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

DTIC Science & Technology

2013-11-01

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

Modelling and analysis of the sugar cataract development process using stochastic hybrid systems.

PubMed

Riley, D; Koutsoukos, X; Riley, K

2009-05-01

Modelling and analysis of biochemical systems such as sugar cataract development (SCD) are critical because they can provide new insights into systems, which cannot be easily tested with experiments; however, they are challenging problems due to the highly coupled chemical reactions that are involved. The authors present a stochastic hybrid system (SHS) framework for modelling biochemical systems and demonstrate the approach for the SCD process. A novel feature of the framework is that it allows modelling the effect of drug treatment on the system dynamics. The authors validate the three sugar cataract models by comparing trajectories computed by two simulation algorithms. Further, the authors present a probabilistic verification method for computing the probability of sugar cataract formation for different chemical concentrations using safety and reachability analysis methods for SHSs. The verification method employs dynamic programming based on a discretisation of the state space and therefore suffers from the curse of dimensionality. To analyse the SCD process, a parallel dynamic programming implementation that can handle large, realistic systems was developed. Although scalability is a limiting factor, this work demonstrates that the proposed method is feasible for realistic biochemical systems.

Formalization, implementation, and modeling of institutional controllers for distributed robotic systems.

PubMed

Pereira, José N; Silva, Porfírio; Lima, Pedro U; Martinoli, Alcherio

2014-01-01

The work described is part of a long term program of introducing institutional robotics, a novel framework for the coordination of robot teams that stems from institutional economics concepts. Under the framework, institutions are cumulative sets of persistent artificial modifications made to the environment or to the internal mechanisms of a subset of agents, thought to be functional for the collective order. In this article we introduce a formal model of institutional controllers based on Petri nets. We define executable Petri nets-an extension of Petri nets that takes into account robot actions and sensing-to design, program, and execute institutional controllers. We use a generalized stochastic Petri net view of the robot team controlled by the institutional controllers to model and analyze the stochastic performance of the resulting distributed robotic system. The ability of our formalism to replicate results obtained using other approaches is assessed through realistic simulations of up to 40 e-puck robots. In particular, we model a robot swarm and its institutional controller with the goal of maintaining wireless connectivity, and successfully compare our model predictions and simulation results with previously reported results, obtained by using finite state automaton models and controllers.

Stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them many leading experts in the field. During the program, the most recent developments, open questions and new ideas in stochastic thermodynamics were presented and discussed. From the talks and debates, the notion of information in stochastic thermodynamics, the fundamental properties of entropy production (rate) in non-equilibrium, the efficiency of small thermodynamic machines and the characteristics of optimal protocols for the applied (cyclic) forces were crystallizing as main themes. Surprisingly, the long-studied adiabatic piston, its peculiarities and its relation to stochastic thermodynamics were also the subject of intense discussions. The comment on the Nordita program Stochastic Thermodynamics published in this issue of Physica Scripta exploits the Jarzynski relation for determining free energy differences in the adiabatic piston. This scientific program and the contribution presented here were made possible by the financial and administrative support of The Nordic Institute for Theoretical Physics.

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.

Sustainable infrastructure system modeling under uncertainties and dynamics

NASA Astrophysics Data System (ADS)

Huang, Yongxi

Infrastructure systems support human activities in transportation, communication, water use, and energy supply. The dissertation research focuses on critical transportation infrastructure and renewable energy infrastructure systems. The goal of the research efforts is to improve the sustainability of the infrastructure systems, with an emphasis on economic viability, system reliability and robustness, and environmental impacts. The research efforts in critical transportation infrastructure concern the development of strategic robust resource allocation strategies in an uncertain decision-making environment, considering both uncertain service availability and accessibility. The study explores the performances of different modeling approaches (i.e., deterministic, stochastic programming, and robust optimization) to reflect various risk preferences. The models are evaluated in a case study of Singapore and results demonstrate that stochastic modeling methods in general offers more robust allocation strategies compared to deterministic approaches in achieving high coverage to critical infrastructures under risks. This general modeling framework can be applied to other emergency service applications, such as, locating medical emergency services. The development of renewable energy infrastructure system development aims to answer the following key research questions: (1) is the renewable energy an economically viable solution? (2) what are the energy distribution and infrastructure system requirements to support such energy supply systems in hedging against potential risks? (3) how does the energy system adapt the dynamics from evolving technology and societal needs in the transition into a renewable energy based society? The study of Renewable Energy System Planning with Risk Management incorporates risk management into its strategic planning of the supply chains. The physical design and operational management are integrated as a whole in seeking mitigations against the potential risks caused by feedstock seasonality and demand uncertainty. Facility spatiality, time variation of feedstock yields, and demand uncertainty are integrated into a two-stage stochastic programming (SP) framework. In the study of Transitional Energy System Modeling under Uncertainty, a multistage stochastic dynamic programming is established to optimize the process of building and operating fuel production facilities during the transition. Dynamics due to the evolving technologies and societal changes and uncertainty due to demand fluctuations are the major issues to be addressed.

Exploring information transmission in gene networks using stochastic simulation and machine learning

NASA Astrophysics Data System (ADS)

Park, Kyemyung; Prüstel, Thorsten; Lu, Yong; Narayanan, Manikandan; Martins, Andrew; Tsang, John

How gene regulatory networks operate robustly despite environmental fluctuations and biochemical noise is a fundamental question in biology. Mathematically the stochastic dynamics of a gene regulatory network can be modeled using chemical master equation (CME), but nonlinearity and other challenges render analytical solutions of CMEs difficult to attain. While approaches of approximation and stochastic simulation have been devised for simple models, obtaining a more global picture of a system's behaviors in high-dimensional parameter space without simplifying the system substantially remains a major challenge. Here we present a new framework for understanding and predicting the behaviors of gene regulatory networks in the context of information transmission among genes. Our approach uses stochastic simulation of the network followed by machine learning of the mapping between model parameters and network phenotypes such as information transmission behavior. We also devised ways to visualize high-dimensional phase spaces in intuitive and informative manners. We applied our approach to several gene regulatory circuit motifs, including both feedback and feedforward loops, to reveal underexplored aspects of their operational behaviors. This work is supported by the Intramural Program of NIAID/NIH.

