral-based family and two regression-based algorithms, in terms of the achieved performance on two synthetic data-sets and two real data-sets. The first data-set models the randomness in measurement data, whereas, the second data-set incorporates uncertainties in the underlying dynamics. The real data-sets are provided by a recent study pertaining to an antibiotic-mediated Clostridium difficile infection. The experimental results demonstrate that SgLV-EKF outperforms the alternative methods in terms of robustness to measurement noise, modeling errors, and tracking the dynamics of the MIN. Performance analysis demonstrates that the proposed SgLV-EKF algorithm represents a powerful and reliable tool to infer MINs and track their dynamics.
Revisiting node-based SIR models in complex networks with degree correlations

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alofi, Abdulaziz; AL-Mazrooei, Abdullah; Elaiw, Ahmed

2015-11-01

In this paper, we consider two growing networks which will lead to the degree-degree correlations between two nearest neighbors in the network. When the network grows to some certain size, we introduce an SIR-like disease such as pandemic influenza H1N1/09 to the population. Due to its rapid spread, the population size changes slowly, and thus the disease spreads on correlated networks with approximately fixed size. To predict the disease evolution on correlated networks, we first review two node-based SIR models incorporating degree correlations and an edge-based SIR model without considering degree correlation, and then compare the predictions of these models with stochastic SIR simulations, respectively. We find that the edge-based model, even without considering degree correlations, agrees much better than the node-based models incorporating degree correlations with stochastic SIR simulations in many respects. Moreover, simulation results show that for networks with positive correlation, the edge-based model provides a better upper bound of the cumulative incidence than the node-based SIR models, whereas for networks with negative correlation, it provides a lower bound of the cumulative incidence.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

PubMed

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
Stochastic inversion of cross-borehole radar data from metalliferous vein detection

NASA Astrophysics Data System (ADS)

Zeng, Zhaofa; Huai, Nan; Li, Jing; Zhao, Xueyu; Liu, Cai; Hu, Yingsa; Zhang, Ling; Hu, Zuzhi; Yang, Hui

2017-12-01

In the exploration and evaluation of the metalliferous veins with a cross-borehole radar system, traditional linear inversion methods (least squares inversion, LSQR) only get indirect parameters (permittivity, resistivity, or velocity) to estimate the target structure. They cannot accurately reflect the geological parameters of the metalliferous veins’ media properties. In order to get the intrinsic geological parameters and internal distribution, in this paper, we build a metalliferous veins model based on the stochastic effective medium theory, and carry out stochastic inversion and parameter estimation based on the Monte Carlo sampling algorithm. Compared with conventional LSQR, the stochastic inversion can get higher resolution inversion permittivity and velocity of the target body. We can estimate more accurately the distribution characteristics of abnormality and target internal parameters. It provides a new research idea to evaluate the properties of complex target media.
Incorporating Wind Power Forecast Uncertainties Into Stochastic Unit Commitment Using Neural Network-Based Prediction Intervals.

PubMed

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2015-09-01

Penetration of renewable energy resources, such as wind and solar power, into power systems significantly increases the uncertainties on system operation, stability, and reliability in smart grids. In this paper, the nonparametric neural network-based prediction intervals (PIs) are implemented for forecast uncertainty quantification. Instead of a single level PI, wind power forecast uncertainties are represented in a list of PIs. These PIs are then decomposed into quantiles of wind power. A new scenario generation method is proposed to handle wind power forecast uncertainties. For each hour, an empirical cumulative distribution function (ECDF) is fitted to these quantile points. The Monte Carlo simulation method is used to generate scenarios from the ECDF. Then the wind power scenarios are incorporated into a stochastic security-constrained unit commitment (SCUC) model. The heuristic genetic algorithm is utilized to solve the stochastic SCUC problem. Five deterministic and four stochastic case studies incorporated with interval forecasts of wind power are implemented. The results of these cases are presented and discussed together. Generation costs, and the scheduled and real-time economic dispatch reserves of different unit commitment strategies are compared. The experimental results show that the stochastic model is more robust than deterministic ones and, thus, decreases the risk in system operations of smart grids.
Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2016-11-01

This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.
A novel stochastic modeling method to simulate cooling loads in residential districts

DOE PAGES

An, Jingjing; Yan, Da; Hong, Tianzhen; ...

2017-09-04

District cooling systems are widely used in urban residential communities in China. Most of such systems are oversized, which leads to wasted investment, low operational efficiency and, thus, waste of energy. The accurate prediction of district cooling loads that can support the rightsizing of cooling plant equipment remains a challenge. This study develops a novel stochastic modeling method that consists of (1) six prototype house models representing most apartments in a district, (2) occupant behavior models of residential buildings reflecting their spatial and temporal diversity as well as their complexity based on a large-scale residential survey in China, and (3)more » a stochastic sampling process to represent all apartments and occupants in the district. The stochastic method was applied to a case study using the Designer's Simulation Toolkit (DeST) to simulate the cooling loads of a residential district in Wuhan, China. The simulation results agreed well with the measured data based on five performance metrics representing the aggregated cooling consumption, the peak cooling loads, the spatial load distribution, the temporal load distribution and the load profiles. Two prevalent simulation methods were also employed to simulate the district cooling loads. Here, the results showed that oversimplified assumptions about occupant behavior could lead to significant overestimation of the peak cooling load and the total cooling loads in the district. Future work will aim to simplify the workflow and data requirements of the stochastic method for its application, and to explore its use in predicting district heating loads and in commercial or mixed-use districts.« less
A novel stochastic modeling method to simulate cooling loads in residential districts

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

An, Jingjing; Yan, Da; Hong, Tianzhen

District cooling systems are widely used in urban residential communities in China. Most of such systems are oversized, which leads to wasted investment, low operational efficiency and, thus, waste of energy. The accurate prediction of district cooling loads that can support the rightsizing of cooling plant equipment remains a challenge. This study develops a novel stochastic modeling method that consists of (1) six prototype house models representing most apartments in a district, (2) occupant behavior models of residential buildings reflecting their spatial and temporal diversity as well as their complexity based on a large-scale residential survey in China, and (3)more » a stochastic sampling process to represent all apartments and occupants in the district. The stochastic method was applied to a case study using the Designer's Simulation Toolkit (DeST) to simulate the cooling loads of a residential district in Wuhan, China. The simulation results agreed well with the measured data based on five performance metrics representing the aggregated cooling consumption, the peak cooling loads, the spatial load distribution, the temporal load distribution and the load profiles. Two prevalent simulation methods were also employed to simulate the district cooling loads. Here, the results showed that oversimplified assumptions about occupant behavior could lead to significant overestimation of the peak cooling load and the total cooling loads in the district. Future work will aim to simplify the workflow and data requirements of the stochastic method for its application, and to explore its use in predicting district heating loads and in commercial or mixed-use districts.« less
Neural Mechanism for Stochastic Behavior During a Competitive Game

PubMed Central

Soltani, Alireza; Lee, Daeyeol; Wang, Xiao-Jing

2006-01-01

Previous studies have shown that non-human primates can generate highly stochastic choice behavior, especially when this is required during a competitive interaction with another agent. To understand the neural mechanism of such dynamic choice behavior, we propose a biologically plausible model of decision making endowed with synaptic plasticity that follows a reward-dependent stochastic Hebbian learning rule. This model constitutes a biophysical implementation of reinforcement learning, and it reproduces salient features of behavioral data from an experiment with monkeys playing a matching pennies game. Due to interaction with an opponent and learning dynamics, the model generates quasi-random behavior robustly in spite of intrinsic biases. Furthermore, non-random choice behavior can also emerge when the model plays against a non-interactive opponent, as observed in the monkey experiment. Finally, when combined with a meta-learning algorithm, our model accounts for the slow drift in the animal’s strategy based on a process of reward maximization. PMID:17015181
3D replicon distributions arise from stochastic initiation and domino-like DNA replication progression.

PubMed

Löb, D; Lengert, N; Chagin, V O; Reinhart, M; Casas-Delucchi, C S; Cardoso, M C; Drossel, B

2016-04-07

DNA replication dynamics in cells from higher eukaryotes follows very complex but highly efficient mechanisms. However, the principles behind initiation of potential replication origins and emergence of typical patterns of nuclear replication sites remain unclear. Here, we propose a comprehensive model of DNA replication in human cells that is based on stochastic, proximity-induced replication initiation. Critical model features are: spontaneous stochastic firing of individual origins in euchromatin and facultative heterochromatin, inhibition of firing at distances below the size of chromatin loops and a domino-like effect by which replication forks induce firing of nearby origins. The model reproduces the empirical temporal and chromatin-related properties of DNA replication in human cells. We advance the one-dimensional DNA replication model to a spatial model by taking into account chromatin folding in the nucleus, and we are able to reproduce the spatial and temporal characteristics of the replication foci distribution throughout S-phase.
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.
An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

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

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less
An inventory-theory-based interval-parameter two-stage stochastic programming model for water resources management

NASA Astrophysics Data System (ADS)

Suo, M. Q.; Li, Y. P.; Huang, G. H.

2011-09-01

In this study, an inventory-theory-based interval-parameter two-stage stochastic programming (IB-ITSP) model is proposed through integrating inventory theory into an interval-parameter two-stage stochastic optimization framework. This method can not only address system uncertainties with complex presentation but also reflect transferring batch (the transferring quantity at once) and period (the corresponding cycle time) in decision making problems. A case of water allocation problems in water resources management planning is studied to demonstrate the applicability of this method. Under different flow levels, different transferring measures are generated by this method when the promised water cannot be met. Moreover, interval solutions associated with different transferring costs also have been provided. They can be used for generating decision alternatives and thus help water resources managers to identify desired policies. Compared with the ITSP method, the IB-ITSP model can provide a positive measure for solving water shortage problems and afford useful information for decision makers under uncertainty.
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.
A stochastic model for density-dependent microwave Snow- and Graupel scattering coefficients of the NOAA JCSDA community radiative transfer model

NASA Astrophysics Data System (ADS)

Stegmann, Patrick G.; Tang, Guanglin; Yang, Ping; Johnson, Benjamin T.

2018-05-01

A structural model is developed for the single-scattering properties of snow and graupel particles with a strongly heterogeneous morphology and an arbitrary variable mass density. This effort is aimed to provide a mechanism to consider particle mass density variation in the microwave scattering coefficients implemented in the Community Radiative Transfer Model (CRTM). The stochastic model applies a bicontinuous random medium algorithm to a simple base shape and uses the Finite-Difference-Time-Domain (FDTD) method to compute the single-scattering properties of the resulting complex morphology.
A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

NASA Astrophysics Data System (ADS)

Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

2018-02-01

The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.
Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Adaptive Optimal Stochastic State Feedback Control of Resistive Wall Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2007-06-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least square method with exponential forgetting factor and covariance resetting is used to identify the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.
Pavement maintenance optimization model using Markov Decision Processes

NASA Astrophysics Data System (ADS)

Mandiartha, P.; Duffield, C. F.; Razelan, I. S. b. M.; Ismail, A. b. H.

2017-09-01

This paper presents an optimization model for selection of pavement maintenance intervention using a theory of Markov Decision Processes (MDP). There are some particular characteristics of the MDP developed in this paper which distinguish it from other similar studies or optimization models intended for pavement maintenance policy development. These unique characteristics include a direct inclusion of constraints into the formulation of MDP, the use of an average cost method of MDP, and the policy development process based on the dual linear programming solution. The limited information or discussions that are available on these matters in terms of stochastic based optimization model in road network management motivates this study. This paper uses a data set acquired from road authorities of state of Victoria, Australia, to test the model and recommends steps in the computation of MDP based stochastic optimization model, leading to the development of optimum pavement maintenance policy.
Evolving cell models for systems and synthetic biology.

PubMed

Cao, Hongqing; Romero-Campero, Francisco J; Heeb, Stephan; Cámara, Miguel; Krasnogor, Natalio

2010-03-01

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm's results as well as of the resulting evolved cell models.
Stochastic Simulation Tool for Aerospace Structural Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F.; Moore, David F.

2006-01-01

Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.
Stochastic Optimization for an Analytical Model of Saltwater Intrusion in Coastal Aquifers

PubMed Central

Stratis, Paris N.; Karatzas, George P.; Papadopoulou, Elena P.; Zakynthinaki, Maria S.; Saridakis, Yiannis G.

2016-01-01

The present study implements a stochastic optimization technique to optimally manage freshwater pumping from coastal aquifers. Our simulations utilize the well-known sharp interface model for saltwater intrusion in coastal aquifers together with its known analytical solution. The objective is to maximize the total volume of freshwater pumped by the wells from the aquifer while, at the same time, protecting the aquifer from saltwater intrusion. In the direction of dealing with this problem in real time, the ALOPEX stochastic optimization method is used, to optimize the pumping rates of the wells, coupled with a penalty-based strategy that keeps the saltwater front at a safe distance from the wells. Several numerical optimization results, that simulate a known real aquifer case, are presented. The results explore the computational performance of the chosen stochastic optimization method as well as its abilities to manage freshwater pumping in real aquifer environments. PMID:27689362
Dynamic phase transitions and dynamic phase diagrams of the Blume-Emery-Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

NASA Astrophysics Data System (ADS)

Ertaş, Mehmet; Keskin, Mustafa

2015-06-01

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume-Emery-Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h0/J), (D/J, T/J) and (K/J, T/J) planes, where T, h0, D, K and z are the temperature, magnetic field amplitude, crystal-field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.
Stochastic filtering for damage identification through nonlinear structural finite element model updating

NASA Astrophysics Data System (ADS)

Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.

2015-03-01

This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.
Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi

2015-04-01

The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be estimated based on the theory of stochastic processes, and it can be applied to the probabilistic risk of flood management.
Noise-induced escape in an excitable system

NASA Astrophysics Data System (ADS)

Khovanov, I. A.; Polovinkin, A. V.; Luchinsky, D. G.; McClintock, P. V. E.

2013-03-01

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation.
Noise stochastic corrected maximum a posteriori estimator for birefringence imaging using polarization-sensitive optical coherence tomography

PubMed Central

Kasaragod, Deepa; Makita, Shuichi; Hong, Young-Joo; Yasuno, Yoshiaki

2017-01-01

This paper presents a noise-stochastic corrected maximum a posteriori estimator for birefringence imaging using Jones matrix optical coherence tomography. The estimator described in this paper is based on the relationship between probability distribution functions of the measured birefringence and the effective signal to noise ratio (ESNR) as well as the true birefringence and the true ESNR. The Monte Carlo method is used to numerically describe this relationship and adaptive 2D kernel density estimation provides the likelihood for a posteriori estimation of the true birefringence. Improved estimation is shown for the new estimator with stochastic model of ESNR in comparison to the old estimator, both based on the Jones matrix noise model. A comparison with the mean estimator is also done. Numerical simulation validates the superiority of the new estimator. The superior performance of the new estimator was also shown by in vivo measurement of optic nerve head. PMID:28270974
Coupled stochastic soil moisture simulation-optimization model of deficit irrigation

NASA Astrophysics Data System (ADS)

Alizadeh, Hosein; Mousavi, S. Jamshid

2013-07-01

This study presents an explicit stochastic optimization-simulation model of short-term deficit irrigation management for large-scale irrigation districts. The model which is a nonlinear nonconvex program with an economic objective function is built on an agrohydrological simulation component. The simulation component integrates (1) an explicit stochastic model of soil moisture dynamics of the crop-root zone considering interaction of stochastic rainfall and irrigation with shallow water table effects, (2) a conceptual root zone salt balance model, and 3) the FAO crop yield model. Particle Swarm Optimization algorithm, linked to the simulation component, solves the resulting nonconvex program with a significantly better computational performance compared to a Monte Carlo-based implicit stochastic optimization model. The model has been tested first by applying it in single-crop irrigation problems through which the effects of the severity of water deficit on the objective function (net benefit), root-zone water balance, and irrigation water needs have been assessed. Then, the model has been applied in Dasht-e-Abbas and Ein-khosh Fakkeh Irrigation Districts (DAID and EFID) of the Karkheh Basin in southwest of Iran. While the maximum net benefit has been obtained for a stress-avoidance (SA) irrigation policy, the highest water profitability has been resulted when only about 60% of the water used in the SA policy is applied. The DAID with respectively 33% of total cultivated area and 37% of total applied water has produced only 14% of the total net benefit due to low-valued crops and adverse soil and shallow water table conditions.
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less
A stochastic modeling of isotope exchange reactions in glutamine synthetase

NASA Astrophysics Data System (ADS)

Kazmiruk, N. V.; Boronovskiy, S. E.; Nartsissov, Ya R.