Pricing foreign equity option with stochastic volatility

NASA Astrophysics Data System (ADS)

Sun, Qi; Xu, Weidong

2015-11-01

In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Lévy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through the use of characteristic function methodology. Numerical tests indicate that stochastic volatility has a dramatic effect on the foreign equity option prices.

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.

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem.

PubMed

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A; Hazen, Terry C; Tiedje, James M; Arkin, Adam P

2014-03-04

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession.

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

A Note on the Stochastic Nature of Feynman Quantum Paths

NASA Astrophysics Data System (ADS)

Botelho, Luiz C. L.

2016-11-01

We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.

New control concepts for uncertain water resources systems: 1. Theory

NASA Astrophysics Data System (ADS)

Georgakakos, Aris P.; Yao, Huaming

1993-06-01

A major complicating factor in water resources systems management is handling unknown inputs. Stochastic optimization provides a sound mathematical framework but requires that enough data exist to develop statistical input representations. In cases where data records are insufficient (e.g., extreme events) or atypical of future input realizations, stochastic methods are inadequate. This article presents a control approach where input variables are only expected to belong in certain sets. The objective is to determine sets of admissible control actions guaranteeing that the system will remain within desirable bounds. The solution is based on dynamic programming and derived for the case where all sets are convex polyhedra. A companion paper (Yao and Georgakakos, this issue) addresses specific applications and problems in relation to reservoir system management.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem

PubMed Central

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D.; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A.; Hazen, Terry C.; Tiedje, James M.; Arkin, Adam P.

2014-01-01

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession. PMID:24550501

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

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

Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu

2016-12-10

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imagingmore » come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.« less

Risk management for sulfur dioxide abatement under multiple uncertainties

NASA Astrophysics Data System (ADS)

Dai, C.; Sun, W.; Tan, Q.; Liu, Y.; Lu, W. T.; Guo, H. C.

2016-03-01

In this study, interval-parameter programming, two-stage stochastic programming (TSP), and conditional value-at-risk (CVaR) were incorporated into a general optimization framework, leading to an interval-parameter CVaR-based two-stage programming (ICTP) method. The ICTP method had several advantages: (i) its objective function simultaneously took expected cost and risk cost into consideration, and also used discrete random variables and discrete intervals to reflect uncertain properties; (ii) it quantitatively evaluated the right tail of distributions of random variables which could better calculate the risk of violated environmental standards; (iii) it was useful for helping decision makers to analyze the trade-offs between cost and risk; and (iv) it was effective to penalize the second-stage costs, as well as to capture the notion of risk in stochastic programming. The developed model was applied to sulfur dioxide abatement in an air quality management system. The results indicated that the ICTP method could be used for generating a series of air quality management schemes under different risk-aversion levels, for identifying desired air quality management strategies for decision makers, and for considering a proper balance between system economy and environmental quality.

Fully probabilistic control design in an adaptive critic framework.

PubMed

Herzallah, Randa; Kárný, Miroslav

2011-12-01

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

Stochastic hybrid systems for studying biochemical processes.

PubMed

Singh, Abhyudai; Hespanha, João P

2010-11-13

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Kernel-Based Approximate Dynamic Programming Using Bellman Residual Elimination

DTIC Science & Technology

2010-02-01

framework is the ability to utilize stochastic system models, thereby allowing the system to make sound decisions even if there is randomness in the system ...approximate policy when a system model is unavailable. We present theoretical analysis of all BRE algorithms proving convergence to the optimal policy in...policies based on MDPs is that there may be parameters of the system model that are poorly known and/or vary with time as the system operates. System

Optimal Operation of Energy Storage in Power Transmission and Distribution

NASA Astrophysics Data System (ADS)

Akhavan Hejazi, Seyed Hossein

In this thesis, we investigate optimal operation of energy storage units in power transmission and distribution grids. At transmission level, we investigate the problem where an investor-owned independently-operated energy storage system seeks to offer energy and ancillary services in the day-ahead and real-time markets. We specifically consider the case where a significant portion of the power generated in the grid is from renewable energy resources and there exists significant uncertainty in system operation. In this regard, we formulate a stochastic programming framework to choose optimal energy and reserve bids for the storage units that takes into account the fluctuating nature of the market prices due to the randomness in the renewable power generation availability. At distribution level, we develop a comprehensive data set to model various stochastic factors on power distribution networks, with focus on networks that have high penetration of electric vehicle charging load and distributed renewable generation. Furthermore, we develop a data-driven stochastic model for energy storage operation at distribution level, where the distribution of nodal voltage and line power flow are modelled as stochastic functions of the energy storage unit's charge and discharge schedules. In particular, we develop new closed-form stochastic models for such key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. By considering the specific characteristics of random variables, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In the proposed stochastic optimization, we consider uncertainty from various elements, such as solar photovoltaic , electric vehicle chargers, and residential baseloads, in the form of discrete probability functions. In the last part of this thesis we address some other resources and concepts for enhancing the operation of power distribution and transmission systems. In particular, we proposed a new framework to determine the best sites, sizes, and optimal payment incentives under special contracts for committed-type DG projects to offset distribution network investment costs. In this framework, the aim is to allocate DGs such that the profit gained by the distribution company is maximized while each DG unit's individual profit is also taken into account to assure that private DG investment remains economical.

A mapping from the unitary to doubly stochastic matrices and symbols on a finite set

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2008-11-01

We prove that the mapping from the unitary to doubly stochastic matrices that maps a unitary matrix (ukl) to the doubly stochastic matrix (|ukl|2) is a submersion at a generic unitary matrix. The proof uses the framework of operator symbols on a finite set.

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

Partial ASL extensions for stochastic programming.

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

Gay, David

2010-03-31

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

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

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

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

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

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

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

2016-07-01

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

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

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

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

A MULTISCALE FRAMEWORK FOR THE STOCHASTIC ASSIMILATION AND MODELING OF UNCERTAINTY ASSOCIATED NCF COMPOSITE MATERIALS

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

Mehrez, Loujaine; Ghanem, Roger; McAuliffe, Colin

multiscale framework to construct stochastic macroscopic constitutive material models is proposed. A spectral projection approach, specifically polynomial chaos expansion, has been used to construct explicit functional relationships between the homogenized properties and input parameters from finer scales. A homogenization engine embedded in Multiscale Designer, software for composite materials, has been used for the upscaling process. The framework is demonstrated using non-crimp fabric composite materials by constructing probabilistic models of the homogenized properties of a non-crimp fabric laminate in terms of the input parameters together with the homogenized properties from finer scales.