2017-11-01

The model presented in this work allows simulation of isotopic exchange reactions at chemical equilibrium catalyzed by a glutamine synthetase. To simulate the functioning of the enzyme the algorithm based on the stochastic approach was applied. The dependence of exchange rates for 14C and 32P on metabolite concentration was estimated. The simulation results confirmed the hypothesis of the ascertained validity for preferred order random binding mechanism. Corresponding values of K0.5 were also obtained.
Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.
Optimizing signal recycling for detecting a stochastic gravitational-wave background

NASA Astrophysics Data System (ADS)

Tao, Duo; Christensen, Nelson

2018-06-01

Signal recycling is applied in laser interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to increase their sensitivity to gravitational waves. In this study, signal recycling configurations for detecting a stochastic gravitational wave background are optimized based on aLIGO parameters. Optimal transmission of the signal recycling mirror (SRM) and detuning phase of the signal recycling cavity under a fixed laser power and low-frequency cutoff are calculated. Based on the optimal configurations, the compatibility with a binary neutron star (BNS) search is discussed. Then, different laser powers and low-frequency cutoffs are considered. Two models for the dimensionless energy density of gravitational waves , the flat model and the model, are studied. For a stochastic background search, it is found that an interferometer using signal recycling has a better sensitivity than an interferometer not using it. The optimal stochastic search configurations are typically found when both the SRM transmission and the signal recycling detuning phase are low. In this region, the BNS range mostly lies between 160 and 180 Mpc. When a lower laser power is used the optimal signal recycling detuning phase increases, the optimal SRM transmission increases and the optimal sensitivity improves. A reduced low-frequency cutoff gives a better sensitivity limit. For both models of , a typical optimal sensitivity limit on the order of 10‑10 is achieved at a reference frequency of Hz.
Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

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

PubMed

Tian, Tianhai; Xu, Songlin; Gao, Junbin; Burrage, Kevin

2007-01-01

Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.
Modelling daily water temperature from air temperature for the Missouri River.

PubMed

Zhu, Senlin; Nyarko, Emmanuel Karlo; Hadzima-Nyarko, Marijana

2018-01-01

The bio-chemical and physical characteristics of a river are directly affected by water temperature, which thereby affects the overall health of aquatic ecosystems. It is a complex problem to accurately estimate water temperature. Modelling of river water temperature is usually based on a suitable mathematical model and field measurements of various atmospheric factors. In this article, the air-water temperature relationship of the Missouri River is investigated by developing three different machine learning models (Artificial Neural Network (ANN), Gaussian Process Regression (GPR), and Bootstrap Aggregated Decision Trees (BA-DT)). Standard models (linear regression, non-linear regression, and stochastic models) are also developed and compared to machine learning models. Analyzing the three standard models, the stochastic model clearly outperforms the standard linear model and nonlinear model. All the three machine learning models have comparable results and outperform the stochastic model, with GPR having slightly better results for stations No. 2 and 3, while BA-DT has slightly better results for station No. 1. The machine learning models are very effective tools which can be used for the prediction of daily river temperature.
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.

Stochastic model for the 3D microstructure of pristine and cyclically aged cathodes in Li-ion batteries

NASA Astrophysics Data System (ADS)

Kuchler, Klaus; Westhoff, Daniel; Feinauer, Julian; Mitsch, Tim; Manke, Ingo; Schmidt, Volker

2018-04-01

It is well-known that the microstructure of electrodes in lithium-ion batteries strongly affects their performance. Vice versa, the microstructure can exhibit strong changes during the usage of the battery due to aging effects. For a better understanding of these effects, mathematical analysis and modeling has turned out to be of great help. In particular, stochastic 3D microstructure models have proven to be a powerful and very flexible tool to generate various kinds of particle-based structures. Recently, such models have been proposed for the microstructure of anodes in lithium-ion energy and power cells. In the present paper, we describe a stochastic modeling approach for the 3D microstructure of cathodes in a lithium-ion energy cell, which differs significantly from the one observed in anodes. The model for the cathode data enhances the ideas of the anode models, which have been developed so far. It is calibrated using 3D tomographic image data from pristine as well as two aged cathodes. A validation based on morphological image characteristics shows that the model is able to realistically describe both, the microstructure of pristine and aged cathodes. Thus, we conclude that the model is suitable to generate virtual, but realistic microstructures of lithium-ion cathodes.
A stochastic evolutionary model generating a mixture of exponential distributions

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2016-02-01

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Calibration of a stochastic health evolution model using NHIS data

NASA Astrophysics Data System (ADS)

Gupta, Aparna; Li, Zhisheng

2011-10-01

This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.
Incorporating variability in simulations of seasonally forced phenology using integral projection models

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

Goodsman, Devin W.; Aukema, Brian H.; McDowell, Nate G.

Phenology models are becoming increasingly important tools to accurately predict how climate change will impact the life histories of organisms. We propose a class of integral projection phenology models derived from stochastic individual-based models of insect development and demography.Our derivation, which is based on the rate-summation concept, produces integral projection models that capture the effect of phenotypic rate variability on insect phenology, but which are typically more computationally frugal than equivalent individual-based phenology models. We demonstrate our approach using a temperature-dependent model of the demography of the mountain pine beetle (Dendroctonus ponderosae Hopkins), an insect that kills mature pine trees.more » This work illustrates how a wide range of stochastic phenology models can be reformulated as integral projection models. Due to their computational efficiency, these integral projection models are suitable for deployment in large-scale simulations, such as studies of altered pest distributions under climate change.« less
Stochastic gain in finite populations

NASA Astrophysics Data System (ADS)

Röhl, Torsten; Traulsen, Arne; Claussen, Jens Christian; Schuster, Heinz Georg

2008-08-01

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen , Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.
Stochastic Dynamical Model of a Growing Citation Network Based on a Self-Exciting Point Process

NASA Astrophysics Data System (ADS)

Golosovsky, Michael; Solomon, Sorin

2012-08-01

We put under experimental scrutiny the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose a citation network of physics papers and traced the citation history of 40 195 papers published in one year. Contrary to common belief, we find that the citation dynamics of the individual papers follows the superlinear preferential attachment, with the exponent α=1.25-1.3. Moreover, we show that the citation process cannot be described as a memoryless Markov chain since there is a substantial correlation between the present and recent citation rates of a paper. Based on our findings we construct a stochastic growth model of the citation network, perform numerical simulations based on this model and achieve an excellent agreement with the measured citation distributions.
An agent-based stochastic Occupancy Simulator

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

Chen, Yixing; Hong, Tianzhen; Luo, Xuan

Occupancy has significant impacts on building performance. However, in current building performance simulation programs, occupancy inputs are static and lack diversity, contributing to discrepancies between the simulated and actual building performance. This work presents an Occupancy Simulator that simulates the stochastic behavior of occupant presence and movement in buildings, capturing the spatial and temporal occupancy diversity. Each occupant and each space in the building are explicitly simulated as an agent with their profiles of stochastic behaviors. The occupancy behaviors are represented with three types of models: (1) the status transition events (e.g., first arrival in office) simulated with probability distributionmore » model, (2) the random moving events (e.g., from one office to another) simulated with a homogeneous Markov chain model, and (3) the meeting events simulated with a new stochastic model. A hierarchical data model was developed for the Occupancy Simulator, which reduces the amount of data input by using the concepts of occupant types and space types. Finally, a case study of a small office building is presented to demonstrate the use of the Simulator to generate detailed annual sub-hourly occupant schedules for individual spaces and the whole building. The Simulator is a web application freely available to the public and capable of performing a detailed stochastic simulation of occupant presence and movement in buildings. Future work includes enhancements in the meeting event model, consideration of personal absent days, verification and validation of the simulated occupancy results, and expansion for use with residential buildings.« less
An agent-based stochastic Occupancy Simulator

DOE PAGES

Chen, Yixing; Hong, Tianzhen; Luo, Xuan

2017-06-01

Occupancy has significant impacts on building performance. However, in current building performance simulation programs, occupancy inputs are static and lack diversity, contributing to discrepancies between the simulated and actual building performance. This work presents an Occupancy Simulator that simulates the stochastic behavior of occupant presence and movement in buildings, capturing the spatial and temporal occupancy diversity. Each occupant and each space in the building are explicitly simulated as an agent with their profiles of stochastic behaviors. The occupancy behaviors are represented with three types of models: (1) the status transition events (e.g., first arrival in office) simulated with probability distributionmore » model, (2) the random moving events (e.g., from one office to another) simulated with a homogeneous Markov chain model, and (3) the meeting events simulated with a new stochastic model. A hierarchical data model was developed for the Occupancy Simulator, which reduces the amount of data input by using the concepts of occupant types and space types. Finally, a case study of a small office building is presented to demonstrate the use of the Simulator to generate detailed annual sub-hourly occupant schedules for individual spaces and the whole building. The Simulator is a web application freely available to the public and capable of performing a detailed stochastic simulation of occupant presence and movement in buildings. Future work includes enhancements in the meeting event model, consideration of personal absent days, verification and validation of the simulated occupancy results, and expansion for use with residential buildings.« less
Dependability and performability analysis

NASA Technical Reports Server (NTRS)

Trivedi, Kishor S.; Ciardo, Gianfranco; Malhotra, Manish; Sahner, Robin A.

1993-01-01

Several practical issues regarding specifications and solution of dependability and performability models are discussed. Model types with and without rewards are compared. Continuous-time Markov chains (CTMC's) are compared with (continuous-time) Markov reward models (MRM's) and generalized stochastic Petri nets (GSPN's) are compared with stochastic reward nets (SRN's). It is shown that reward-based models could lead to more concise model specifications and solution of a variety of new measures. With respect to the solution of dependability and performability models, three practical issues were identified: largeness, stiffness, and non-exponentiality, and a variety of approaches are discussed to deal with them, including some of the latest research efforts.
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
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 dynamic analysis of marine risers considering Gaussian system uncertainties

NASA Astrophysics Data System (ADS)

Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong

2018-03-01

This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.
Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

PubMed Central

2011-01-01

Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance. PMID:21324153
IMPLICIT DUAL CONTROL BASED ON PARTICLE FILTERING AND FORWARD DYNAMIC PROGRAMMING.

PubMed

Bayard, David S; Schumitzky, Alan

2010-03-01

This paper develops a sampling-based approach to implicit dual control. Implicit dual control methods synthesize stochastic control policies by systematically approximating the stochastic dynamic programming equations of Bellman, in contrast to explicit dual control methods that artificially induce probing into the control law by modifying the cost function to include a term that rewards learning. The proposed implicit dual control approach is novel in that it combines a particle filter with a policy-iteration method for forward dynamic programming. The integration of the two methods provides a complete sampling-based approach to the problem. Implementation of the approach is simplified by making use of a specific architecture denoted as an H-block. Practical suggestions are given for reducing computational loads within the H-block for real-time applications. As an example, the method is applied to the control of a stochastic pendulum model having unknown mass, length, initial position and velocity, and unknown sign of its dc gain. Simulation results indicate that active controllers based on the described method can systematically improve closed-loop performance with respect to other more common stochastic control approaches.
Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.
Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

NASA Astrophysics Data System (ADS)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.
Influence of vectors' risk-spreading strategies and environmental stochasticity on the epidemiology and evolution of vector-borne diseases: the example of Chagas' disease.

PubMed

Pelosse, Perrine; Kribs-Zaleta, Christopher M; Ginoux, Marine; Rabinovich, Jorge E; Gourbière, Sébastien; Menu, Frédéric

2013-01-01

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control.
Influence of Vectors’ Risk-Spreading Strategies and Environmental Stochasticity on the Epidemiology and Evolution of Vector-Borne Diseases: The Example of Chagas’ Disease

PubMed Central

Pelosse, Perrine; Kribs-Zaleta, Christopher M.; Ginoux, Marine; Rabinovich, Jorge E.; Gourbière, Sébastien; Menu, Frédéric

2013-01-01

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas’ disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments. We developed a simplified multi-stage vector-borne SI epidemiological model to investigate how vector risk-spreading strategies and environmental stochasticity influence the prevalence and evolution of a parasite. This model is based on available knowledge on triatomine biodemography, but its conceptual outcomes apply, to a certain extent, to other vector-borne diseases. Model comparisons between deterministic and stochastic settings led to the conclusion that environmental stochasticity, vector risk-spreading strategies (in particular an increase in the length and variability of development time) and their interaction have drastic consequences on vector population dynamics, disease prevalence, and the relative short-term evolution of parasite virulence. Our work shows that stochastic environments and associated risk-spreading strategies can increase the prevalence of vector-borne diseases and favor the invasion of more virulent parasite strains on relatively short evolutionary timescales. This study raises new questions and challenges in a context of increasingly unpredictable environmental variations as a result of global climate change and human interventions such as habitat destruction or vector control. PMID:23951018
Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Developing stochastic model of thrust and flight dynamics for small UAVs

NASA Astrophysics Data System (ADS)

Tjhai, Chandra

This thesis presents a stochastic thrust model and aerodynamic model for small propeller driven UAVs whose power plant is a small electric motor. First a model which relates thrust generated by a small propeller driven electric motor as a function of throttle setting and commanded engine RPM is developed. A perturbation of this model is then used to relate the uncertainty in throttle and engine RPM commanded to the error in the predicted thrust. Such a stochastic model is indispensable in the design of state estimation and control systems for UAVs where the performance requirements of the systems are specied in stochastic terms. It is shown that thrust prediction models for small UAVs are not a simple, explicit functions relating throttle input and RPM command to thrust generated. Rather they are non-linear, iterative procedures which depend on a geometric description of the propeller and mathematical model of the motor. A detailed derivation of the iterative procedure is presented and the impact of errors which arise from inaccurate propeller and motor descriptions are discussed. Validation results from a series of wind tunnel tests are presented. The results show a favorable statistical agreement between the thrust uncertainty predicted by the model and the errors measured in the wind tunnel. The uncertainty model of aircraft aerodynamic coefficients developed based on wind tunnel experiment will be discussed at the end of this thesis.
Nonlinear stochastic exclusion financial dynamics modeling and time-dependent intrinsic detrended cross-correlation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2017-09-01

In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.
Stochastic Multi-Commodity Facility Location Based on a New Scenario Generation Technique

NASA Astrophysics Data System (ADS)

Mahootchi, M.; Fattahi, M.; Khakbazan, E.

2011-11-01

This paper extends two models for stochastic multi-commodity facility location problem. The problem is formulated as two-stage stochastic programming. As a main point of this study, a new algorithm is applied to efficiently generate scenarios for uncertain correlated customers' demands. This algorithm uses Latin Hypercube Sampling (LHS) and a scenario reduction approach. The relation between customer satisfaction level and cost are considered in model I. The risk measure using Conditional Value-at-Risk (CVaR) is embedded into the optimization model II. Here, the structure of the network contains three facility layers including plants, distribution centers, and retailers. The first stage decisions are the number, locations, and the capacity of distribution centers. In the second stage, the decisions are the amount of productions, the volume of transportation between plants and customers.
Joint pricing, inventory, and preservation decisions for deteriorating items with stochastic demand and promotional efforts

NASA Astrophysics Data System (ADS)

Soni, Hardik N.; Chauhan, Ashaba D.

2018-03-01

This study models a joint pricing, inventory, and preservation decision-making problem for deteriorating items subject to stochastic demand and promotional effort. The generalized price-dependent stochastic demand, time proportional deterioration, and partial backlogging rates are used to model the inventory system. The objective is to find the optimal pricing, replenishment, and preservation technology investment strategies while maximizing the total profit per unit time. Based on the partial backlogging and lost sale cases, we first deduce the criterion for optimal replenishment schedules for any given price and technology investment cost. Second, we show that, respectively, total profit per time unit is concave function of price and preservation technology cost. At the end, some numerical examples and the results of a sensitivity analysis are used to illustrate the features of the proposed model.
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 model of cell rearrangements in convergent extension of ascidian notochord

NASA Astrophysics Data System (ADS)

Lubkin, Sharon; Backes, Tracy; Latterman, Russell; Small, Stephen

2007-03-01

We present a discrete stochastic cell based model of convergent extension of the ascidian notochord. Our work derives from research that clarifies the coupling of invagination and convergent extension in ascidian notochord morphogenesis (Odell and Munro, 2002). We have tested the roles of cell-cell adhesion, cell-extracellular matrix adhesion, random motion, and extension of individual cells, as well as the presence or absence of various tissue types, and determined which factors are necessary and/or sufficient for convergent extension.
Stochastical modeling for Viral Disease: Statistical Mechanics and Network Theory

NASA Astrophysics Data System (ADS)

Zhou, Hao; Deem, Michael

2007-04-01

Theoretical methods of statistical mechanics are developed and applied to study the immunological response against viral disease, such as dengue. We use this theory to show how the immune response to four different dengue serotypes may be sculpted. It is the ability of avian influenza, to change and to mix, that has given rise to the fear of a new human flu pandemic. Here we propose to utilize a scale free network based stochastic model to investigate the mitigation strategies and analyze the risk.
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
A discontinuous Galerkin method for numerical pricing of European options under Heston stochastic volatility

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2016-12-01

The paper is based on the results from our recent research on multidimensional option pricing problems. We focus on European option valuation when the price movement of the underlying asset is driven by a stochastic volatility following a square root process proposed by Heston. The stochastic approach incorporates a new additional spatial variable into this model and makes it very robust, i.e. it provides a framework to price a variety of options that is closer to reality. The main topic is to present the numerical scheme arising from the concept of discontinuous Galerkin methods and applicable to the Heston option pricing model. The numerical results are presented on artificial benchmarks as well as on reference market data.
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.
Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

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

NASA Technical Reports Server (NTRS)

Fedotov, S.; Ihme, M.; Pitsch, H.

2003-01-01

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
Using genetic algorithm to solve a new multi-period stochastic optimization model

NASA Astrophysics Data System (ADS)

Zhang, Xin-Li; Zhang, Ke-Cun

2009-09-01

This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren't considered in that paper. In this paper, we improve Hibiki's model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.
A Learning Framework for Winner-Take-All Networks with Stochastic Synapses.

PubMed

Mostafa, Hesham; Cauwenberghs, Gert

2018-06-01

Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks operate along similar principles to implement a probabilistic model of the environment through transformations of intrinsic noise processes. The intrinsic neural and synaptic noise processes in biological networks, however, are quite different from the noise processes used in current abstract generative networks. This, together with the discrete nature of spikes and local circuit interactions among the neurons, raises several difficulties when using recent generative modeling frameworks to train biologically motivated models. In this letter, we show that a biologically motivated model based on multilayer winner-take-all circuits and stochastic synapses admits an approximate analytical description. This allows us to use the proposed networks in a variational learning setting where stochastic backpropagation is used to optimize a lower bound on the data log likelihood, thereby learning a generative model of the data. We illustrate the generality of the proposed networks and learning technique by using them in a structured output prediction task and a semisupervised learning task. Our results extend the domain of application of modern stochastic network architectures to networks where synaptic transmission failure is the principal noise mechanism.
A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.
Designing seasonal initial attack resource deployment and dispatch rules using a two-stage stochastic programming procedure

Treesearch

Yu Wei; Michael Bevers; Erin J. Belval

2015-01-01

Initial attack dispatch rules can help shorten fire suppression response times by providing easy-to-follow recommendations based on fire weather, discovery time, location, and other factors that may influence fire behavior and the appropriate response. A new procedure is combined with a stochastic programming model and tested in this study for designing initial attack...
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.
Recent topographic evolution and erosion of the deglaciated Washington Cascades inferred from a stochastic landscape evolution model

NASA Astrophysics Data System (ADS)

Moon, S.; Shelef, E.; Hilley, G. E.

2013-12-01

The Washington Cascades is currently in topographic and erosional disequilibrium after deglaciation occurred around 11- 17 ka ago. The topography still shows the features inherited from prior alpine glacial processes (e.g., cirques, steep side-valleys, and flat valley bottoms), though postglacial processes are currently denuding this landscape. Our previous study in this area calculated the thousand-year-timescale denudation rates using cosmogenic 10Be concentration (CRN-denudation rates), and showed that they were ~ four times higher than million-year-timescale uplift rates. In addition, the spatial distribution of denudation rates showed a good correlation with a factor-of-ten variation in precipitation. We interpreted this correlation as reflecting the sensitivity of landslide triggering in over-steepened deglaciated topography to precipitation, which produced high denudation rates in wet areas that experienced frequent landsliding. We explored this interpretation using a model of postglacial surface processes that predicts the evolution of the topography and denudation rates within the deglaciated Washington Cascades. Specifically, we used the model to understand the controls on and timescales of landscape response to changes in the surface process regime after deglaciation. The postglacial adjustment of this landscape is modeled using a geomorphic-transport-law-based numerical model that includes processes of river incision, hillslope diffusion, and stochastic landslides. The surface lowering due to landslides is parameterized using a physically-based slope stability model coupled to a stochastic model of the generation of landslides. The model parameters of river incision and stochastic landslides are calibrated based on the rates and distribution of thousand-year-timescale denudation rates measured from cosmogenic 10Be isotopes. The probability distribution of model parameters required to fit the observed denudation rates shows comparable ranges from previous studies in similar rock types and climatic conditions. The calibrated parameters suggest that the dominant sediment source of river sediments originates from stochastic landslides. The magnitude of landslide denudation rates is determined by failure density (similar to landslide frequency), while their spatial distribution is largely controlled by precipitation and slope angles. Simulation results show that denudation rates decay over time and take approximately 130-180 ka to reach steady-state rates. This response timescale is longer than glacial/interglacial cycles, suggesting that frequent climatic perturbations during the Quaternary may prevent these types of landscapes from reaching a dynamic equilibrium with postglacial processes.
A guide to differences between stochastic point-source and stochastic finite-fault simulations

USGS Publications Warehouse

Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.

2009-01-01

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control observed ground motions.
Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids

PubMed Central

Ali, S. M.; Mehmood, C. A; Khan, B.; Jawad, M.; Farid, U; Jadoon, J. K.; Ali, M.; Tareen, N. K.; Usman, S.; Majid, M.; Anwar, S. M.

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion. PMID:27314229

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

PubMed

Ali, S M; Mehmood, C A; Khan, B; Jawad, M; Farid, U; Jadoon, J K; Ali, M; Tareen, N K; Usman, S; Majid, M; Anwar, S M

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.
Creating wavelet-based models for real-time synthesis of perceptually convincing environmental sounds

NASA Astrophysics Data System (ADS)

Miner, Nadine Elizabeth

1998-09-01

This dissertation presents a new wavelet-based method for synthesizing perceptually convincing, dynamic sounds using parameterized sound models. The sound synthesis method is applicable to a variety of applications including Virtual Reality (VR), multi-media, entertainment, and the World Wide Web (WWW). A unique contribution of this research is the modeling of the stochastic, or non-pitched, sound components. This stochastic-based modeling approach leads to perceptually compelling sound synthesis. Two preliminary studies conducted provide data on multi-sensory interaction and audio-visual synchronization timing. These results contributed to the design of the new sound synthesis method. The method uses a four-phase development process, including analysis, parameterization, synthesis and validation, to create the wavelet-based sound models. A patent is pending for this dynamic sound synthesis method, which provides perceptually-realistic, real-time sound generation. This dissertation also presents a battery of perceptual experiments developed to verify the sound synthesis results. These experiments are applicable for validation of any sound synthesis technique.
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.
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.
Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.
Stochastic simulation in systems biology

PubMed Central

Székely, Tamás; Burrage, Kevin

2014-01-01

Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503
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
Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
Event-based recursive filtering for a class of nonlinear stochastic parameter systems over fading channels

NASA Astrophysics Data System (ADS)

Shen, Yuxuan; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2018-07-01

In this paper, the recursive filtering problem is studied for a class of time-varying nonlinear systems with stochastic parameter matrices. The measurement transmission between the sensor and the filter is conducted through a fading channel characterized by the Rice fading model. An event-based transmission mechanism is adopted to decide whether the sensor measurement should be transmitted to the filter. A recursive filter is designed such that, in the simultaneous presence of the stochastic parameter matrices and fading channels, the filtering error covariance is guaranteed to have an upper bound and such an upper bound is then minimized by appropriately choosing filter gain matrix. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed filtering scheme.
Simulation of earthquake ground motions in the eastern United States using deterministic physics‐based and site‐based stochastic approaches

USGS Publications Warehouse

Rezaeian, Sanaz; Hartzell, Stephen; Sun, Xiaodan; Mendoza, Carlos

2017-01-01

Earthquake ground‐motion recordings are scarce in the central and eastern United States (CEUS) for large‐magnitude events and at close distances. We use two different simulation approaches, a deterministic physics‐based method and a site‐based stochastic method, to simulate ground motions over a wide range of magnitudes. Drawing on previous results for the modeling of recordings from the 2011 Mw 5.8 Mineral, Virginia, earthquake and using the 2001 Mw 7.6 Bhuj, India, earthquake as a tectonic analog for a large magnitude CEUS event, we are able to calibrate the two simulation methods over this magnitude range. Both models show a good fit to the Mineral and Bhuj observations from 0.1 to 10 Hz. Model parameters are then adjusted to obtain simulations for Mw 6.5, 7.0, and 7.6 events in the CEUS. Our simulations are compared with the 2014 U.S. Geological Survey weighted combination of existing ground‐motion prediction equations in the CEUS. The physics‐based simulations show comparable response spectral amplitudes and a fairly similar attenuation with distance. The site‐based stochastic simulations suggest a slightly faster attenuation of the response spectral amplitudes with distance for larger magnitude events and, as a result, slightly lower amplitudes at distances greater than 200 km. Both models are plausible alternatives and, given the few available data points in the CEUS, can be used to represent the epistemic uncertainty in modeling of postulated CEUS large‐magnitude events.
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.
Global behavior analysis for stochastic system of 1,3-PD continuous fermentation

NASA Astrophysics Data System (ADS)

Zhu, Xi; Kliemann, Wolfgang; Li, Chunfa; Feng, Enmin; Xiu, Zhilong

2017-12-01

Global behavior for stochastic system of continuous fermentation in glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae is analyzed in this paper. This bioprocess cannot avoid the stochastic perturbation caused by internal and external disturbance which reflect on the growth rate. These negative factors can limit and degrade the achievable performance of controlled systems. Based on multiplicity phenomena, the equilibriums and bifurcations of the deterministic system are analyzed. Then, a stochastic model is presented by a bounded Markov diffusion process. In order to analyze the global behavior, we compute the control sets for the associated control system. The probability distributions of relative supports are also computed. The simulation results indicate that how the disturbed biosystem tend to stationary behavior globally.
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.
Research Note: The consequences of different methods for handling missing network data in Stochastic Actor Based Models

PubMed Central

Hipp, John R.; Wang, Cheng; Butts, Carter T.; Jose, Rupa; Lakon, Cynthia M.

2015-01-01

Although stochastic actor based models (e.g., as implemented in the SIENA software program) are growing in popularity as a technique for estimating longitudinal network data, a relatively understudied issue is the consequence of missing network data for longitudinal analysis. We explore this issue in our research note by utilizing data from four schools in an existing dataset (the AddHealth dataset) over three time points, assessing the substantive consequences of using four different strategies for addressing missing network data. The results indicate that whereas some measures in such models are estimated relatively robustly regardless of the strategy chosen for addressing missing network data, some of the substantive conclusions will differ based on the missing data strategy chosen. These results have important implications for this burgeoning applied research area, implying that researchers should more carefully consider how they address missing data when estimating such models. PMID:25745276
Research Note: The consequences of different methods for handling missing network data in Stochastic Actor Based Models.

PubMed

Hipp, John R; Wang, Cheng; Butts, Carter T; Jose, Rupa; Lakon, Cynthia M

2015-05-01

Although stochastic actor based models (e.g., as implemented in the SIENA software program) are growing in popularity as a technique for estimating longitudinal network data, a relatively understudied issue is the consequence of missing network data for longitudinal analysis. We explore this issue in our research note by utilizing data from four schools in an existing dataset (the AddHealth dataset) over three time points, assessing the substantive consequences of using four different strategies for addressing missing network data. The results indicate that whereas some measures in such models are estimated relatively robustly regardless of the strategy chosen for addressing missing network data, some of the substantive conclusions will differ based on the missing data strategy chosen. These results have important implications for this burgeoning applied research area, implying that researchers should more carefully consider how they address missing data when estimating such models.
Network-based stochastic semisupervised learning.

PubMed

Silva, Thiago Christiano; Zhao, Liang

2012-03-01

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.
Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions

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

Caprini, Chiara, E-mail: chiara.caprini@cea.fr; Hindmarsh, Mark; Huber, Stephan

We investigate the potential for the eLISA space-based interferometer to detect the stochastic gravitational wave background produced by strong first-order cosmological phase transitions. We discuss the resulting contributions from bubble collisions, magnetohydrodynamic turbulence, and sound waves to the stochastic background, and estimate the total corresponding signal predicted in gravitational waves. The projected sensitivity of eLISA to cosmological phase transitions is computed in a model-independent way for various detector designs and configurations. By applying these results to several specific models, we demonstrate that eLISA is able to probe many well-motivated scenarios beyond the Standard Model of particle physics predicting strong first-ordermore » cosmological phase transitions in the early Universe.« less
Qualitative modeling of normal blood coagulation and its pathological states using stochastic activity networks.

PubMed

Mounts, W M; Liebman, M N

1997-07-01

We have developed a method for representing biological pathways and simulating their behavior based on the use of stochastic activity networks (SANs). SANs, an extension of the original Petri net, have been used traditionally to model flow systems including data-communications networks and manufacturing processes. We apply the methodology to the blood coagulation cascade, a biological flow system, and present the representation method as well as results of simulation studies based on published experimental data. In addition to describing the dynamic model, we also present the results of its utilization to perform simulations of clinical states including hemophilia's A and B as well as sensitivity analysis of individual factors and their impact on thrombin production.
Stochastic Analysis and Design of Heterogeneous Microstructural Materials System

NASA Astrophysics Data System (ADS)

Xu, Hongyi

Advanced materials system refers to new materials that are comprised of multiple traditional constituents but complex microstructure morphologies, which lead to superior properties over the conventional materials. To accelerate the development of new advanced materials system, the objective of this dissertation is to develop a computational design framework and the associated techniques for design automation of microstructure materials systems, with an emphasis on addressing the uncertainties associated with the heterogeneity of microstructural materials. Five key research tasks are identified: design representation, design evaluation, design synthesis, material informatics and uncertainty quantification. Design representation of microstructure includes statistical characterization and stochastic reconstruction. This dissertation develops a new descriptor-based methodology, which characterizes 2D microstructures using descriptors of composition, dispersion and geometry. Statistics of 3D descriptors are predicted based on 2D information to enable 2D-to-3D reconstruction. An efficient sequential reconstruction algorithm is developed to reconstruct statistically equivalent random 3D digital microstructures. In design evaluation, a stochastic decomposition and reassembly strategy is developed to deal with the high computational costs and uncertainties induced by material heterogeneity. The properties of Representative Volume Elements (RVE) are predicted by stochastically reassembling SVE elements with stochastic properties into a coarse representation of the RVE. In design synthesis, a new descriptor-based design framework is developed, which integrates computational methods of microstructure characterization and reconstruction, sensitivity analysis, Design of Experiments (DOE), metamodeling and optimization the enable parametric optimization of the microstructure for achieving the desired material properties. Material informatics is studied to efficiently reduce the dimension of microstructure design space. This dissertation develops a machine learning-based methodology to identify the key microstructure descriptors that highly impact properties of interest. In uncertainty quantification, a comparative study on data-driven random process models is conducted to provide guidance for choosing the most accurate model in statistical uncertainty quantification. Two new goodness-of-fit metrics are developed to provide quantitative measurements of random process models' accuracy. The benefits of the proposed methods are demonstrated by the example of designing the microstructure of polymer nanocomposites. This dissertation provides material-generic, intelligent modeling/design methodologies and techniques to accelerate the process of analyzing and designing new microstructural materials system.

3D replicon distributions arise from stochastic initiation and domino-like DNA replication progression

PubMed Central

Löb, D.; Lengert, N.; Chagin, V. O.; Reinhart, M.; Casas-Delucchi, C. S.; Cardoso, M. C.; Drossel, B.

2016-01-01

DNA replication dynamics in cells from higher eukaryotes follows very complex but highly efficient mechanisms. However, the principles behind initiation of potential replication origins and emergence of typical patterns of nuclear replication sites remain unclear. Here, we propose a comprehensive model of DNA replication in human cells that is based on stochastic, proximity-induced replication initiation. Critical model features are: spontaneous stochastic firing of individual origins in euchromatin and facultative heterochromatin, inhibition of firing at distances below the size of chromatin loops and a domino-like effect by which replication forks induce firing of nearby origins. The model reproduces the empirical temporal and chromatin-related properties of DNA replication in human cells. We advance the one-dimensional DNA replication model to a spatial model by taking into account chromatin folding in the nucleus, and we are able to reproduce the spatial and temporal characteristics of the replication foci distribution throughout S-phase. PMID:27052359
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.
Two-stage stochastic unit commitment model including non-generation resources with conditional value-at-risk constraints

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

Huang, Yuping; Zheng, Qipeng P.; Wang, Jianhui

2014-11-01

tThis paper presents a two-stage stochastic unit commitment (UC) model, which integrates non-generation resources such as demand response (DR) and energy storage (ES) while including riskconstraints to balance between cost and system reliability due to the fluctuation of variable genera-tion such as wind and solar power. This paper uses conditional value-at-risk (CVaR) measures to modelrisks associated with the decisions in a stochastic environment. In contrast to chance-constrained modelsrequiring extra binary variables, risk constraints based on CVaR only involve linear constraints and con-tinuous variables, making it more computationally attractive. The proposed models with risk constraintsare able to avoid over-conservative solutions butmore » still ensure system reliability represented by loss ofloads. Then numerical experiments are conducted to study the effects of non-generation resources ongenerator schedules and the difference of total expected generation costs with risk consideration. Sen-sitivity analysis based on reliability parameters is also performed to test the decision preferences ofconfidence levels and load-shedding loss allowances on generation cost reduction.« less
An uncertainty model of acoustic metamaterials with random parameters

NASA Astrophysics Data System (ADS)

He, Z. C.; Hu, J. Y.; Li, Eric

2018-01-01

Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully.
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.
Galactic Cosmic-ray Transport in the Global Heliosphere: A Four-Dimensional Stochastic Model

NASA Astrophysics Data System (ADS)

Florinski, V.