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

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

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

A coupled stochastic inverse-management framework for dealing with nonpoint agriculture pollution under groundwater parameter uncertainty

NASA Astrophysics Data System (ADS)

Llopis-Albert, Carlos; Palacios-Marqués, Daniel; Merigó, José M.

2014-04-01

In this paper a methodology for the stochastic management of groundwater quality problems is presented, which can be used to provide agricultural advisory services. A stochastic algorithm to solve the coupled flow and mass transport inverse problem is combined with a stochastic management approach to develop methods for integrating uncertainty; thus obtaining more reliable policies on groundwater nitrate pollution control from agriculture. The stochastic inverse model allows identifying non-Gaussian parameters and reducing uncertainty in heterogeneous aquifers by constraining stochastic simulations to data. The management model determines the spatial and temporal distribution of fertilizer application rates that maximizes net benefits in agriculture constrained by quality requirements in groundwater at various control sites. The quality constraints can be taken, for instance, by those given by water laws such as the EU Water Framework Directive (WFD). Furthermore, the methodology allows providing the trade-off between higher economic returns and reliability in meeting the environmental standards. Therefore, this new technology can help stakeholders in the decision-making process under an uncertainty environment. The methodology has been successfully applied to a 2D synthetic aquifer, where an uncertainty assessment has been carried out by means of Monte Carlo simulation techniques.

Fractional noise destroys or induces a stochastic bifurcation

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

Yang, Qigui, E-mail: qgyang@scut.edu.cn; Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640

2013-12-15

Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

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

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

PubMed

Kilinc, Deniz; Demir, Alper

2017-08-01

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2016-05-01

Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

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...

The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation.

PubMed

Drawert, Brian; Lawson, Michael J; Petzold, Linda; Khammash, Mustafa

2010-02-21

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

PubMed

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

Stochastic Semidefinite Programming: Applications and Algorithms

DTIC Science & Technology

2012-03-03

doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming

Dynamic analysis for solid waste management systems: an inexact multistage integer programming approach.

PubMed

Li, Yongping; Huang, Guohe

2009-03-01

In this study, a dynamic analysis approach based on an inexact multistage integer programming (IMIP) model is developed for supporting municipal solid waste (MSW) management under uncertainty. Techniques of interval-parameter programming and multistage stochastic programming are incorporated within an integer-programming framework. The developed IMIP can deal with uncertainties expressed as probability distributions and interval numbers, and can reflect the dynamics in terms of decisions for waste-flow allocation and facility-capacity expansion over a multistage context. Moreover, the IMIP can be used for analyzing various policy scenarios that are associated with different levels of economic consequences. The developed method is applied to a case study of long-term waste-management planning. The results indicate that reasonable solutions have been generated for binary and continuous variables. They can help generate desired decisions of system-capacity expansion and waste-flow allocation with a minimized system cost and maximized system reliability.

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

NASA Astrophysics Data System (ADS)

Yuan, Ruoshi; Tang, Ying; Ao, Ping

2017-12-01

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

PubMed

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

2006-03-01

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

A Vision for Co-optimized T&D System Interaction with Renewables and Demand Response

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

Anderson, Lindsay; Zéphyr, Luckny; Cardell, Judith B.

The evolution of the power system to the reliable, efficient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. The use of demand response to counterbalance the intermittency of renewable generation brings the consumer into the spotlight. Though individual consumers are interconnected at the low-voltage distribution system, these resources are typically modeled as variables at the transmission network level. In this paper, a vision for cooptimized interaction of distribution systems, or microgrids, with the high-voltage transmission system is described. In this framework, microgrids encompass consumers, distributed renewables and storage. The energy managementmore » system of the microgrid can also sell (buy) excess (necessary) energy from the transmission system. Preliminary work explores price mechanisms to manage the microgrid and its interactions with the transmission system. Wholesale market operations are addressed through the development of scalable stochastic optimization methods that provide the ability to co-optimize interactions between the transmission and distribution systems. Modeling challenges of the co-optimization are addressed via solution methods for large-scale stochastic optimization, including decomposition and stochastic dual dynamic programming.« less

A Stochastic Water Balance Framework for Lowland Watersheds

NASA Astrophysics Data System (ADS)

Thompson, Sally; MacVean, Lissa; Sivapalan, Murugesu

2017-11-01

The water balance dynamics in lowland watersheds are influenced not only by local hydroclimatic controls on energy and water availability, but also by imports of water from the upstream watershed. These imports result in a stochastic extent of inundation in lowland watersheds that is determined by the local flood regime, watershed topography, and the rate of loss processes such as drainage and evaporation. Thus, lowland watershed water balances depend on two stochastic processes—rainfall and local inundation dynamics. Lowlands are high productivity environments that are disproportionately associated with urbanization, high productivity agriculture, biodiversity, and flood risk. Consequently, they are being rapidly altered by human development—generally with clear economic and social motivation—but also with significant trade-offs in ecosystem services provision, directly related to changes in the components and variability of the lowland water balance. We present a stochastic framework to assess the lowland water balance and its sensitivity to two common human interventions—replacement of native vegetation with alternative land uses, and construction of local flood protection levees. By providing analytical solutions for the mean and PDF of the water balance components, the proposed framework provides a mechanism to connect human interventions to hydrologic outcomes, and, in conjunction with ecosystem service production estimates, to evaluate trade-offs associated with lowland watershed development.

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.

A Framework for the Optimization of Discrete-Event Simulation Models

NASA Technical Reports Server (NTRS)

Joshi, B. D.; Unal, R.; White, N. H.; Morris, W. D.

1996-01-01

With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the model. This paper outlines a general purpose framework for optimization of terminating discrete-event simulation models. The methodology combines a chance constraint approach for problem formulation, together with standard statistical estimation and analyses techniques. The applicability of the optimization framework is illustrated by minimizing the operation and support resources of a launch vehicle, through a simulation model.