2009-04-01

We study galactic cosmic-ray transport in the outer heliosphere and heliosheath using a newly developed transport model based on stochastic integration of the phase-space trajectories of Parker's equation. The model employs backward integration of the diffusion-convection transport equation using Ito calculus and is four-dimensional in space+momentum. We apply the model to the problem of galactic proton transport in the heliosphere during a negative solar minimum. Model results are compared with the Voyager measurements of galactic proton radial gradients and spectra in the heliosheath. We show that the heliosheath is not as efficient in diverting cosmic rays during solar minima as predicted by earlier two-dimensional models.
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.
A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks.

PubMed

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

2016-01-01

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

PubMed Central

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

2016-01-01

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

NASA Astrophysics Data System (ADS)

Dorrestijn, Jesse; Crommelin, Daan T.; Siebesma, A. Pier.; Jonker, Harm J. J.

2013-02-01

In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES.
Finite element modelling of woven composite failure modes at the mesoscopic scale: deterministic versus stochastic approaches

NASA Astrophysics Data System (ADS)

Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.

2017-09-01

Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.
Some Results of Weak Anticipative Concept Applied in Simulation Based Decision Support in Enterprise

NASA Astrophysics Data System (ADS)

Kljajić, Miroljub; Kofjač, Davorin; Kljajić Borštnar, Mirjana; Škraba, Andrej

2010-11-01

The simulation models are used as for decision support and learning in enterprises and in schools. Tree cases of successful applications demonstrate usefulness of weak anticipative information. Job shop scheduling production with makespan criterion presents a real case customized flexible furniture production optimization. The genetic algorithm for job shop scheduling optimization is presented. Simulation based inventory control for products with stochastic lead time and demand describes inventory optimization for products with stochastic lead time and demand. Dynamic programming and fuzzy control algorithms reduce the total cost without producing stock-outs in most cases. Values of decision making information based on simulation were discussed too. All two cases will be discussed from optimization, modeling and learning point of view.
Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

PubMed Central

Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang

2011-01-01

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons. PMID:22096452
A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks

PubMed Central

Zaikin, Alexey; Míguez, Joaquín

2017-01-01

We compare three state-of-the-art Bayesian inference methods for the estimation of the unknown parameters in a stochastic model of a genetic network. In particular, we introduce a stochastic version of the paradigmatic synthetic multicellular clock model proposed by Ullner et al., 2007. By introducing dynamical noise in the model and assuming that the partial observations of the system are contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we tackle the Bayesian estimation of a subset of the model parameters. Specifically, we compare three Monte Carlo based numerical methods for the approximation of the posterior probability density function of the unknown parameters given a set of partial and noisy observations of the system. The schemes we assess are the particle Metropolis-Hastings (PMH) algorithm, the nonlinear population Monte Carlo (NPMC) method and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) scheme. We present an extensive numerical simulation study, which shows that while the three techniques can effectively solve the problem there are significant differences both in estimation accuracy and computational efficiency. PMID:28797087
A stochastic wind turbine wake model based on new metrics for wake characterization: A stochastic wind turbine wake model based on new metrics for wake characterization

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

Doubrawa, Paula; Barthelmie, Rebecca J.; Wang, Hui

Understanding the detailed dynamics of wind turbine wakes is critical to predicting the performance and maximizing the efficiency of wind farms. This knowledge requires atmospheric data at a high spatial and temporal resolution, which are not easily obtained from direct measurements. Therefore, research is often based on numerical models, which vary in fidelity and computational cost. The simplest models produce axisymmetric wakes and are only valid beyond the near wake. Higher-fidelity results can be obtained by solving the filtered Navier-Stokes equations at a resolution that is sufficient to resolve the relevant turbulence scales. This work addresses the gap between thesemore » two extremes by proposing a stochastic model that produces an unsteady asymmetric wake. The model is developed based on a large-eddy simulation (LES) of an offshore wind farm. Because there are several ways of characterizing wakes, the first part of this work explores different approaches to defining global wake characteristics. From these, a model is developed that captures essential features of a LES-generated wake at a small fraction of the cost. The synthetic wake successfully reproduces the mean characteristics of the original LES wake, including its area and stretching patterns, and statistics of the mean azimuthal radius. The mean and standard deviation of the wake width and height are also reproduced. This preliminary study focuses on reproducing the wake shape, while future work will incorporate velocity deficit and meandering, as well as different stability scenarios.« less
Stochastic satisficing account of confidence in uncertain value-based decisions

PubMed Central

Bahrami, Bahador; Keramati, Mehdi

2018-01-01

Every day we make choices under uncertainty; choosing what route to work or which queue in a supermarket to take, for example. It is unclear how outcome variance, e.g. uncertainty about waiting time in a queue, affects decisions and confidence when outcome is stochastic and continuous. How does one evaluate and choose between an option with unreliable but high expected reward, and an option with more certain but lower expected reward? Here we used an experimental design where two choices’ payoffs took continuous values, to examine the effect of outcome variance on decision and confidence. We found that our participants’ probability of choosing the good (high expected reward) option decreased when the good or the bad options’ payoffs were more variable. Their confidence ratings were affected by outcome variability, but only when choosing the good option. Unlike perceptual detection tasks, confidence ratings correlated only weakly with decisions’ time, but correlated with the consistency of trial-by-trial choices. Inspired by the satisficing heuristic, we propose a “stochastic satisficing” (SSAT) model for evaluating options with continuous uncertain outcomes. In this model, options are evaluated by their probability of exceeding an acceptability threshold, and confidence reports scale with the chosen option’s thus-defined satisficing probability. Participants’ decisions were best explained by an expected reward model, while the SSAT model provided the best prediction of decision confidence. We further tested and verified the predictions of this model in a second experiment. Our model and experimental results generalize the models of metacognition from perceptual detection tasks to continuous-value based decisions. Finally, we discuss how the stochastic satisficing account of decision confidence serves psychological and social purposes associated with the evaluation, communication and justification of decision-making. PMID:29621325
Characteristic time scales of tick quotes on foreign currency markets: an empirical study and agent-based model

NASA Astrophysics Data System (ADS)

Sato, A.-H.

2006-03-01

Power spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) for periods from January 1999 to December 2000 are analyzed. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and confirm that stochastic resonance occurs for the market activity of this model. We propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to stochastic resonance.
Study of detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance model.

PubMed

Jingyi, Zhu

2015-01-01

The detecting mechanism of carbon nanotubes gas sensor based on multi-stable stochastic resonance (MSR) model was studied in this paper. A numerically stimulating model based on MSR was established. And gas-ionizing experiment by adding electronic white noise to induce 1.65 MHz periodic component in the carbon nanotubes gas sensor was performed. It was found that the signal-to-noise ratio (SNR) spectrum displayed 2 maximal values, which accorded to the change of the broken-line potential function. The experimental results of gas-ionizing experiment demonstrated that periodic component of 1.65 MHz had multiple MSR phenomena, which was in accordance with the numerical stimulation results. In this way, the numerical stimulation method provides an innovative method for the detecting mechanism research of carbon nanotubes gas sensor.
Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.
Stochastic simulation and decadal prediction of hydroclimate in the Western Himalayas

NASA Astrophysics Data System (ADS)

Robertson, A. W.; Chekroun, M. D.; Cook, E.; D'Arrigo, R.; Ghil, M.; Greene, A. M.; Holsclaw, T.; Kondrashov, D. A.; Lall, U.; Lu, M.; Smyth, P.

2012-12-01

Improved estimates of climate over the next 10 to 50 years are needed for long-term planning in water resource and flood management. However, the task of effectively incorporating the results of climate change research into decision-making face a ``double conflict of scales'': the temporal scales of climate model projections are too long, while their usable spatial scales (global to planetary) are much larger than those needed for actual decision making (at the regional to local level). This work is designed to help tackle this ``double conflict'' in the context of water management over monsoonal Asia, based on dendroclimatic multi-century reconstructions of drought indices and river flows. We identify low-frequency modes of variability with time scales from interannual to interdecadal based on these series, and then generate future scenarios based on (a) empirical model decadal predictions, and (b) stochastic simulations generated with autoregressive models that reproduce the power spectrum of the data. Finally, we consider how such scenarios could be used to develop reservoir optimization models. Results will be presented based on multi-century Upper Indus river discharge reconstructions that exhibit a strong periodicity near 27 years that is shown to yield some retrospective forecasting skill over the 1700-2000 period, at a 15-yr yield time. Stochastic simulations of annual PDSI drought index values over the Upper Indus basin are constructed using Empirical Model Reduction; their power spectra are shown to be quite realistic, with spectral peaks near 5--8 years.

The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

NASA Astrophysics Data System (ADS)

Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

2012-06-01

A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Control of Complex Dynamic Systems by Neural Networks

NASA Technical Reports Server (NTRS)

Spall, James C.; Cristion, John A.

1993-01-01

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.
On temporal stochastic modeling of precipitation, nesting models across scales

NASA Astrophysics Data System (ADS)

Paschalis, Athanasios; Molnar, Peter; Fatichi, Simone; Burlando, Paolo

2014-01-01

We analyze the performance of composite stochastic models of temporal precipitation which can satisfactorily reproduce precipitation properties across a wide range of temporal scales. The rationale is that a combination of stochastic precipitation models which are most appropriate for specific limited temporal scales leads to better overall performance across a wider range of scales than single models alone. We investigate different model combinations. For the coarse (daily) scale these are models based on Alternating renewal processes, Markov chains, and Poisson cluster models, which are then combined with a microcanonical Multiplicative Random Cascade model to disaggregate precipitation to finer (minute) scales. The composite models were tested on data at four sites in different climates. The results show that model combinations improve the performance in key statistics such as probability distributions of precipitation depth, autocorrelation structure, intermittency, reproduction of extremes, compared to single models. At the same time they remain reasonably parsimonious. No model combination was found to outperform the others at all sites and for all statistics, however we provide insight on the capabilities of specific model combinations. The results for the four different climates are similar, which suggests a degree of generality and wider applicability of the approach.
A stochastic global identification framework for aerospace structures operating under varying flight states

NASA Astrophysics Data System (ADS)

Kopsaftopoulos, Fotis; Nardari, Raphael; Li, Yu-Hung; Chang, Fu-Kuo

2018-01-01

In this work, a novel data-based stochastic "global" identification framework is introduced for aerospace structures operating under varying flight states and uncertainty. In this context, the term "global" refers to the identification of a model that is capable of representing the structure under any admissible flight state based on data recorded from a sample of these states. The proposed framework is based on stochastic time-series models for representing the structural dynamics and aeroelastic response under multiple flight states, with each state characterized by several variables, such as the airspeed, angle of attack, altitude and temperature, forming a flight state vector. The method's cornerstone lies in the new class of Vector-dependent Functionally Pooled (VFP) models which allow the explicit analytical inclusion of the flight state vector into the model parameters and, hence, system dynamics. This is achieved via the use of functional data pooling techniques for optimally treating - as a single entity - the data records corresponding to the various flight states. In this proof-of-concept study the flight state vector is defined by two variables, namely the airspeed and angle of attack of the vehicle. The experimental evaluation and assessment is based on a prototype bio-inspired self-sensing composite wing that is subjected to a series of wind tunnel experiments under multiple flight states. Distributed micro-sensors in the form of stretchable sensor networks are embedded in the composite layup of the wing in order to provide the sensing capabilities. Experimental data collected from piezoelectric sensors are employed for the identification of a stochastic global VFP model via appropriate parameter estimation and model structure selection methods. The estimated VFP model parameters constitute two-dimensional functions of the flight state vector defined by the airspeed and angle of attack. The identified model is able to successfully represent the wing's aeroelastic response under the admissible flight states via a minimum number of estimated parameters compared to standard identification approaches. The obtained results demonstrate the high accuracy and effectiveness of the proposed global identification framework, thus constituting a first step towards the next generation of "fly-by-feel" aerospace vehicles with state awareness capabilities.
Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

PubMed

Lin, Zhongwei; Tropper, Carl; Mcdougal, Robert A; Patoary, Mohammand Nazrul Ishlam; Lytton, William W; Yao, Yiping; Hines, Michael L

2017-07-01

Cells exhibit stochastic behavior when the number of molecules is small. Hence a stochastic reaction-diffusion simulator capable of working at scale can provide a more accurate view of molecular dynamics within the cell. This paper describes a parallel discrete event simulator, Neuron Time Warp-Multi Thread (NTW-MT), developed for the simulation of reaction diffusion models of neurons. To the best of our knowledge, this is the first parallel discrete event simulator oriented towards stochastic simulation of chemical reactions in a neuron. The simulator was developed as part of the NEURON project. NTW-MT is optimistic and thread-based, which attempts to capitalize on multi-core architectures used in high performance machines. It makes use of a multi-level queue for the pending event set and a single roll-back message in place of individual anti-messages to disperse contention and decrease the overhead of processing rollbacks. Global Virtual Time is computed asynchronously both within and among processes to get rid of the overhead for synchronizing threads. Memory usage is managed in order to avoid locking and unlocking when allocating and de-allocating memory and to maximize cache locality. We verified our simulator on a calcium buffer model. We examined its performance on a calcium wave model, comparing it to the performance of a process based optimistic simulator and a threaded simulator which uses a single priority queue for each thread. Our multi-threaded simulator is shown to achieve superior performance to these simulators. Finally, we demonstrated the scalability of our simulator on a larger CICR model and a more detailed CICR model.
A two-stage stochastic rule-based model to determine pre-assembly buffer content

NASA Astrophysics Data System (ADS)

Gunay, Elif Elcin; Kula, Ufuk

2018-01-01

This study considers instant decision-making needs of the automobile manufactures for resequencing vehicles before final assembly (FA). We propose a rule-based two-stage stochastic model to determine the number of spare vehicles that should be kept in the pre-assembly buffer to restore the altered sequence due to paint defects and upstream department constraints. First stage of the model decides the spare vehicle quantities, where the second stage model recovers the scrambled sequence respect to pre-defined rules. The problem is solved by sample average approximation (SAA) algorithm. We conduct a numerical study to compare the solutions of heuristic model with optimal ones and provide following insights: (i) as the mismatch between paint entrance and scheduled sequence decreases, the rule-based heuristic model recovers the scrambled sequence as good as the optimal resequencing model, (ii) the rule-based model is more sensitive to the mismatch between the paint entrance and scheduled sequences for recovering the scrambled sequence, (iii) as the defect rate increases, the difference in recovery effectiveness between rule-based heuristic and optimal solutions increases, (iv) as buffer capacity increases, the recovery effectiveness of the optimization model outperforms heuristic model, (v) as expected the rule-based model holds more inventory than the optimization model.
A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets.

PubMed

Chen, Jiao; Weihs, Daphne; Vermolen, Fred J

2018-04-01

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler-Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.
Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

PubMed Central

Ramirez, Samuel A.; Elston, Timothy C.

2018-01-01

Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism. PMID:29529021
Tipping point analysis of atmospheric oxygen concentration

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

Livina, V. N.; Forbes, A. B.; Vaz Martins, T. M.

2015-03-15

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.
Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...
Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection.

PubMed

Chai, Bian-fang; Yu, Jian; Jia, Cai-Yan; Yang, Tian-bao; Jiang, Ya-wen

2013-07-01

Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.
Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection

NASA Astrophysics Data System (ADS)

Chai, Bian-fang; Yu, Jian; Jia, Cai-yan; Yang, Tian-bao; Jiang, Ya-wen

2013-07-01

Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.
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.
Stochastic nonlinear mixed effects: a metformin case study.

PubMed

Matzuka, Brett; Chittenden, Jason; Monteleone, Jonathan; Tran, Hien

2016-02-01

In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi for their stochastic deconvolution.
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.
Compensating for estimation smoothing in kriging

USGS Publications Warehouse

Olea, R.A.; Pawlowsky, Vera

1996-01-01

Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator-compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-fr2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well - better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. ?? 1996 International Association for Mathematical Geology.
Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy.

PubMed

Morimoto, Satoshi; Remijn, Gerard B; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord.
Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy

PubMed Central

Morimoto, Satoshi; Remijn, Gerard B.; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord. PMID:27003807
A Unified Statistical Rain-Attenuation Model for Communication Link Fade Predictions and Optimal Stochastic Fade Control Design Using a Location-Dependent Rain-Statistic Database

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1990-01-01

A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.
A Two-Step Approach to Uncertainty Quantification of Core Simulators

DOE PAGES

Yankov, Artem; Collins, Benjamin; Klein, Markus; ...

2012-01-01

For the multiple sources of error introduced into the standard computational regime for simulating reactor cores, rigorous uncertainty analysis methods are available primarily to quantify the effects of cross section uncertainties. Two methods for propagating cross section uncertainties through core simulators are the XSUSA statistical approach and the “two-step” method. The XSUSA approach, which is based on the SUSA code package, is fundamentally a stochastic sampling method. Alternatively, the two-step method utilizes generalized perturbation theory in the first step and stochastic sampling in the second step. The consistency of these two methods in quantifying uncertainties in the multiplication factor andmore » in the core power distribution was examined in the framework of phase I-3 of the OECD Uncertainty Analysis in Modeling benchmark. With the Three Mile Island Unit 1 core as a base model for analysis, the XSUSA and two-step methods were applied with certain limitations, and the results were compared to those produced by other stochastic sampling-based codes. Based on the uncertainty analysis results, conclusions were drawn as to the method that is currently more viable for computing uncertainties in burnup and transient calculations.« less

Stochastic Fluctuations in a Babcock-Leighton Model of the Solar Cycle

NASA Astrophysics Data System (ADS)

Charbonneau, Paul; Dikpati, Mausumi

2000-11-01

We investigate the effect of stochastic fluctuations on a flux transport model of the solar cycle based on the Babcock-Leighton mechanism. Specifically, we make use of our recent flux transport model (Dikpati & Charbonneau) to investigate the consequences of introducing large-amplitude stochastic fluctuations in either or both the meridional flow and poloidal source term in the model. Solar cycle-like oscillatory behavior persists even for fluctuation amplitudes as high as 300%, thus demonstrating the inherent robustness of this class of solar cycle models. We also find that high-amplitude fluctuations lead to a spread of cycle amplitude and duration showing a statistically significant anticorrelation, comparable to that observed in sunspot data. This is a feature of the solar cycle that is notoriously difficult to reproduce with dynamo models based on mean field electrodynamics and relying only on nonlinearities associated with the back-reaction of the Lorentz force to produce amplitude modulation. Another noteworthy aspect of our flux transport model is the fact that meridional circulation in the convective envelope acts as a ``clock'' regulating the tempo of the solar cycle; shorter-than-average cycles are typically soon followed by longer-than-average cycles. In other words, the oscillation exhibits good phase locking, a property that also characterizes the solar activity cycle. This shows up quite clearly in our model, but we argue that it is in fact a generic property of flux transport models based on the Babcock-Leighton mechanism, and relies on meridional circulation as the primary magnetic field transport agent.
Towards a Stochastic Predictive Understanding of Ecosystem Functioning and Resilience to Environmental Changes

NASA Astrophysics Data System (ADS)

Pappas, C.

2017-12-01

Terrestrial ecosystem processes respond differently to hydrometeorological variability across timescales, and so does our scientific understanding of the underlying mechanisms. Process-based modeling of ecosystem functioning is therefore challenging, especially when long-term predictions are envisioned. Here we analyze the statistical properties of hydrometeorological and ecosystem variability, i.e., the variability of ecosystem process related to vegetation carbon dynamics, from hourly to decadal timescales. 23 extra-tropical forest sites, covering different climatic zones and vegetation characteristics, are examined. Micrometeorological and reanalysis data of precipitation, air temperature, shortwave radiation and vapor pressure deficit are used to describe hydrometeorological variability. Ecosystem variability is quantified using long-term eddy covariance flux data of hourly net ecosystem exchange of CO2 between land surface and atmosphere, monthly remote sensing vegetation indices, annual tree-ring widths and above-ground biomass increment estimates. We find that across sites and timescales ecosystem variability is confined within a hydrometeorological envelope that describes the range of variability of the available resources, i.e., water and energy. Furthermore, ecosystem variability demonstrates long-term persistence, highlighting ecological memory and slow ecosystem recovery rates after disturbances. We derive an analytical model, combining deterministic harmonics and stochastic processes, that represents major mechanisms and uncertainties and mimics the observed pattern of hydrometeorological and ecosystem variability. This stochastic framework offers a parsimonious and mathematically tractable approach for modelling ecosystem functioning and for understanding its response and resilience to environmental changes. Furthermore, this framework reflects well the observed ecological memory, an inherent property of ecosystem functioning that is currently not captured by simulation results with process-based models. Our analysis offers a perspective for terrestrial ecosystem modelling, combining current process understanding with stochastic methods, and paves the way for new model-data integration opportunities in Earth system sciences.
Stochastic Seismic Inversion and Migration for Offshore Site Investigation in the Northern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Son, J.; Medina-Cetina, Z.

2017-12-01

We discuss the comparison between deterministic and stochastic optimization approaches to the nonlinear geophysical full-waveform inverse problem, based on the seismic survey data from Mississippi Canyon in the Northern Gulf of Mexico. Since the subsea engineering and offshore construction projects actively require reliable ground models from various site investigations, the primary goal of this study is to reconstruct the accurate subsurface information of the soil and rock material profiles under the seafloor. The shallow sediment layers have naturally formed heterogeneous formations which may cause unwanted marine landslides or foundation failures of underwater infrastructure. We chose the quasi-Newton and simulated annealing as deterministic and stochastic optimization algorithms respectively. Seismic forward modeling based on finite difference method with absorbing boundary condition implements the iterative simulations in the inverse modeling. We briefly report on numerical experiments using a synthetic data as an offshore ground model which contains shallow artificial target profiles of geomaterials under the seafloor. We apply the seismic migration processing and generate Voronoi tessellation on two-dimensional space-domain to improve the computational efficiency of the imaging stratigraphical velocity model reconstruction. We then report on the detail of a field data implementation, which shows the complex geologic structures in the Northern Gulf of Mexico. Lastly, we compare the new inverted image of subsurface site profiles in the space-domain with the previously processed seismic image in the time-domain at the same location. Overall, stochastic optimization for seismic inversion with migration and Voronoi tessellation show significant promise to improve the subsurface imaging of ground models and improve the computational efficiency required for the full waveform inversion. We anticipate that by improving the inversion process of shallow layers from geophysical data will better support the offshore site investigation.
Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2011-12-01

The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.
Stochastic Geometric Network Models for Groups of Functional and Structural Connectomes

PubMed Central

Friedman, Eric J.; Landsberg, Adam S.; Owen, Julia P.; Li, Yi-Ou; Mukherjee, Pratik

2014-01-01

Structural and functional connectomes are emerging as important instruments in the study of normal brain function and in the development of new biomarkers for a variety of brain disorders. In contrast to single-network studies that presently dominate the (non-connectome) network literature, connectome analyses typically examine groups of empirical networks and then compare these against standard (stochastic) network models. Current practice in connectome studies is to employ stochastic network models derived from social science and engineering contexts as the basis for the comparison. However, these are not necessarily best suited for the analysis of connectomes, which often contain groups of very closely related networks, such as occurs with a set of controls or a set of patients with a specific disorder. This paper studies important extensions of standard stochastic models that make them better adapted for analysis of connectomes, and develops new statistical fitting methodologies that account for inter-subject variations. The extensions explicitly incorporate geometric information about a network based on distances and inter/intra hemispherical asymmetries (to supplement ordinary degree-distribution information), and utilize a stochastic choice of networks' density levels (for fixed threshold networks) to better capture the variance in average connectivity among subjects. The new statistical tools introduced here allow one to compare groups of networks by matching both their average characteristics and the variations among them. A notable finding is that connectomes have high “smallworldness” beyond that arising from geometric and degree considerations alone. PMID:25067815
Pan-European stochastic flood event set

NASA Astrophysics Data System (ADS)

Kadlec, Martin; Pinto, Joaquim G.; He, Yi; Punčochář, Petr; Kelemen, Fanni D.; Manful, Desmond; Palán, Ladislav

2017-04-01

Impact Forecasting (IF), the model development center of Aon Benfield, has been developing a large suite of catastrophe flood models on probabilistic bases for individual countries in Europe. Such natural catastrophes do not follow national boundaries: for example, the major flood in 2016 was responsible for the Europe's largest insured loss of USD3.4bn and affected Germany, France, Belgium, Austria and parts of several other countries. Reflecting such needs, IF initiated a pan-European flood event set development which combines cross-country exposures with country based loss distributions to provide more insightful data to re/insurers. Because the observed discharge data are not available across the whole Europe in sufficient quantity and quality to permit a detailed loss evaluation purposes, a top-down approach was chosen. This approach is based on simulating precipitation from a GCM/RCM model chain followed by a calculation of discharges using rainfall-runoff modelling. IF set up this project in a close collaboration with Karlsruhe Institute of Technology (KIT) regarding the precipitation estimates and with University of East Anglia (UEA) in terms of the rainfall-runoff modelling. KIT's main objective is to provide high resolution daily historical and stochastic time series of key meteorological variables. A purely dynamical downscaling approach with the regional climate model COSMO-CLM (CCLM) is used to generate the historical time series, using re-analysis data as boundary conditions. The resulting time series are validated against the gridded observational dataset E-OBS, and different bias-correction methods are employed. The generation of the stochastic time series requires transfer functions between large-scale atmospheric variables and regional temperature and precipitation fields. These transfer functions are developed for the historical time series using reanalysis data as predictors and bias-corrected CCLM simulated precipitation and temperature as predictands. Finally, the transfer functions are applied to a large ensemble of GCM simulations with forcing corresponding to present day climate conditions to generate highly resolved stochastic time series of precipitation and temperature for several thousand years. These time series form the input for the rainfall-runoff model developed by the UEA team. It is a spatially distributed model adapted from the HBV model and will be calibrated for individual basins using historical discharge data. The calibrated model will be driven by the precipitation time series generated by the KIT team to simulate discharges at a daily time step. The uncertainties in the simulated discharges will be analysed using multiple model parameter sets. A number of statistical methods will be used to assess return periods, changes in the magnitudes, changes in the characteristics of floods such as time base and time to peak, and spatial correlations of large flood events. The Pan-European flood stochastic event set will permit a better view of flood risk for market applications.
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.
Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.
Stochastic effects in a discretized kinetic model of economic exchange

NASA Astrophysics Data System (ADS)

Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.

2017-04-01

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
NEXT GENERATION MULTIMEDIA/MULTIPATHWAY EXPOSURE MODELING

EPA Science Inventory

The Stochastic Human Exposure and Dose Simulation model for pesticides (SHEDS-Pesticides) supports the efforts of EPA to better understand human exposures and doses to multimedia, multipathway pollutants. It is a physically-based, probabilistic computer model that predicts, for u...
An advanced environment for hybrid modeling of biological systems based on modelica.

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.
Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.
Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.
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
Statistical signatures of a targeted search by bacteria

NASA Astrophysics Data System (ADS)

Jashnsaz, Hossein; Anderson, Gregory G.; Pressé, Steve

2017-12-01

Chemoattractant gradients are rarely well-controlled in nature and recent attention has turned to bacterial chemotaxis toward typical bacterial food sources such as food patches or even bacterial prey. In environments with localized food sources reminiscent of a bacterium’s natural habitat, striking phenomena—such as the volcano effect or banding—have been predicted or expected to emerge from chemotactic models. However, in practice, from limited bacterial trajectory data it is difficult to distinguish targeted searches from an untargeted search strategy for food sources. Here we use a theoretical model to identify statistical signatures of a targeted search toward point food sources, such as prey. Our model is constructed on the basis that bacteria use temporal comparisons to bias their random walk, exhibit finite memory and are subject to random (Brownian) motion as well as signaling noise. The advantage with using a stochastic model-based approach is that a stochastic model may be parametrized from individual stochastic bacterial trajectories but may then be used to generate a very large number of simulated trajectories to explore average behaviors obtained from stochastic search strategies. For example, our model predicts that a bacterium’s diffusion coefficient increases as it approaches the point source and that, in the presence of multiple sources, bacteria may take substantially longer to locate their first source giving the impression of an untargeted search strategy.
Stochastic modelling of human exposure to food chemicals and nutrients within the "Montecarlo" project: an exploration of the influence of brand loyalty and market share on intake estimates of intense sweeteners from sugar-free soft drinks.

PubMed

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

2003-04-11

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

NASA Astrophysics Data System (ADS)

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-01

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.
Magnetic Tunnel Junction Based Long-Term Short-Term Stochastic Synapse for a Spiking Neural Network with On-Chip STDP Learning.

PubMed

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-13

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.
Shallow cumuli ensemble statistics for development of a stochastic parameterization

NASA Astrophysics Data System (ADS)

Sakradzija, Mirjana; Seifert, Axel; Heus, Thijs

2014-05-01

According to a conventional deterministic approach to the parameterization of moist convection in numerical atmospheric models, a given large scale forcing produces an unique response from the unresolved convective processes. This representation leaves out the small-scale variability of convection, as it is known from the empirical studies of deep and shallow convective cloud ensembles, there is a whole distribution of sub-grid states corresponding to the given large scale forcing. Moreover, this distribution gets broader with the increasing model resolution. This behavior is also consistent with our theoretical understanding of a coarse-grained nonlinear system. We propose an approach to represent the variability of the unresolved shallow-convective states, including the dependence of the sub-grid states distribution spread and shape on the model horizontal resolution. Starting from the Gibbs canonical ensemble theory, Craig and Cohen (2006) developed a theory for the fluctuations in a deep convective ensemble. The micro-states of a deep convective cloud ensemble are characterized by the cloud-base mass flux, which, according to the theory, is exponentially distributed (Boltzmann distribution). Following their work, we study the shallow cumulus ensemble statistics and the distribution of the cloud-base mass flux. We employ a Large-Eddy Simulation model (LES) and a cloud tracking algorithm, followed by a conditional sampling of clouds at the cloud base level, to retrieve the information about the individual cloud life cycles and the cloud ensemble as a whole. In the case of shallow cumulus cloud ensemble, the distribution of micro-states is a generalized exponential distribution. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate the shallow convective cloud ensemble and to test the convective ensemble theory. Stochastic model simulates a compound random process, with the number of convective elements drawn from a Poisson distribution, and cloud properties sub-sampled from a generalized ensemble distribution. We study the role of the different cloud subtypes in a shallow convective ensemble and how the diverse cloud properties and cloud lifetimes affect the system macro-state. To what extent does the cloud-base mass flux distribution deviate from the simple Boltzmann distribution and how does it affect the results from the stochastic model? Is the memory, provided by the finite lifetime of individual clouds, of importance for the ensemble statistics? We also test for the minimal information given as an input to the stochastic model, able to reproduce the ensemble mean statistics and the variability in a convective ensemble. An important property of the resulting distribution of the sub-grid convective states is its scale-adaptivity - the smaller the grid-size, the broader the compound distribution of the sub-grid states.

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model.

PubMed

Paninski, Liam; Haith, Adrian; Szirtes, Gabor

2008-02-01

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.
Statistical Compression of Wind Speed Data

NASA Astrophysics Data System (ADS)

Tagle, F.; Castruccio, S.; Crippa, P.; Genton, M.

2017-12-01

In this work we introduce a lossy compression approach that utilizes a stochastic wind generator based on a non-Gaussian distribution to reproduce the internal climate variability of daily wind speed as represented by the CESM Large Ensemble over Saudi Arabia. Stochastic wind generators, and stochastic weather generators more generally, are statistical models that aim to match certain statistical properties of the data on which they are trained. They have been used extensively in applications ranging from agricultural models to climate impact studies. In this novel context, the parameters of the fitted model can be interpreted as encoding the information contained in the original uncompressed data. The statistical model is fit to only 3 of the 30 ensemble members and it adequately captures the variability of the ensemble in terms of seasonal internannual variability of daily wind speed. To deal with such a large spatial domain, it is partitioned into 9 region, and the model is fit independently to each of these. We further discuss a recent refinement of the model, which relaxes this assumption of regional independence, by introducing a large-scale component that interacts with the fine-scale regional effects.
Ecological invasion, roughened fronts, and a competitor's extreme advance: integrating stochastic spatial-growth models.

PubMed

O'Malley, Lauren; Korniss, G; Caraco, Thomas

2009-07-01

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibits universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.
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.
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less
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.
On an interface of the online system for a stochastic analysis of the varied information flows

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

Gorshenin, Andrey K.; MIREA, MGUPI; Kuzmin, Victor Yu.

The article describes a possible approach to the construction of an interface of an online asynchronous system that allows researchers to analyse varied information flows. The implemented stochastic methods are based on the mixture models and the method of moving separation of mixtures. The general ideas of the system functionality are demonstrated on an example for some moments of a finite normal mixture.
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.
Bed Capacity Planning Using Stochastic Simulation Approach in Cardiac-surgery Department of Teaching Hospitals, Tehran, Iran

PubMed Central

TORABIPOUR, Amin; ZERAATI, Hojjat; ARAB, Mohammad; RASHIDIAN, Arash; AKBARI SARI, Ali; SARZAIEM, Mahmuod Reza

2016-01-01

Background: To determine the hospital required beds using stochastic simulation approach in cardiac surgery departments. Methods: This study was performed from Mar 2011 to Jul 2012 in three phases: First, collection data from 649 patients in cardiac surgery departments of two large teaching hospitals (in Tehran, Iran). Second, statistical analysis and formulate a multivariate linier regression model to determine factors that affect patient's length of stay. Third, develop a stochastic simulation system (from admission to discharge) based on key parameters to estimate required bed capacity. Results: Current cardiac surgery department with 33 beds can only admit patients in 90.7% of days. (4535 d) and will be required to over the 33 beds only in 9.3% of days (efficient cut off point). According to simulation method, studied cardiac surgery department will requires 41–52 beds for admission of all patients in the 12 next years. Finally, one-day reduction of length of stay lead to decrease need for two hospital beds annually. Conclusion: Variation of length of stay and its affecting factors can affect required beds. Statistic and stochastic simulation model are applied and useful methods to estimate and manage hospital beds based on key hospital parameters. PMID:27957466
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.
A stochastic evolution model for residue Insertion-Deletion Independent from Substitution.