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

PubMed

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Statement Verification: A Stochastic Model of Judgment and Response.

ERIC Educational Resources Information Center

Wallsten, Thomas S.; Gonzalez-Vallejo, Claudia

1994-01-01

A stochastic judgment model (SJM) is presented as a framework for addressing issues in statement verification and probability judgment. Results of 5 experiments with 264 undergraduates support the validity of the model and provide new information that is interpreted in terms of the SJM. (SLD)

Debates - Stochastic subsurface hydrology from theory to practice: Introduction

NASA Astrophysics Data System (ADS)

Rajaram, Harihar

2016-12-01

This paper introduces the papers in the "Debates - Stochastic Subsurface Hydrology from Theory to Practice" series. Beginning in the 1970s, the field of stochastic subsurface hydrology has been an active field of research, with over 3500 journal publications, of which over 850 have appeared in Water Resources Research. We are fortunate to have insightful contributions from four groups of distinguished authors who discuss the reasons why the advanced research framework established in stochastic subsurface hydrology has not impacted the practice of groundwater flow and transport modeling and design significantly. There is reasonable consensus that a community effort aimed at developing "toolboxes" for applications of stochastic methods will make them more accessible and encourage practical applications.

Stochastic Dynamic Mixed-Integer Programming (SD-MIP)

DTIC Science & Technology

2015-05-05

stochastic linear programming ( SLP ) problems. By using a combination of ideas from cutting plane theory of deterministic MIP (especially disjunctive...developed to date. b) As part of this project, we have also developed tools for very large scale Stochastic Linear Programming ( SLP ). There are...several reasons for this. First, SLP models continue to challenge many of the fastest computers to date, and many applications within the DoD (e.g

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.

Implementation of equity in resource allocation for regional earthquake risk mitigation using two-stage stochastic programming.

PubMed

Zolfaghari, Mohammad R; Peyghaleh, Elnaz

2015-03-01

This article presents a new methodology to implement the concept of equity in regional earthquake risk mitigation programs using an optimization framework. It presents a framework that could be used by decisionmakers (government and authorities) to structure budget allocation strategy toward different seismic risk mitigation measures, i.e., structural retrofitting for different building structural types in different locations and planning horizons. A two-stage stochastic model is developed here to seek optimal mitigation measures based on minimizing mitigation expenditures, reconstruction expenditures, and especially large losses in highly seismically active countries. To consider fairness in the distribution of financial resources among different groups of people, the equity concept is incorporated using constraints in model formulation. These constraints limit inequity to the user-defined level to achieve the equity-efficiency tradeoff in the decision-making process. To present practical application of the proposed model, it is applied to a pilot area in Tehran, the capital city of Iran. Building stocks, structural vulnerability functions, and regional seismic hazard characteristics are incorporated to compile a probabilistic seismic risk model for the pilot area. Results illustrate the variation of mitigation expenditures by location and structural type for buildings. These expenditures are sensitive to the amount of available budget and equity consideration for the constant risk aversion. Most significantly, equity is more easily achieved if the budget is unlimited. Conversely, increasing equity where the budget is limited decreases the efficiency. The risk-return tradeoff, equity-reconstruction expenditures tradeoff, and variation of per-capita expected earthquake loss in different income classes are also presented. © 2015 Society for Risk Analysis.

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

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

PubMed Central

Calcagno, Cristina; Coppo, Mario

2014-01-01

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

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

PubMed

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

2014-01-01

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

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

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

DOE PAGES

Chen, Zheng; Liu, Liu; Mu, Lin

2017-05-03

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof ofmore » the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.« less

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...

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

Optimality, stochasticity, and variability in motor behavior

PubMed Central

Guigon, Emmanuel; Baraduc, Pierre; Desmurget, Michel

2008-01-01

Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability. PMID:18202922

Evaluating a multispecies adaptive management framework: Must uncertainty impede effective decision-making?

USGS Publications Warehouse

Smith, David R.; McGowan, Conor P.; Daily, Jonathan P.; Nichols, James D.; Sweka, John A.; Lyons, James E.

2013-01-01

Application of adaptive management to complex natural resource systems requires careful evaluation to ensure that the process leads to improved decision-making. As part of that evaluation, adaptive policies can be compared with alternative nonadaptive management scenarios. Also, the value of reducing structural (ecological) uncertainty to achieving management objectives can be quantified.A multispecies adaptive management framework was recently adopted by the Atlantic States Marine Fisheries Commission for sustainable harvest of Delaware Bay horseshoe crabs Limulus polyphemus, while maintaining adequate stopover habitat for migrating red knots Calidris canutus rufa, the focal shorebird species. The predictive model set encompassed the structural uncertainty in the relationships between horseshoe crab spawning, red knot weight gain and red knot vital rates. Stochastic dynamic programming was used to generate a state-dependent strategy for harvest decisions given that uncertainty. In this paper, we employed a management strategy evaluation approach to evaluate the performance of this adaptive management framework. Active adaptive management was used by including model weights as state variables in the optimization and reducing structural uncertainty by model weight updating.We found that the value of information for reducing structural uncertainty is expected to be low, because the uncertainty does not appear to impede effective management. Harvest policy responded to abundance levels of both species regardless of uncertainty in the specific relationship that generated those abundances. Thus, the expected horseshoe crab harvest and red knot abundance were similar when the population generating model was uncertain or known, and harvest policy was robust to structural uncertainty as specified.Synthesis and applications. The combination of management strategy evaluation with state-dependent strategies from stochastic dynamic programming was an informative approach to evaluate adaptive management performance and value of learning. Although natural resource decisions are characterized by uncertainty, not all uncertainty will cause decisions to be altered substantially, as we found in this case. It is important to incorporate uncertainty into the decision framing and evaluate the effect of reducing that uncertainty on achieving the desired outcomes

Compressing random microstructures via stochastic Wang tilings.

PubMed

Novák, Jan; Kučerová, Anna; Zeman, Jan

2012-10-01

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

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

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

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

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Stochastic 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.

Stochastic simulation of ecohydrological interactions between vegetation and groundwater

NASA Astrophysics Data System (ADS)

Dwelle, M. C.; Ivanov, V. Y.; Sargsyan, K.