PubMed

Lèbre, Sophie; Michel, Christian J

2010-12-01

We develop here a new class of stochastic models of gene evolution based on residue Insertion-Deletion Independent from Substitution (IDIS). Indeed, in contrast to all existing evolution models, insertions and deletions are modeled here by a concept in population dynamics. Therefore, they are not only independent from each other, but also independent from the substitution process. After a separate stochastic analysis of the substitution and the insertion-deletion processes, we obtain a matrix differential equation combining these two processes defining the IDIS model. By deriving a general solution, we give an analytical expression of the residue occurrence probability at evolution time t as a function of a substitution rate matrix, an insertion rate vector, a deletion rate and an initial residue probability vector. Various mathematical properties of the IDIS model in relation with time t are derived: time scale, time step, time inversion and sequence length. Particular expressions of the nucleotide occurrence probability at time t are given for classical substitution rate matrices in various biological contexts: equal insertion rate, insertion-deletion only and substitution only. All these expressions can be directly used for biological evolutionary applications. The IDIS model shows a strongly different stochastic behavior from the classical substitution only model when compared on a gene dataset. Indeed, by considering three processes of residue insertion, deletion and substitution independently from each other, it allows a more realistic representation of gene evolution and opens new directions and applications in this research field. Copyright © 2010 Elsevier Ltd. All rights reserved.
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…
PDC-SGB: Prediction of effective drug combinations using a stochastic gradient boosting algorithm.

PubMed

Xu, Qian; Xiong, Yi; Dai, Hao; Kumari, Kotni Meena; Xu, Qin; Ou, Hong-Yu; Wei, Dong-Qing

2017-03-21

Combinatorial therapy is a promising strategy for combating complex diseases by improving the efficacy and reducing the side effects. To facilitate the identification of drug combinations in pharmacology, we proposed a new computational model, termed PDC-SGB, to predict effective drug combinations by integrating biological, chemical and pharmacological information based on a stochastic gradient boosting algorithm. To begin with, a set of 352 golden positive samples were collected from the public drug combination database. Then, a set of 732 dimensional feature vector involving biological, chemical and pharmaceutical information was constructed for each drug combination to describe its properties. To avoid overfitting, the maximum relevance & minimum redundancy (mRMR) method was performed to extract useful ones by removing redundant subsets. Based on the selected features, the three different type of classification algorithms were employed to build the drug combination prediction models. Our results demonstrated that the model based on the stochastic gradient boosting algorithm yield out the best performance. Furthermore, it is indicated that the feature patterns of therapy had powerful ability to discriminate effective drug combinations from non-effective ones. By analyzing various features, it is shown that the enriched features occurred frequently in golden positive samples can help predict novel drug combinations. Copyright © 2017 Elsevier Ltd. All rights reserved.
A Time-Variant Reliability Model for Copper Bending Pipe under Seawater-Active Corrosion Based on the Stochastic Degradation Process

PubMed Central

Li, Mengmeng; Feng, Qiang; Yang, Dezhen

2018-01-01

In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion. PMID:29584695
Method of conditional moments (MCM) for the Chemical Master Equation: a unified framework for the method of moments and hybrid stochastic-deterministic models.

PubMed

Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J

2014-09-01

The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.
Stochastic Models for Precipitable Water in Convection

NASA Astrophysics Data System (ADS)

Leung, Kimberly

Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test-of-concept for eventual inclusion in a general circulation model. The stochastic scheme was designed to be coupled with the deterministic single-column simulation by modifying results of the existing convective scheme (Zhang-McFarlane) and was able to produce a 20-second resolution time series that effectively simulated observed PWV, as measured by correlation coefficient (0.5510), fractal dimension (1.9), statistics, and visual examination of temporal trends. Results indicate that simulation of a highly volatile time series of observed PWV is certainly achievable and has potential to improve prediction capabilities in climate modeling. Further, this study demonstrates the feasibility of adding a mathematics- and statistics-based stochastic scheme to an existing deterministic parameterization to simulate observed fractal behavior.
Application of IFT and SPSA to servo system control.

PubMed

Rădac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan

2011-12-01

This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.
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
Modeling stochastic noise in gene regulatory systems

PubMed Central

Meister, Arwen; Du, Chao; Li, Ye Henry; Wong, Wing Hung

2014-01-01

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems. PMID:25632368

STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB.

PubMed

Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K

2011-04-15

The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user's models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. The software is open source under the GPL v3 and available at http://www.maths.ox.ac.uk/cmb/STOCHSIMGPU. The web site also contains supplementary information. klingbeil@maths.ox.ac.uk Supplementary data are available at Bioinformatics online.
Random noise effects in pulse-mode digital multilayer neural networks.

PubMed

Kim, Y C; Shanblatt, M A

1995-01-01

A pulse-mode digital multilayer neural network (DMNN) based on stochastic computing techniques is implemented with simple logic gates as basic computing elements. The pulse-mode signal representation and the use of simple logic gates for neural operations lead to a massively parallel yet compact and flexible network architecture, well suited for VLSI implementation. Algebraic neural operations are replaced by stochastic processes using pseudorandom pulse sequences. The distributions of the results from the stochastic processes are approximated using the hypergeometric distribution. Synaptic weights and neuron states are represented as probabilities and estimated as average pulse occurrence rates in corresponding pulse sequences. A statistical model of the noise (error) is developed to estimate the relative accuracy associated with stochastic computing in terms of mean and variance. Computational differences are then explained by comparison to deterministic neural computations. DMNN feedforward architectures are modeled in VHDL using character recognition problems as testbeds. Computational accuracy is analyzed, and the results of the statistical model are compared with the actual simulation results. Experiments show that the calculations performed in the DMNN are more accurate than those anticipated when Bernoulli sequences are assumed, as is common in the literature. Furthermore, the statistical model successfully predicts the accuracy of the operations performed in the DMNN.
Stochastic control of smart home energy management with plug-in electric vehicle battery energy storage and photovoltaic array

NASA Astrophysics Data System (ADS)

Wu, Xiaohua; Hu, Xiaosong; Moura, Scott; Yin, Xiaofeng; Pickert, Volker

2016-11-01

Energy management strategies are instrumental in the performance and economy of smart homes integrating renewable energy and energy storage. This article focuses on stochastic energy management of a smart home with PEV (plug-in electric vehicle) energy storage and photovoltaic (PV) array. It is motivated by the challenges associated with sustainable energy supplies and the local energy storage opportunity provided by vehicle electrification. This paper seeks to minimize a consumer's energy charges under a time-of-use tariff, while satisfying home power demand and PEV charging requirements, and accommodating the variability of solar power. First, the random-variable models are developed, including Markov Chain model of PEV mobility, as well as predictive models of home power demand and PV power supply. Second, a stochastic optimal control problem is mathematically formulated for managing the power flow among energy sources in the smart home. Finally, based on time-varying electricity price, we systematically examine the performance of the proposed control strategy. As a result, the electric cost is 493.6% less for a Tesla Model S with optimal stochastic dynamic programming (SDP) control relative to the no optimal control case, and it is by 175.89% for a Nissan Leaf.
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...
A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term.

PubMed

Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W

2014-01-01

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Microdose Induced Drain Leakage Effects in Power Trench MOSFETs: Experiment and Modeling

NASA Astrophysics Data System (ADS)

Zebrev, Gennady I.; Vatuev, Alexander S.; Useinov, Rustem G.; Emeliyanov, Vladimir V.; Anashin, Vasily S.; Gorbunov, Maxim S.; Turin, Valentin O.; Yesenkov, Kirill A.

2014-08-01

We study experimentally and theoretically the micro-dose induced drain-source leakage current in the trench power MOSFETs under irradiation with high-LET heavy ions. We found experimentally that cumulative increase of leakage current occurs by means of stochastic spikes corresponding to a strike of single heavy ion into the MOSFET gate oxide. We simulate this effect with the proposed analytic model allowing to describe (including Monte Carlo methods) both the deterministic (cumulative dose) and stochastic (single event) aspects of the problem. Based on this model the survival probability assessment in space heavy ion environment with high LETs was proposed.
MODELING HUMAN EXPOSURES AND DOSE USING A 2-DIMENSIONAL MONTE-CARLO MODEL (SHEDS)

EPA Science Inventory

Since 1998, US EPA's National Exposure Research Laboratory (NERL) has been developing the Stochastic Human Exposure and Dose Simulation (SHEDS) model for various classes of pollutants. SHEDS is a physically-based probabilistic model intended for improving estimates of human ex...
Stochastic modelling of animal movement.

PubMed

Smouse, Peter E; Focardi, Stefano; Moorcroft, Paul R; Kie, John G; Forester, James D; Morales, Juan M

2010-07-27

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal 'settling down', accomplished by including one or more focal points that attract the animal's movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.
Determining Reduced Order Models for Optimal Stochastic Reduced Order Models

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

Bonney, Matthew S.; Brake, Matthew R.W.

2015-08-01

The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better representmore » the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.« less
Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time.

PubMed

Dhar, Amrit; Minin, Vladimir N

2017-05-01

Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences.
Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

PubMed Central

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780
The importance of environmental variability and management control error to optimal harvest policies

USGS Publications Warehouse

Hunter, C.M.; Runge, M.C.

2004-01-01

State-dependent strategies (SDSs) are the most general form of harvest policy because they allow the harvest rate to depend, without constraint, on the state of the system. State-dependent strategies that provide an optimal harvest rate for any system state can be calculated, and stochasticity can be appropriately accommodated in this optimization. Stochasticity poses 2 challenges to harvest policies: (1) the population will never be at the equilibrium state; and (2) stochasticity induces uncertainty about future states. We investigated the effects of 2 types of stochasticity, environmental variability and management control error, on SDS harvest policies for a white-tailed deer (Odocoileus virginianus) model, and contrasted these with a harvest policy based on maximum sustainable yield (MSY). Increasing stochasticity resulted in more conservative SDSs; that is, higher population densities were required to support the same harvest rate, but these effects were generally small. As stochastic effects increased, SDSs performed much better than MSY. Both deterministic and stochastic SDSs maintained maximum mean annual harvest yield (AHY) and optimal equilibrium population size (Neq) in a stochastic environment, whereas an MSY policy could not. We suggest 3 rules of thumb for harvest management of long-lived vertebrates in stochastic systems: (1) an SDS is advantageous over an MSY policy, (2) using an SDS rather than an MSY is more important than whether a deterministic or stochastic SDS is used, and (3) for SDSs, rankings of the variability in management outcomes (e.g., harvest yield) resulting from parameter stochasticity can be predicted by rankings of the deterministic elasticities.
A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.
Stochastic thermodynamics of a chemical nanomachine: The channeling enzyme tryptophan synthase.

PubMed

Loutchko, Dimitri; Eisbach, Maximilian; Mikhailov, Alexander S

2017-01-14

The enzyme tryptophan synthase is characterized by a complex pattern of allosteric interactions that regulate the catalytic activity of its two subunits and opening or closing of their ligand gates. As a single macromolecule, it implements 13 different reaction steps, with an intermediate product directly channeled from one subunit to another. Based on experimental data, a stochastic model for the operation of tryptophan synthase has been earlier constructed [D. Loutchko, D. Gonze, and A. S. Mikhailov, J. Phys. Chem. B 120, 2179 (2016)]. Here, this model is used to consider stochastic thermodynamics of such a chemical nanomachine. The Gibbs energy landscape of the internal molecular states is determined, the production of entropy and its flow within the enzyme are analyzed, and the information exchange between the subunits resulting from allosteric cross-regulations and channeling is discussed.
Restoring the encoding properties of a stochastic neuron model by an exogenous noise

PubMed Central

Paffi, Alessandra; Camera, Francesca; Apollonio, Francesca; d'Inzeo, Guglielmo; Liberti, Micaela

2015-01-01

Here we evaluate the possibility of improving the encoding properties of an impaired neuronal system by superimposing an exogenous noise to an external electric stimulation signal. The approach is based on the use of mathematical neuron models consisting of stochastic HH-like circuit, where the impairment of the endogenous presynaptic inputs is described as a subthreshold injected current and the exogenous stimulation signal is a sinusoidal voltage perturbation across the membrane. Our results indicate that a correlated Gaussian noise, added to the sinusoidal signal can significantly increase the encoding properties of the impaired system, through the Stochastic Resonance (SR) phenomenon. These results suggest that an exogenous noise, suitably tailored, could improve the efficacy of those stimulation techniques used in neuronal systems, where the presynaptic sensory neurons are impaired and have to be artificially bypassed. PMID:25999845
Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.
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

Accounting for parameter uncertainty in the definition of parametric distributions used to describe individual patient variation in health economic models.

PubMed

Degeling, Koen; IJzerman, Maarten J; Koopman, Miriam; Koffijberg, Hendrik

2017-12-15

Parametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty. Although general guidance is available on how parameter uncertainty should be accounted for in probabilistic sensitivity analysis, there is no comprehensive guidance on reflecting parameter uncertainty in the (correlated) parameters of distributions used to represent stochastic uncertainty in patient-level models. This study aims to provide this guidance by proposing appropriate methods and illustrating the impact of this uncertainty on modeling outcomes. Two approaches, 1) using non-parametric bootstrapping and 2) using multivariate Normal distributions, were applied in a simulation and case study. The approaches were compared based on point-estimates and distributions of time-to-event and health economic outcomes. To assess sample size impact on the uncertainty in these outcomes, sample size was varied in the simulation study and subgroup analyses were performed for the case-study. Accounting for parameter uncertainty in distributions that reflect stochastic uncertainty substantially increased the uncertainty surrounding health economic outcomes, illustrated by larger confidence ellipses surrounding the cost-effectiveness point-estimates and different cost-effectiveness acceptability curves. Although both approaches performed similar for larger sample sizes (i.e. n = 500), the second approach was more sensitive to extreme values for small sample sizes (i.e. n = 25), yielding infeasible modeling outcomes. Modelers should be aware that parameter uncertainty in distributions used to describe stochastic uncertainty needs to be reflected in probabilistic sensitivity analysis, as it could substantially impact the total amount of uncertainty surrounding health economic outcomes. If feasible, the bootstrap approach is recommended to account for this uncertainty.
Real-world datasets for portfolio selection and solutions of some stochastic dominance portfolio models.

PubMed

Bruni, Renato; Cesarone, Francesco; Scozzari, Andrea; Tardella, Fabio

2016-09-01

A large number of portfolio selection models have appeared in the literature since the pioneering work of Markowitz. However, even when computational and empirical results are described, they are often hard to replicate and compare due to the unavailability of the datasets used in the experiments. We provide here several datasets for portfolio selection generated using real-world price values from several major stock markets. The datasets contain weekly return values, adjusted for dividends and for stock splits, which are cleaned from errors as much as possible. The datasets are available in different formats, and can be used as benchmarks for testing the performances of portfolio selection models and for comparing the efficiency of the algorithms used to solve them. We also provide, for these datasets, the portfolios obtained by several selection strategies based on Stochastic Dominance models (see "On Exact and Approximate Stochastic Dominance Strategies for Portfolio Selection" (Bruni et al. [2])). We believe that testing portfolio models on publicly available datasets greatly simplifies the comparison of the different portfolio selection strategies.
Analyzing the carbon mitigation potential of tradable green certificates based on a TGC-FFSRO model: A case study in the Beijing-Tianjin-Hebei region, China.

PubMed

Chen, Cong; Zhu, Ying; Zeng, Xueting; Huang, Guohe; Li, Yongping

2018-07-15

Contradictions of increasing carbon mitigation pressure and electricity demand have been aggravated significantly. A heavy emphasis is placed on analyzing the carbon mitigation potential of electric energy systems via tradable green certificates (TGC). This study proposes a tradable green certificate (TGC)-fractional fuzzy stochastic robust optimization (FFSRO) model through integrating fuzzy possibilistic, two-stage stochastic and stochastic robust programming techniques into a linear fractional programming framework. The framework can address uncertainties expressed as stochastic and fuzzy sets, and effectively deal with issues of multi-objective tradeoffs between the economy and environment. The proposed model is applied to the major economic center of China, the Beijing-Tianjin-Hebei region. The generated results of proposed model indicate that a TGC mechanism is a cost-effective pathway to cope with carbon reduction and support the sustainable development pathway of electric energy systems. In detail, it can: (i) effectively promote renewable power development and reduce fossil fuel use; (ii) lead to higher CO 2 mitigation potential than non-TGC mechanism; and (iii) greatly alleviate financial pressure on the government to provide renewable energy subsidies. The TGC-FFSRO model can provide a scientific basis for making related management decisions of electric energy systems. Copyright © 2017 Elsevier B.V. All rights reserved.
Revisions to some parameters used in stochastic-method simulations of ground motion

USGS Publications Warehouse

Boore, David; Thompson, Eric M.

2015-01-01

The stochastic method of ground‐motion simulation specifies the amplitude spectrum as a function of magnitude (M) and distance (R). The manner in which the amplitude spectrum varies with M and R depends on physical‐based parameters that are often constrained by recorded motions for a particular region (e.g., stress parameter, geometrical spreading, quality factor, and crustal amplifications), which we refer to as the seismological model. The remaining ingredient for the stochastic method is the ground‐motion duration. Although the duration obviously affects the character of the ground motion in the time domain, it also significantly affects the response of a single‐degree‐of‐freedom oscillator. Recently published updates to the stochastic method include a new generalized double‐corner‐frequency source model, a new finite‐fault correction, a new parameterization of duration, and a new duration model for active crustal regions. In this article, we augment these updates with a new crustal amplification model and a new duration model for stable continental regions. Random‐vibration theory (RVT) provides a computationally efficient method to compute the peak oscillator response directly from the ground‐motion amplitude spectrum and duration. Because the correction factor used to account for the nonstationarity of the ground motion depends on the ground‐motion amplitude spectrum and duration, we also present new RVT correction factors for both active and stable regions.
A minimum stochastic model evaluating the interplay between population density and drift for species coexistence

NASA Astrophysics Data System (ADS)

Guariento, Rafael Dettogni; Caliman, Adriano

2017-02-01

Despite the general acknowledgment of the role of niche and stochastic process in community dynamics, the role of species relative abundances according to both perspectives may have different effects regarding coexistence patterns. In this study, we explore a minimum probabilistic stochastic model to determine the relationship of populations relative and total abundances with species chances to outcompete each other and their persistence in time (i.e., unstable coexistence). Our model is focused on the effects drift (i.e., random sampling of recruitment) under different scenarios of selection (i.e., fitness differences between species). Our results show that taking into account the stochasticity in demographic properties and conservation of individuals in closed communities (zero-sum assumption), initial population abundance can strongly influence species chances to outcompete each other, despite fitness inequalities between populations, and also, influence the period of coexistence of these species in a particular time interval. Systems carrying capacity can have an important role in species coexistence by exacerbating fitness inequalities and affecting the size of the period of coexistence. Overall, the simple stochastic formulation used in this study demonstrated that populations initial abundances could act as an equalizing mechanism, reducing fitness inequalities, which can favor species coexistence and even make less fitted species to be more likely to outcompete better-fitted species, and thus to dominate ecological communities in the absence of niche mechanisms. Although our model is restricted to a pair of interacting species, and overall conclusions are already predicted by the Neutral Theory of Biodiversity, our main objective was to derive a model that can explicitly show the functional relationship between population densities and community mono-dominance odds. Overall, our study provides a straightforward understanding of how a stochastic process (i.e., drift) may affect the expected outcome based on species selection (i.e., fitness inequalities among species) and the resulting outcome regarding unstable coexistence among species.
Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

PubMed

Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

2016-10-21

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.
Stochastic Modeling of Overtime Occupancy and Its Application in Building Energy Simulation and Calibration

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

Sun, Kaiyu; Yan, Da; Hong, Tianzhen

2014-02-28

Overtime is a common phenomenon around the world. Overtime drives both internal heat gains from occupants, lighting and plug-loads, and HVAC operation during overtime periods. Overtime leads to longer occupancy hours and extended operation of building services systems beyond normal working hours, thus overtime impacts total building energy use. Current literature lacks methods to model overtime occupancy because overtime is stochastic in nature and varies by individual occupants and by time. To address this gap in the literature, this study aims to develop a new stochastic model based on the statistical analysis of measured overtime occupancy data from an officemore » building. A binomial distribution is used to represent the total number of occupants working overtime, while an exponential distribution is used to represent the duration of overtime periods. The overtime model is used to generate overtime occupancy schedules as an input to the energy model of a second office building. The measured and simulated cooling energy use during the overtime period is compared in order to validate the overtime model. A hybrid approach to energy model calibration is proposed and tested, which combines ASHRAE Guideline 14 for the calibration of the energy model during normal working hours, and a proposed KS test for the calibration of the energy model during overtime. The developed stochastic overtime model and the hybrid calibration approach can be used in building energy simulations to improve the accuracy of results, and better understand the characteristics of overtime in office buildings.« less
Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.

PubMed

Chang, Joshua; Paydarfar, David

2014-12-01

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.
Sustainability of transport structures - some aspects of the nonlinear reliability assessment

NASA Astrophysics Data System (ADS)

Pukl, Radomír; Sajdlová, Tereza; Strauss, Alfred; Lehký, David; Novák, Drahomír

2017-09-01

Efficient techniques for both nonlinear numerical analysis of concrete structures and advanced stochastic simulation methods have been combined in order to offer an advanced tool for assessment of realistic behaviour, failure and safety assessment of transport structures. The utilized approach is based on randomization of the non-linear finite element analysis of the structural models. Degradation aspects such as carbonation of concrete can be accounted in order predict durability of the investigated structure and its sustainability. Results can serve as a rational basis for the performance and sustainability assessment based on advanced nonlinear computer analysis of the structures of transport infrastructure such as bridges or tunnels. In the stochastic simulation the input material parameters obtained from material tests including their randomness and uncertainty are represented as random variables or fields. Appropriate identification of material parameters is crucial for the virtual failure modelling of structures and structural elements. Inverse analysis using artificial neural networks and virtual stochastic simulations approach is applied to determine the fracture mechanical parameters of the structural material and its numerical model. Structural response, reliability and sustainability have been investigated on different types of transport structures made from various materials using the above mentioned methodology and tools.
Neuronal spike-train responses in the presence of threshold noise.

PubMed

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

2011-03-01

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

PubMed

Chen, Xiujuan; Huang, Guohe; Zhao, Shan; Cheng, Guanhui; Wu, Yinghui; Zhu, Hua

2017-11-01

In this study, a stochastic fractional inventory-theory-based waste management planning (SFIWP) model was developed and applied for supporting long-term planning of the municipal solid waste (MSW) management in Xiamen City, the special economic zone of Fujian Province, China. In the SFIWP model, the techniques of inventory model, stochastic linear fractional programming, and mixed-integer linear programming were integrated in a framework. Issues of waste inventory in MSW management system were solved, and the system efficiency was maximized through considering maximum net-diverted wastes under various constraint-violation risks. Decision alternatives for waste allocation and capacity expansion were also provided for MSW management planning in Xiamen. The obtained results showed that about 4.24 × 10 6 t of waste would be diverted from landfills when p i is 0.01, which accounted for 93% of waste in Xiamen City, and the waste diversion per unit of cost would be 26.327 × 10 3 t per $10 6 . The capacities of MSW management facilities including incinerators, composting facility, and landfills would be expanded due to increasing waste generation rate.
Threat driven modeling framework using petri nets for e-learning system.

PubMed

Khamparia, Aditya; Pandey, Babita

2016-01-01

Vulnerabilities at various levels are main cause of security risks in e-learning system. This paper presents a modified threat driven modeling framework, to identify the threats after risk assessment which requires mitigation and how to mitigate those threats. To model those threat mitigations aspects oriented stochastic petri nets are used. This paper included security metrics based on vulnerabilities present in e-learning system. The Common Vulnerability Scoring System designed to provide a normalized method for rating vulnerabilities which will be used as basis in metric definitions and calculations. A case study has been also proposed which shows the need and feasibility of using aspect oriented stochastic petri net models for threat modeling which improves reliability, consistency and robustness of the e-learning system.
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.
Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

PubMed

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.
Event-triggered resilient filtering with stochastic uncertainties and successive packet dropouts via variance-constrained approach

NASA Astrophysics Data System (ADS)

Jia, Chaoqing; Hu, Jun; Chen, Dongyan; Liu, Yurong; Alsaadi, Fuad E.

2018-07-01

In this paper, we discuss the event-triggered resilient filtering problem for a class of time-varying systems subject to stochastic uncertainties and successive packet dropouts. The event-triggered mechanism is employed with hope to reduce the communication burden and save network resources. The stochastic uncertainties are considered to describe the modelling errors and the phenomenon of successive packet dropouts is characterized by a random variable obeying the Bernoulli distribution. The aim of the paper is to provide a resilient event-based filtering approach for addressed time-varying systems such that, for all stochastic uncertainties, successive packet dropouts and filter gain perturbation, an optimized upper bound of the filtering error covariance is obtained by designing the filter gain. Finally, simulations are provided to demonstrate the effectiveness of the proposed robust optimal filtering strategy.
The Stochastic Human Exposure and Dose Simulation Model for Multimedia, Multipathway Chemicals: Dietary Module Version 1: Technical Manual

EPA Pesticide Factsheets

SHEDS - Multimedia is EPA's premier physically-based, probabilistic model, that can simulate cumulative or aggregate exposures for a population across a variety of multimedia, multipathway environmental chemicals.
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.
Model identification using stochastic differential equation grey-box models in diabetes.

PubMed

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

2013-03-01

The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.
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.
Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-01-01

An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

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…
Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.
Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

NASA Technical Reports Server (NTRS)

Deavours, Daniel D.; Qureshi, M. Akber; Sanders, William H.

1997-01-01

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.
Learning abstract visual concepts via probabilistic program induction in a Language of Thought.

PubMed

Overlan, Matthew C; Jacobs, Robert A; Piantadosi, Steven T

2017-11-01

The ability to learn abstract concepts is a powerful component of human cognition. It has been argued that variable binding is the key element enabling this ability, but the computational aspects of variable binding remain poorly understood. Here, we address this shortcoming by formalizing the Hierarchical Language of Thought (HLOT) model of rule learning. Given a set of data items, the model uses Bayesian inference to infer a probability distribution over stochastic programs that implement variable binding. Because the model makes use of symbolic variables as well as Bayesian inference and programs with stochastic primitives, it combines many of the advantages of both symbolic and statistical approaches to cognitive modeling. To evaluate the model, we conducted an experiment in which human subjects viewed training items and then judged which test items belong to the same concept as the training items. We found that the HLOT model provides a close match to human generalization patterns, significantly outperforming two variants of the Generalized Context Model, one variant based on string similarity and the other based on visual similarity using features from a deep convolutional neural network. Additional results suggest that variable binding happens automatically, implying that binding operations do not add complexity to peoples' hypothesized rules. Overall, this work demonstrates that a cognitive model combining symbolic variables with Bayesian inference and stochastic program primitives provides a new perspective for understanding people's patterns of generalization. Copyright © 2017 Elsevier B.V. All rights reserved.
An approach to the drone fleet survivability assessment based on a stochastic continues-time model

NASA Astrophysics Data System (ADS)

Kharchenko, Vyacheslav; Fesenko, Herman; Doukas, Nikos

2017-09-01

An approach and the algorithm to the drone fleet survivability assessment based on a stochastic continues-time model are proposed. The input data are the number of the drones, the drone fleet redundancy coefficient, the drone stability and restoration rate, the limit deviation from the norms of the drone fleet recovery, the drone fleet operational availability coefficient, the probability of the drone failure-free operation, time needed for performing the required tasks by the drone fleet. The ways for improving the recoverable drone fleet survivability taking into account amazing factors of system accident are suggested. Dependencies of the drone fleet survivability rate both on the drone stability and the number of the drones are analysed.
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.
A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments

PubMed Central

Collignon, Bertrand; Séguret, Axel; Halloy, José

2016-01-01

Collective motion is one of the most ubiquitous behaviours displayed by social organisms and has led to the development of numerous models. Recent advances in the understanding of sensory system and information processing by animals impels one to revise classical assumptions made in decisional algorithms. In this context, we present a model describing the three-dimensional visual sensory system of fish that adjust their trajectory according to their perception field. Furthermore, we introduce a stochastic process based on a probability distribution function to move in targeted directions rather than on a summation of influential vectors as is classically assumed by most models. In parallel, we present experimental results of zebrafish (alone or in group of 10) swimming in both homogeneous and heterogeneous environments. We use these experimental data to set the parameter values of our model and show that this perception-based approach can simulate the collective motion of species showing cohesive behaviour in heterogeneous environments. Finally, we discuss the advances of this multilayer model and its possible outcomes in biological, physical and robotic sciences. PMID:26909173
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.
Comparative analysis of the effectiveness of three immunization strategies in controlling disease outbreaks in realistic social networks.

PubMed

Xu, Zhijing; Zu, Zhenghu; Zheng, Tao; Zhang, Wendou; Xu, Qing; Liu, Jinjie

2014-01-01

The high incidence of emerging infectious diseases has highlighted the importance of effective immunization strategies, especially the stochastic algorithms based on local available network information. Present stochastic strategies are mainly evaluated based on classical network models, such as scale-free networks and small-world networks, and thus are insufficient. Three frequently referred stochastic immunization strategies-acquaintance immunization, community-bridge immunization, and ring vaccination-were analyzed in this work. The optimal immunization ratios for acquaintance immunization and community-bridge immunization strategies were investigated, and the effectiveness of these three strategies in controlling the spreading of epidemics were analyzed based on realistic social contact networks. The results show all the strategies have decreased the coverage of the epidemics compared to baseline scenario (no control measures). However the effectiveness of acquaintance immunization and community-bridge immunization are very limited, with acquaintance immunization slightly outperforming community-bridge immunization. Ring vaccination significantly outperforms acquaintance immunization and community-bridge immunization, and the sensitivity analysis shows it could be applied to controlling the epidemics with a wide infectivity spectrum. The effectiveness of several classical stochastic immunization strategies was evaluated based on realistic contact networks for the first time in this study. These results could have important significance for epidemic control research and practice.
Noise-induced shifts in the population model with a weak Allee effect

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev

2018-02-01

We consider the Truscott-Brindley system of interacting phyto- and zooplankton populations with a weak Allee effect. We add a random noise to the parameter of the prey carrying capacity, and study how the noise affects the dynamic behavior of this nonlinear prey-predator model. Phenomena of the stochastic excitement and noise-induced shifts in zones of the Andronov-Hopf bifurcation and Canard explosion are analyzed on the base of the direct numerical simulation and stochastic sensitivity functions technique. A relationship of these phenomena with transitions between order and chaos is discussed.
Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

NASA Astrophysics Data System (ADS)

Gelß, Patrick; Matera, Sebastian; Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.
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.
Testing the Predictive Power of Coulomb Stress on Aftershock Sequences

NASA Astrophysics Data System (ADS)

Woessner, J.; Lombardi, A.; Werner, M. J.; Marzocchi, W.

2009-12-01

Empirical and statistical models of clustered seismicity are usually strongly stochastic and perceived to be uninformative in their forecasts, since only marginal distributions are used, such as the Omori-Utsu and Gutenberg-Richter laws. In contrast, so-called physics-based aftershock models, based on seismic rate changes calculated from Coulomb stress changes and rate-and-state friction, make more specific predictions: anisotropic stress shadows and multiplicative rate changes. We test the predictive power of models based on Coulomb stress changes against statistical models, including the popular Short Term Earthquake Probabilities and Epidemic-Type Aftershock Sequences models: We score and compare retrospective forecasts on the aftershock sequences of the 1992 Landers, USA, the 1997 Colfiorito, Italy, and the 2008 Selfoss, Iceland, earthquakes. To quantify predictability, we use likelihood-based metrics that test the consistency of the forecasts with the data, including modified and existing tests used in prospective forecast experiments within the Collaboratory for the Study of Earthquake Predictability (CSEP). Our results indicate that a statistical model performs best. Moreover, two Coulomb model classes seem unable to compete: Models based on deterministic Coulomb stress changes calculated from a given fault-slip model, and those based on fixed receiver faults. One model of Coulomb stress changes does perform well and sometimes outperforms the statistical models, but its predictive information is diluted, because of uncertainties included in the fault-slip model. Our results suggest that models based on Coulomb stress changes need to incorporate stochastic features that represent model and data uncertainty.
Stochastic Optimization for Unit Commitment-A Review

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

Zheng, Qipeng P.; Wang, Jianhui; Liu, Andrew L.