2017-12-01

The complex interactions between groundwater and vegetation in the Amazon rainforest may yield vital ecophysiological interactions in specific landscape niches such as buffering plant water stress during dry season or suppression of water uptake due to anoxic conditions. Representation of such processes is greatly impacted by both external and internal sources of uncertainty: inaccurate data and subjective choice of model representation. The models that can simulate these processes are complex and computationally expensive, and therefore make it difficult to address uncertainty using traditional methods. We use the ecohydrologic model tRIBS+VEGGIE and a novel uncertainty quantification framework applied to the ZF2 watershed near Manaus, Brazil. We showcase the capability of this framework for stochastic simulation of vegetation-hydrology dynamics. This framework is useful for simulation with internal and external stochasticity, but this work will focus on internal variability of groundwater depth distribution and model parameterizations. We demonstrate the capability of this framework to make inferences on uncertain states of groundwater depth from limited in situ data, and how the realizations of these inferences affect the ecohydrological interactions between groundwater dynamics and vegetation function. We place an emphasis on the probabilistic representation of quantities of interest and how this impacts the understanding and interpretation of the dynamics at the groundwater-vegetation interface.

Stochastic maps, continuous approximation, and stable distribution

NASA Astrophysics Data System (ADS)

Kessler, David A.; Burov, Stanislav

2017-10-01

A continuous approximation framework for general nonlinear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the Itô lemma, we obtain a Langevin type of equation. Specifically, we show how nonlinear maps give rise to a Langevin description that involves multiplicative noise. The multiplicative nature of the noise induces an additional effective force, not present in the absence of noise. We further exploit the continuum description and provide an explicit formula for the stable distribution of the stochastic map and conditions for its existence. Our results are in good agreement with numerical simulations of several maps.

Portable parallel portfolio optimization in the Aurora Financial Management System

NASA Astrophysics Data System (ADS)

Laure, Erwin; Moritsch, Hans

2001-07-01

Financial planning problems are formulated as large scale, stochastic, multiperiod, tree structured optimization problems. An efficient technique for solving this kind of problems is the nested Benders decomposition method. In this paper we present a parallel, portable, asynchronous implementation of this technique. To achieve our portability goals we elected the programming language Java for our implementation and used a high level Java based framework, called OpusJava, for expressing the parallelism potential as well as synchronization constraints. Our implementation is embedded within a modular decision support tool for portfolio and asset liability management, the Aurora Financial Management System.

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

NASA Astrophysics Data System (ADS)

Han, Fei; Cheng, Lin

2017-04-01

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.

A fuzzy reinforcement learning approach to power control in wireless transmitters.

PubMed

Vengerov, David; Bambos, Nicholas; Berenji, Hamid R

2005-08-01

We address the issue of power-controlled shared channel access in wireless networks supporting packetized data traffic. We formulate this problem using the dynamic programming framework and present a new distributed fuzzy reinforcement learning algorithm (ACFRL-2) capable of adequately solving a class of problems to which the power control problem belongs. Our experimental results show that the algorithm converges almost deterministically to a neighborhood of optimal parameter values, as opposed to a very noisy stochastic convergence of earlier algorithms. The main tradeoff facing a transmitter is to balance its current power level with future backlog in the presence of stochastically changing interference. Simulation experiments demonstrate that the ACFRL-2 algorithm achieves significant performance gains over the standard power control approach used in CDMA2000. Such a large improvement is explained by the fact that ACFRL-2 allows transmitters to learn implicit coordination policies, which back off under stressful channel conditions as opposed to engaging in escalating "power wars."

Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes.

PubMed

Li, Jinghao; Zhang, Qingling; Yan, Xing-Gang; Spurgeon, Sarah K

2017-09-19

This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.

Dynamic Infinite Mixed-Membership Stochastic Blockmodel.

PubMed

Fan, Xuhui; Cao, Longbing; Xu, Richard Yi Da

2015-09-01

Directional and pairwise measurements are often used to model interactions in a social network setting. The mixed-membership stochastic blockmodel (MMSB) was a seminal work in this area, and its ability has been extended. However, models such as MMSB face particular challenges in modeling dynamic networks, for example, with the unknown number of communities. Accordingly, this paper proposes a dynamic infinite mixed-membership stochastic blockmodel, a generalized framework that extends the existing work to potentially infinite communities inside a network in dynamic settings (i.e., networks are observed over time). Additional model parameters are introduced to reflect the degree of persistence among one's memberships at consecutive time stamps. Under this framework, two specific models, namely mixture time variant and mixture time invariant models, are proposed to depict two different time correlation structures. Two effective posterior sampling strategies and their results are presented, respectively, using synthetic and real-world data.

On convergence of the unscented Kalman-Bucy filter using contraction theory

NASA Astrophysics Data System (ADS)

Maree, J. P.; Imsland, L.; Jouffroy, J.

2016-06-01

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman-Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual-actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman-Bucy filter. The theoretical concepts are illustrated in two case studies.

Dealing with equality and benefit for water allocation in a lake watershed: A Gini-coefficient based stochastic optimization approach

NASA Astrophysics Data System (ADS)

Dai, C.; Qin, X. S.; Chen, Y.; Guo, H. C.

2018-06-01

A Gini-coefficient based stochastic optimization (GBSO) model was developed by integrating the hydrological model, water balance model, Gini coefficient and chance-constrained programming (CCP) into a general multi-objective optimization modeling framework for supporting water resources allocation at a watershed scale. The framework was advantageous in reflecting the conflicting equity and benefit objectives for water allocation, maintaining the water balance of watershed, and dealing with system uncertainties. GBSO was solved by the non-dominated sorting Genetic Algorithms-II (NSGA-II), after the parameter uncertainties of the hydrological model have been quantified into the probability distribution of runoff as the inputs of CCP model, and the chance constraints were converted to the corresponding deterministic versions. The proposed model was applied to identify the Pareto optimal water allocation schemes in the Lake Dianchi watershed, China. The optimal Pareto-front results reflected the tradeoff between system benefit (αSB) and Gini coefficient (αG) under different significance levels (i.e. q) and different drought scenarios, which reveals the conflicting nature of equity and efficiency in water allocation problems. A lower q generally implies a lower risk of violating the system constraints and a worse drought intensity scenario corresponds to less available water resources, both of which would lead to a decreased system benefit and a less equitable water allocation scheme. Thus, the proposed modeling framework could help obtain the Pareto optimal schemes under complexity and ensure that the proposed water allocation solutions are effective for coping with drought conditions, with a proper tradeoff between system benefit and water allocation equity.

Modeling sustainability in renewable energy supply chain systems

NASA Astrophysics Data System (ADS)

Xie, Fei

This dissertation aims at modeling sustainability of renewable fuel supply chain systems against emerging challenges. In particular, the dissertation focuses on the biofuel supply chain system design, and manages to develop advanced modeling framework and corresponding solution methods in tackling challenges in sustaining biofuel supply chain systems. These challenges include: (1) to integrate "environmental thinking" into the long-term biofuel supply chain planning; (2) to adopt multimodal transportation to mitigate seasonality in biofuel supply chain operations; (3) to provide strategies in hedging against uncertainty from conversion technology; and (4) to develop methodologies in long-term sequential planning of the biofuel supply chain under uncertainties. All models are mixed integer programs, which also involves multi-objective programming method and two-stage/multistage stochastic programming methods. In particular for the long-term sequential planning under uncertainties, to reduce the computational challenges due to the exponential expansion of the scenario tree, I also developed efficient ND-Max method which is more efficient than CPLEX and Nested Decomposition method. Through result analysis of four independent studies, it is found that the proposed modeling frameworks can effectively improve the economic performance, enhance environmental benefits and reduce risks due to systems uncertainties for the biofuel supply chain systems.

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki

2013-01-01

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

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.

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.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

NASA Astrophysics Data System (ADS)

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

2017-04-01

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

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 Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

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 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

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

DTIC Science & Technology

2016-08-29

nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics . Nonequilibrium steady states...equilibrium [2], spontaneous relaxation towards equilibrium [3], nonequilibrium steady states generated by fixed thermodynamic forces [4], and stochastic pumps...paradigm, a system driven by fixed thermodynamic forces—such as temperature gradients or chemical potential differences— reaches a steady state in

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Scenario Decomposition for 0-1 Stochastic Programs: Improvements and Asynchronous Implementation

DOE PAGES

Ryan, Kevin; Rajan, Deepak; Ahmed, Shabbir

2016-05-01

We recently proposed scenario decomposition algorithm for stochastic 0-1 programs finds an optimal solution by evaluating and removing individual solutions that are discovered by solving scenario subproblems. In our work, we develop an asynchronous, distributed implementation of the algorithm which has computational advantages over existing synchronous implementations of the algorithm. Improvements to both the synchronous and asynchronous algorithm are proposed. We also test the results on well known stochastic 0-1 programs from the SIPLIB test library and is able to solve one previously unsolved instance from the test set.

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

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

Wu, Wei; Wang, Jin, E-mail: jin.wang.1@stonybrook.edu; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic andmore » thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.« less

A Stochastic Simulation Framework for the Prediction of Strategic Noise Mapping and Occupational Noise Exposure Using the Random Walk Approach

PubMed Central

Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri

2015-01-01

Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019

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…

Stochastic approximation methods-Powerful tools for simulation and optimization: A survey of some recent work on multi-agent systems and cyber-physical systems

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

Yin, George; Wang, Le Yi; Zhang, Hongwei

2014-12-10

Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomlymore » switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.« less

Mimicking Nonequilibrium Steady States with Time-Periodic Driving (Open Source)

DTIC Science & Technology

2016-05-18

nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics . Nonequilibrium steady states...equilibrium [2], spontaneous relaxation towards equilibrium [3], nonequilibrium steady states generated by fixed thermodynamic forces [4], and stochastic pumps...paradigm, a system driven by fixed thermodynamic forces—such as temperature gradients or chemical potential differences— reaches a steady state in

Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

Treesearch

Patrick C. Tobin; Ottar N. Bjornstad

2005-01-01

Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

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

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Stochastic calculus of protein filament formation under spatial confinement

NASA Astrophysics Data System (ADS)

Michaels, Thomas C. T.; Dear, Alexander J.; Knowles, Tuomas P. J.

2018-05-01

The growth of filamentous aggregates from precursor proteins is a process of central importance to both normal and aberrant biology, for instance as the driver of devastating human disorders such as Alzheimer's and Parkinson's diseases. The conventional theoretical framework for describing this class of phenomena in bulk is based upon the mean-field limit of the law of mass action, which implicitly assumes deterministic dynamics. However, protein filament formation processes under spatial confinement, such as in microdroplets or in the cellular environment, show intrinsic variability due to the molecular noise associated with small-volume effects. To account for this effect, in this paper we introduce a stochastic differential equation approach for investigating protein filament formation processes under spatial confinement. Using this framework, we study the statistical properties of stochastic aggregation curves, as well as the distribution of reaction lag-times. Moreover, we establish the gradual breakdown of the correlation between lag-time and normalized growth rate under spatial confinement. Our results establish the key role of spatial confinement in determining the onset of stochasticity in protein filament formation and offer a formalism for studying protein aggregation kinetics in small volumes in terms of the kinetic parameters describing the aggregation dynamics in bulk.

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

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

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

Application of stochastic discrete event system framework for detection of induced low rate TCP attack.

PubMed

Barbhuiya, F A; Agarwal, Mayank; Purwar, Sanketh; Biswas, Santosh; Nandi, Sukumar

2015-09-01

TCP is the most widely accepted transport layer protocol. The major emphasis during the development of TCP was its functionality and efficiency. However, not much consideration was given on studying the possibility of attackers exploiting the protocol, which has lead to several attacks on TCP. This paper deals with the induced low rate TCP attack. Since the attack is relatively new, only a few schemes have been proposed to mitigate it. However, the main issues with these schemes are scalability, change in TCP header, lack of formal frameworks, etc. In this paper, we have adapted the stochastic DES framework for detecting the attack, which addresses most of these issues. We have successfully deployed and tested the proposed DES based IDS on a test bed. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

LAMMPS framework for dynamic bonding and an application modeling DNA

NASA Astrophysics Data System (ADS)