2015-07-01

Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC's birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave ismore » focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.« less
Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.
USEPA SHEDS MODEL: METHODOLOGY FOR EXPOSURE ASSESSMENT FOR WOOD PRESERVATIVES

EPA Science Inventory

A physically-based, Monte Carlo probabilistic model (SHEDS-Wood: Stochastic Human Exposure and Dose Simulation model for wood preservatives) has been applied to assess the exposure and dose of children to arsenic (As) and chromium (Cr) from contact with chromated copper arsenat...
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
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.
Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure Induced by HZE Particles

NASA Technical Reports Server (NTRS)

Ponomarev, Artem; Plante, Ianik; George, Kerry; Wu, Honglu

2014-01-01

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high-energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05-0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta-rays becomes more important.
Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure iIduced by HZE Particles

NASA Technical Reports Server (NTRS)

Ponomarev, Artem; Plante, Ianik; George, Kerry; Wu, Honglu

2014-01-01

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high-energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05-0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta-rays becomes more important.
The Stochastic Human Exposure and Dose Simulation Model for Multimedia, Multipathway Chemicals: Residential Module Version 4: User Guide, June 2012

EPA Pesticide Factsheets

SHEDS - Multimedia is EPA's premier physically-based, probabilistic model, that can simulate cumulative or aggregate exposures for a population across a variety of multimedia, multipathway environmental chemicals.
The Stochastic Human Exposure and Dose Simulation Model for Multimedia, Multipathway Chemicals: Residential Module Version 4: Technical Manual, May 2012

EPA Pesticide Factsheets

SHEDS - Multimedia is EPA's premier physically-based, probabilistic model, that can simulate cumulative or aggregate exposures for a population across a variety of multimedia, multipathway environmental chemicals.
The Stochastic Human Exposure and Dose Simulation Model for Multimedia, Multipathway Chemicals: Dietary Module Version 1: User Guide, June 2012

EPA Pesticide Factsheets

SHEDS - Multimedia is EPA's premier physically-based, probabilistic model, that can simulate cumulative or aggregate exposures for a population across a variety of multimedia, multipathway environmental chemicals.
An improved method to represent DEM uncertainty in glacial lake outburst flood propagation using stochastic simulations

NASA Astrophysics Data System (ADS)

Watson, Cameron S.; Carrivick, Jonathan; Quincey, Duncan

2015-10-01

Modelling glacial lake outburst floods (GLOFs) or 'jökulhlaups', necessarily involves the propagation of large and often stochastic uncertainties throughout the source to impact process chain. Since flood routing is primarily a function of underlying topography, communication of digital elevation model (DEM) uncertainty should accompany such modelling efforts. Here, a new stochastic first-pass assessment technique was evaluated against an existing GIS-based model and an existing 1D hydrodynamic model, using three DEMs with different spatial resolution. The analysis revealed the effect of DEM uncertainty and model choice on several flood parameters and on the prediction of socio-economic impacts. Our new model, which we call MC-LCP (Monte Carlo Least Cost Path) and which is distributed in the supplementary information, demonstrated enhanced 'stability' when compared to the two existing methods, and this 'stability' was independent of DEM choice. The MC-LCP model outputs an uncertainty continuum within its extent, from which relative socio-economic risk can be evaluated. In a comparison of all DEM and model combinations, the Shuttle Radar Topography Mission (SRTM) DEM exhibited fewer artefacts compared to those with the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM), and were comparable to those with a finer resolution Advanced Land Observing Satellite Panchromatic Remote-sensing Instrument for Stereo Mapping (ALOS PRISM) derived DEM. Overall, we contend that the variability we find between flood routing model results suggests that consideration of DEM uncertainty and pre-processing methods is important when assessing flow routing and when evaluating potential socio-economic implications of a GLOF event. Incorporation of a stochastic variable provides an illustration of uncertainty that is important when modelling and communicating assessments of an inherently complex process.
Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.
A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

PubMed

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.
Physical Models of Cognition

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.
Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.
Genetic programming assisted stochastic optimization strategies for optimization of glucose to gluconic acid fermentation.

PubMed

Cheema, Jitender Jit Singh; Sankpal, Narendra V; Tambe, Sanjeev S; Kulkarni, Bhaskar D

2002-01-01

This article presents two hybrid strategies for the modeling and optimization of the glucose to gluconic acid batch bioprocess. In the hybrid approaches, first a novel artificial intelligence formalism, namely, genetic programming (GP), is used to develop a process model solely from the historic process input-output data. In the next step, the input space of the GP-based model, representing process operating conditions, is optimized using two stochastic optimization (SO) formalisms, viz., genetic algorithms (GAs) and simultaneous perturbation stochastic approximation (SPSA). These SO formalisms possess certain unique advantages over the commonly used gradient-based optimization techniques. The principal advantage of the GP-GA and GP-SPSA hybrid techniques is that process modeling and optimization can be performed exclusively from the process input-output data without invoking the detailed knowledge of the process phenomenology. The GP-GA and GP-SPSA techniques have been employed for modeling and optimization of the glucose to gluconic acid bioprocess, and the optimized process operating conditions obtained thereby have been compared with those obtained using two other hybrid modeling-optimization paradigms integrating artificial neural networks (ANNs) and GA/SPSA formalisms. Finally, the overall optimized operating conditions given by the GP-GA method, when verified experimentally resulted in a significant improvement in the gluconic acid yield. The hybrid strategies presented here are generic in nature and can be employed for modeling and optimization of a wide variety of batch and continuous bioprocesses.
Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.
Reconstruction of pulse noisy images via stochastic resonance

PubMed Central

Han, Jing; Liu, Hongjun; Sun, Qibing; Huang, Nan

2015-01-01

We investigate a practical technology for reconstructing nanosecond pulse noisy images via stochastic resonance, which is based on the modulation instability. A theoretical model of this method for optical pulse signal is built to effectively recover the pulse image. The nanosecond noise-hidden images grow at the expense of noise during the stochastic resonance process in a photorefractive medium. The properties of output images are mainly determined by the input signal-to-noise intensity ratio, the applied voltage across the medium, and the correlation length of noise background. A high cross-correlation gain is obtained by optimizing these parameters. This provides a potential method for detecting low-level or hidden pulse images in various imaging applications. PMID:26067911
Assessing performance and validating finite element simulations using probabilistic knowledge

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

Dolin, Ronald M.; Rodriguez, E. A.

Two probabilistic approaches for assessing performance are presented. The first approach assesses probability of failure by simultaneously modeling all likely events. The probability each event causes failure along with the event's likelihood of occurrence contribute to the overall probability of failure. The second assessment method is based on stochastic sampling using an influence diagram. Latin-hypercube sampling is used to stochastically assess events. The overall probability of failure is taken as the maximum probability of failure of all the events. The Likelihood of Occurrence simulation suggests failure does not occur while the Stochastic Sampling approach predicts failure. The Likelihood of Occurrencemore » results are used to validate finite element predictions.« less
Tests of oceanic stochastic parameterisation in a seasonal forecast system.

NASA Astrophysics Data System (ADS)

Cooper, Fenwick; Andrejczuk, Miroslaw; Juricke, Stephan; Zanna, Laure; Palmer, Tim

2015-04-01

Over seasonal time scales, our aim is to compare the relative impact of ocean initial condition and model uncertainty, upon the ocean forecast skill and reliability. Over seasonal timescales we compare four oceanic stochastic parameterisation schemes applied in a 1x1 degree ocean model (NEMO) with a fully coupled T159 atmosphere (ECMWF IFS). The relative impacts upon the ocean of the resulting eddy induced activity, wind forcing and typical initial condition perturbations are quantified. Following the historical success of stochastic parameterisation in the atmosphere, two of the parameterisations tested were multiplicitave in nature: A stochastic variation of the Gent-McWilliams scheme and a stochastic diffusion scheme. We also consider a surface flux parameterisation (similar to that introduced by Williams, 2012), and stochastic perturbation of the equation of state (similar to that introduced by Brankart, 2013). The amplitude of the stochastic term in the Williams (2012) scheme was set to the physically reasonable amplitude considered in that paper. The amplitude of the stochastic term in each of the other schemes was increased to the limits of model stability. As expected, variability was increased. Up to 1 month after initialisation, ensemble spread induced by stochastic parameterisation is greater than that induced by the atmosphere, whilst being smaller than the initial condition perturbations currently used at ECMWF. After 1 month, the wind forcing becomes the dominant source of model ocean variability, even at depth.
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.
Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection.

PubMed

Lai, Zhi-Hui; Leng, Yong-Gang

2015-08-28

A two-dimensional Duffing oscillator which can produce stochastic resonance (SR) is studied in this paper. We introduce its SR mechanism and present a generalized parameter-adjusted SR (GPASR) model of this oscillator for the necessity of parameter adjustments. The Kramers rate is chosen as the theoretical basis to establish a judgmental function for judging the occurrence of SR in this model; and to analyze and summarize the parameter-adjusted rules under unmatched signal amplitude, frequency, and/or noise-intensity. Furthermore, we propose the weak-signal detection approach based on this GPASR model. Finally, we employ two practical examples to demonstrate the feasibility of the proposed approach in practical engineering application.
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
Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less
Artificial emotion triggered stochastic behavior transitions with motivational gain effects for multi-objective robot tasks

NASA Astrophysics Data System (ADS)

Dağlarli, Evren; Temeltaş, Hakan

2007-04-01

This paper presents artificial emotional system based autonomous robot control architecture. Hidden Markov model developed as mathematical background for stochastic emotional and behavior transitions. Motivation module of architecture considered as behavioral gain effect generator for achieving multi-objective robot tasks. According to emotional and behavioral state transition probabilities, artificial emotions determine sequences of behaviors. Also motivational gain effects of proposed architecture can be observed on the executing behaviors during simulation.
Electrical conductivity modeling and experimental study of densely packed SWCNT networks.

PubMed

Jack, D A; Yeh, C-S; Liang, Z; Li, S; Park, J G; Fielding, J C

2010-05-14

Single-walled carbon nanotube (SWCNT) networks have become a subject of interest due to their ability to support structural, thermal and electrical loadings, but to date their application has been hindered due, in large part, to the inability to model macroscopic responses in an industrial product with any reasonable confidence. This paper seeks to address the relationship between macroscale electrical conductivity and the nanostructure of a dense network composed of SWCNTs and presents a uniquely formulated physics-based computational model for electrical conductivity predictions. The proposed model incorporates physics-based stochastic parameters for the individual nanotubes to construct the nanostructure such as: an experimentally obtained orientation distribution function, experimentally derived length and diameter distributions, and assumed distributions of chirality and registry of individual CNTs. Case studies are presented to investigate the relationship between macroscale conductivity and nanostructured variations in the bulk stochastic length, diameter and orientation distributions. Simulation results correspond nicely with those available in the literature for case studies of conductivity versus length and conductivity versus diameter. In addition, predictions for the increasing anisotropy of the bulk conductivity as a function of the tube orientation distribution are in reasonable agreement with our experimental results. Examples are presented to demonstrate the importance of incorporating various stochastic characteristics in bulk conductivity predictions. Finally, a design consideration for industrial applications is discussed based on localized network power emission considerations and may lend insight to the design engineer to better predict network failure under high current loading applications.
Uncertainty quantification and validation of 3D lattice scaffolds for computer-aided biomedical applications.

PubMed

Gorguluarslan, Recep M; Choi, Seung-Kyum; Saldana, Christopher J

2017-07-01

A methodology is proposed for uncertainty quantification and validation to accurately predict the mechanical response of lattice structures used in the design of scaffolds. Effective structural properties of the scaffolds are characterized using a developed multi-level stochastic upscaling process that propagates the quantified uncertainties at strut level to the lattice structure level. To obtain realistic simulation models for the stochastic upscaling process and minimize the experimental cost, high-resolution finite element models of individual struts were reconstructed from the micro-CT scan images of lattice structures which are fabricated by selective laser melting. The upscaling method facilitates the process of determining homogenized strut properties to reduce the computational cost of the detailed simulation model for the scaffold. Bayesian Information Criterion is utilized to quantify the uncertainties with parametric distributions based on the statistical data obtained from the reconstructed strut models. A systematic validation approach that can minimize the experimental cost is also developed to assess the predictive capability of the stochastic upscaling method used at the strut level and lattice structure level. In comparison with physical compression test results, the proposed methodology of linking the uncertainty quantification with the multi-level stochastic upscaling method enabled an accurate prediction of the elastic behavior of the lattice structure with minimal experimental cost by accounting for the uncertainties induced by the additive manufacturing process. Copyright © 2017 Elsevier Ltd. All rights reserved.
Developments in Stochastic Fuel Efficient Cruise Control and Constrained Control with Applications to Aircraft

NASA Astrophysics Data System (ADS)

McDonough, Kevin K.

The dissertation presents contributions to fuel-efficient control of vehicle speed and constrained control with applications to aircraft. In the first part of this dissertation a stochastic approach to fuel-efficient vehicle speed control is developed. This approach encompasses stochastic modeling of road grade and traffic speed, modeling of fuel consumption through the use of a neural network, and the application of stochastic dynamic programming to generate vehicle speed control policies that are optimized for the trade-off between fuel consumption and travel time. The fuel economy improvements with the proposed policies are quantified through simulations and vehicle experiments. It is shown that the policies lead to the emergence of time-varying vehicle speed patterns that are referred to as time-varying cruise. Through simulations and experiments it is confirmed that these time-varying vehicle speed profiles are more fuel-efficient than driving at a comparable constant speed. Motivated by these results, a simpler implementation strategy that is more appealing for practical implementation is also developed. This strategy relies on a finite state machine and state transition threshold optimization, and its benefits are quantified through model-based simulations and vehicle experiments. Several additional contributions are made to approaches for stochastic modeling of road grade and vehicle speed that include the use of Kullback-Liebler divergence and divergence rate and a stochastic jump-like model for the behavior of the road grade. In the second part of the dissertation, contributions to constrained control with applications to aircraft are described. Recoverable sets and integral safe sets of initial states of constrained closed-loop systems are introduced first and computational procedures of such sets based on linear discrete-time models are given. The use of linear discrete-time models is emphasized as they lead to fast computational procedures. Examples of these sets for aircraft longitudinal and lateral aircraft dynamics are reported, and it is shown that these sets can be larger in size compared to the more commonly used safe sets. An approach to constrained maneuver planning based on chaining recoverable sets or integral safe sets is described and illustrated with a simulation example. To facilitate the application of this maneuver planning approach in aircraft loss of control (LOC) situations when the model is only identified at the current trim condition but when these sets need to be predicted at other flight conditions, the dependence trends of the safe and recoverable sets on aircraft flight conditions are characterized. The scaling procedure to estimate subsets of safe and recoverable sets at one trim condition based on their knowledge at another trim condition is defined. Finally, two control schemes that exploit integral safe sets are proposed. The first scheme, referred to as the controller state governor (CSG), resets the controller state (typically an integrator) to enforce the constraints and enlarge the set of plant states that can be recovered without constraint violation. The second scheme, referred to as the controller state and reference governor (CSRG), combines the controller state governor with the reference governor control architecture and provides the capability of simultaneously modifying the reference command and the controller state to enforce the constraints. Theoretical results that characterize the response properties of both schemes are presented. Examples are reported that illustrate the operation of these schemes on aircraft flight dynamics models and gas turbine engine dynamic models.
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.
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.
Global sensitivity analysis in stochastic simulators of uncertain reaction networks.

PubMed

Navarro Jimenez, M; Le Maître, O P; Knio, O M

2016-12-28

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.
Shallow slip amplification and enhanced tsunami hazard unravelled by dynamic simulations of mega-thrust earthquakes

PubMed Central

Murphy, S.; Scala, A.; Herrero, A.; Lorito, S.; Festa, G.; Trasatti, E.; Tonini, R.; Romano, F.; Molinari, I.; Nielsen, S.

2016-01-01

The 2011 Tohoku earthquake produced an unexpected large amount of shallow slip greatly contributing to the ensuing tsunami. How frequent are such events? How can they be efficiently modelled for tsunami hazard? Stochastic slip models, which can be computed rapidly, are used to explore the natural slip variability; however, they generally do not deal specifically with shallow slip features. We study the systematic depth-dependence of slip along a thrust fault with a number of 2D dynamic simulations using stochastic shear stress distributions and a geometry based on the cross section of the Tohoku fault. We obtain a probability density for the slip distribution, which varies both with depth, earthquake size and whether the rupture breaks the surface. We propose a method to modify stochastic slip distributions according to this dynamically-derived probability distribution. This method may be efficiently applied to produce large numbers of heterogeneous slip distributions for probabilistic tsunami hazard analysis. Using numerous M9 earthquake scenarios, we demonstrate that incorporating the dynamically-derived probability distribution does enhance the conditional probability of exceedance of maximum estimated tsunami wave heights along the Japanese coast. This technique for integrating dynamic features in stochastic models can be extended to any subduction zone and faulting style. PMID:27725733
Global sensitivity analysis in stochastic simulators of uncertain reaction networks

DOE PAGES

Navarro Jimenez, M.; Le Maître, O. P.; Knio, O. M.

2016-12-23

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes thatmore » the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.« less
Global sensitivity analysis in stochastic simulators of uncertain reaction networks

NASA Astrophysics Data System (ADS)

Navarro Jimenez, M.; Le Maître, O. P.; Knio, O. M.

2016-12-01

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.
Wave-optics modeling of the optical-transport line for passive optical stochastic cooling

NASA Astrophysics Data System (ADS)

Andorf, M. B.; Lebedev, V. A.; Piot, P.; Ruan, J.

2018-03-01

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystemcritical to the OSC scheme is the focusing optics used to image radiation from the upstream "pickup" undulator to the downstream "kicker" undulator. In this paper, we present simulation results using wave-optics calculation carried out with the SYNCHROTRON RADIATION WORKSHOP (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.
Stochastic determination of matrix determinants

NASA Astrophysics Data System (ADS)

Dorn, Sebastian; Enßlin, Torsten A.

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations—matrices—acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.
A note on: "A Gaussian-product stochastic Gent-McWilliams parameterization"

NASA Astrophysics Data System (ADS)

Jansen, Malte F.

2017-02-01

This note builds on a recent article by Grooms (2016), which introduces a new stochastic parameterization for eddy buoyancy fluxes. The closure proposed by Grooms accounts for the fact that eddy fluxes arise as the product of two approximately Gaussian variables, which in turn leads to a distinctly non-Gaussian distribution. The directionality of the stochastic eddy fluxes, however, remains somewhat ad-hoc and depends on the reference frame of the chosen coordinate system. This note presents a modification of the approach proposed by Grooms, which eliminates this shortcoming. Eddy fluxes are computed based on a stochastic mixing length model, which leads to a frame invariant formulation. As in the original closure proposed by Grooms, eddy fluxes are proportional to the product of two Gaussian variables, and the parameterization reduces to the Gent and McWilliams parameterization for the mean buyoancy fluxes.

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