Svaneborg, Carsten

2012-08-01

We have extended the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to support directional bonds and dynamic bonding. The framework supports stochastic formation of new bonds, breakage of existing bonds, and conversion between bond types. Bond formation can be controlled to limit the maximal functionality of a bead with respect to various bond types. Concomitant with the bond dynamics, angular and dihedral interactions are dynamically introduced between newly connected triplets and quartets of beads, where the interaction type is determined from the local pattern of bead and bond types. When breaking bonds, all angular and dihedral interactions involving broken bonds are removed. The framework allows chemical reactions to be modeled, and use it to simulate a simplistic, coarse-grained DNA model. The resulting DNA dynamics illustrates the power of the present framework. Catalogue identifier: AEME_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEME_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence No. of lines in distributed program, including test data, etc.: 2 243 491 No. of bytes in distributed program, including test data, etc.: 771 Distribution format: tar.gz Programming language: C++ Computer: Single and multiple core servers Operating system: Linux/Unix/Windows Has the code been vectorized or parallelized?: Yes. The code has been parallelized by the use of MPI directives. RAM: 1 Gb Classification: 16.11, 16.12 Nature of problem: Simulating coarse-grain models capable of chemistry e.g. DNA hybridization dynamics. Solution method: Extending LAMMPS to handle dynamic bonding and directional bonds. Unusual features: Allows bonds to be created and broken while angular and dihedral interactions are kept consistent. Additional comments: The distribution file for this program is approximately 36 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead an html file giving details of how the program can be obtained is sent. Running time: Hours to days. The examples provided in the distribution take just seconds to run.

ASSESSING POPULATION EXPOSURES TO MULTIPLE AIR POLLUTANTS USING A MECHANISTIC SOURCE-TO-DOSE MODELING FRAMEWORK

EPA Science Inventory

The Modeling Environment for Total Risks studies (MENTOR) system, combined with an extension of the SHEDS (Stochastic Human Exposure and Dose Simulation) methodology, provide a mechanistically consistent framework for conducting source-to-dose exposure assessments of multiple pol...

An application of different dioids in public key cryptography

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

Durcheva, Mariana I., E-mail: mdurcheva66@gmail.com

2014-11-18

Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme ismore » presented.« less

On existence and approximate solutions for stochastic differential equations in the framework of G-Brownian motion

NASA Astrophysics Data System (ADS)

Ullah, Rahman; Faizullah, Faiz

2017-10-01

This investigation aims at studying a Euler-Maruyama (EM) approximate solutions scheme for stochastic differential equations (SDEs) in the framework of G-Brownian motion. Subject to the growth condition, it is shown that the EM solutions Z^q(t) are bounded, in particular, Z^q(t)\\in M_G^2([t_0,T];R^n) . Letting Z( t) as a unique solution to SDEs in the G-framework and utilizing the growth and Lipschitz conditions, the convergence of Z^q(t) to Z( t) is revealed. The Burkholder-Davis-Gundy (BDG) inequalities, Hölder's inequality, Gronwall's inequality and Doobs martingale's inequality are used to derive the results. In addition, without assuming a solution of the stated SDE, we have shown that the Euler-Maruyama approximation sequence {Z^q(t)} is Cauchy in M_G^2([t_0,T];R^n) thus converges to a limit which is a unique solution to SDE in the G-framework.

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.

Multiscale stochastic simulations of chemical reactions with regulated scale separation

NASA Astrophysics Data System (ADS)

Koumoutsakos, Petros; Feigelman, Justin

2013-07-01

We present a coupling of multiscale frameworks with accelerated stochastic simulation algorithms for systems of chemical reactions with disparate propensities. The algorithms regulate the propensities of the fast and slow reactions of the system, using alternating micro and macro sub-steps simulated with accelerated algorithms such as τ and R-leaping. The proposed algorithms are shown to provide significant speedups in simulations of stiff systems of chemical reactions with a trade-off in accuracy as controlled by a regulating parameter. More importantly, the error of the methods exhibits a cutoff phenomenon that allows for optimal parameter choices. Numerical experiments demonstrate that hybrid algorithms involving accelerated stochastic simulations can be, in certain cases, more accurate while faster, than their corresponding stochastic simulation algorithm counterparts.

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

DOE PAGES

Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; ...

2016-04-02

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

DOE PAGES

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; ...

2017-01-25

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to notmore » only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. Furthermore, the algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.« less

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

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.

Tipping point analysis of ocean acoustic noise

NASA Astrophysics Data System (ADS)

Livina, Valerie N.; Brouwer, Albert; Harris, Peter; Wang, Lian; Sotirakopoulos, Kostas; Robinson, Stephen

2018-02-01

We apply tipping point analysis to a large record of ocean acoustic data to identify the main components of the acoustic dynamical system and study possible bifurcations and transitions of the system. The analysis is based on a statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the data using time-series techniques. We analyse long-term and seasonal trends, system states and acoustic fluctuations to reconstruct a one-dimensional stochastic equation to approximate the acoustic dynamical system. We apply potential analysis to acoustic fluctuations and detect several changes in the system states in the past 14 years. These are most likely caused by climatic phenomena. We analyse trends in sound pressure level within different frequency bands and hypothesize a possible anthropogenic impact on the acoustic environment. The tipping point analysis framework provides insight into the structure of the acoustic data and helps identify its dynamic phenomena, correctly reproducing the probability distribution and scaling properties (power-law correlations) of the time series.

Markov State Models of gene regulatory networks.

PubMed

Chu, Brian K; Tse, Margaret J; Sato, Royce R; Read, Elizabeth L

2017-02-06

Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking. The method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models. Application of transition path theory to the constructed Markov State Model decomposes global dynamics into a set of dominant transition paths and associated relative probabilities for stochastic state-switching. In this proof-of-concept study, we found that the Markov State Model provides a general framework for analyzing and visualizing stochastic multistability and state-transitions in gene networks. Our results suggest that this framework-adopted from the field of atomistic Molecular Dynamics-can be a useful tool for quantitative Systems Biology at the network scale.

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.

H∞ state estimation of stochastic memristor-based neural networks with time-varying delays.

PubMed

Bao, Haibo; Cao, Jinde; Kurths, Jürgen; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

This paper addresses the problem of H ∞ state estimation for a class of stochastic memristor-based neural networks with time-varying delays. Under the framework of Filippov solution, the stochastic memristor-based neural networks are transformed into systems with interval parameters. The present paper is the first to investigate the H ∞ state estimation problem for continuous-time Itô-type stochastic memristor-based neural networks. By means of Lyapunov functionals and some stochastic technique, sufficient conditions are derived to ensure that the estimation error system is asymptotically stable in the mean square with a prescribed H ∞ performance. An explicit expression of the state estimator gain is given in terms of linear matrix inequalities (LMIs). Compared with other results, our results reduce control gain and control cost effectively. Finally, numerical simulations are provided to demonstrate the efficiency of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Engineered Resilient Systems: Knowledge Capture and Transfer

DTIC Science & Technology

2014-08-29

development, but the work has not progressed significantly. 71 Peter Kall and Stein W. Wallace, Stochastic Programming, John Wiley & Sons, Chichester, 1994...John Wiley and Sons: Hoboken, 2008. Peter Kall and Stein W. Wallace, Stochastic Programming, John Wiley & Sons, Chichester, 1994. Rhodes, D.H., Lamb

Real-Time Optimal Flood Control Decision Making and Risk Propagation Under Multiple Uncertainties

NASA Astrophysics Data System (ADS)

Zhu, Feilin; Zhong, Ping-An; Sun, Yimeng; Yeh, William W.-G.

2017-12-01

Multiple uncertainties exist in the optimal flood control decision-making process, presenting risks involving flood control decisions. This paper defines the main steps in optimal flood control decision making that constitute the Forecast-Optimization-Decision Making (FODM) chain. We propose a framework for supporting optimal flood control decision making under multiple uncertainties and evaluate risk propagation along the FODM chain from a holistic perspective. To deal with uncertainties, we employ stochastic models at each link of the FODM chain. We generate synthetic ensemble flood forecasts via the martingale model of forecast evolution. We then establish a multiobjective stochastic programming with recourse model for optimal flood control operation. The Pareto front under uncertainty is derived via the constraint method coupled with a two-step process. We propose a novel SMAA-TOPSIS model for stochastic multicriteria decision making. Then we propose the risk assessment model, the risk of decision-making errors and rank uncertainty degree to quantify the risk propagation process along the FODM chain. We conduct numerical experiments to investigate the effects of flood forecast uncertainty on optimal flood control decision making and risk propagation. We apply the proposed methodology to a flood control system in the Daduhe River basin in China. The results indicate that the proposed method can provide valuable risk information in each link of the FODM chain and enable risk-informed decisions with higher reliability.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

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

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Stochastic Feedforward Control Technique

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1990-01-01

Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.

Stochasticity in materials structure, properties, and processing—A review

NASA Astrophysics Data System (ADS)

Hull, Robert; Keblinski, Pawel; Lewis, Dan; Maniatty, Antoinette; Meunier, Vincent; Oberai, Assad A.; Picu, Catalin R.; Samuel, Johnson; Shephard, Mark S.; Tomozawa, Minoru; Vashishth, Deepak; Zhang, Shengbai

2018-03-01

We review the concept of stochasticity—i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes—in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by—or amplify—stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

Approximate Dynamic Programming and Aerial Refueling

DTIC Science & Technology

2007-06-01

by two Army Air Corps de Havilland DH -4Bs (9). While crude by modern standards, the passing of hoses be- tween planes is effectively the same approach...incorporating stochastic data sets. . . . . . . . . . . 106 55 Total Cost Stochastically Trained Simulations versus Deterministically Trained Simulations...incorporating stochastic data sets. 106 To create meaningful results when testing stochastic data, the data sets are av- eraged so that conclusions are not

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

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.

Integrating Sediment Connectivity into Water Resources Management Trough a Graph Theoretic, Stochastic Modeling Framework.

NASA Astrophysics Data System (ADS)

Schmitt, R. J. P.; Castelletti, A.; Bizzi, S.

2014-12-01

Understanding sediment transport processes at the river basin scale, their temporal spectra and spatial patterns is key to identify and minimize morphologic risks associated to channel adjustments processes. This work contributes a stochastic framework for modeling bed-load connectivity based on recent advances in the field (e.g., Bizzi & Lerner, 2013; Czubas & Foufoulas-Georgiu, 2014). It presents river managers with novel indicators from reach scale vulnerability to channel adjustment in large river networks with sparse hydrologic and sediment observations. The framework comprises three steps. First, based on a distributed hydrological model and remotely sensed information, the framework identifies a representative grain size class for each reach. Second, sediment residence time distributions are calculated for each reach in a Monte-Carlo approach applying standard sediment transport equations driven by local hydraulic conditions. Third, a network analysis defines the up- and downstream connectivity for various travel times resulting in characteristic up/downstream connectivity signatures for each reach. Channel vulnerability indicators quantify the imbalance between up/downstream connectivity for each travel time domain, representing process dependent latency of morphologic response. Last, based on the stochastic core of the model, a sensitivity analysis identifies drivers of change and major sources of uncertainty in order to target key detrimental processes and to guide effective gathering of additional data. The application, limitation and integration into a decision analytic framework is demonstrated for a major part of the Red River Basin in Northern Vietnam (179.000 km2). Here, a plethora of anthropic alterations ranging from large reservoir construction to land-use changes results in major downstream deterioration and calls for deriving concerted sediment management strategies to mitigate current and limit future morphologic alterations.

Accelerating numerical solution of stochastic differential equations with CUDA

NASA Astrophysics Data System (ADS)

Januszewski, M.; Kostur, M.

2010-01-01

Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedup can be as high as 675× compared to a typical CPU, which corresponds to several billion integration steps per second. This means that calculations which took weeks can now be completed in less than one hour. This brings stochastic simulation to a completely new level, opening for research a whole new range of problems which can now be solved interactively. Program summaryProgram title: SDE Catalogue identifier: AEFG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Gnu GPL v3 No. of lines in distributed program, including test data, etc.: 978 No. of bytes in distributed program, including test data, etc.: 5905 Distribution format: tar.gz Programming language: CUDA C Computer: any system with a CUDA-compatible GPU Operating system: Linux RAM: 64 MB of GPU memory Classification: 4.3 External routines: The program requires the NVIDIA CUDA Toolkit Version 2.0 or newer and the GNU Scientific Library v1.0 or newer. Optionally gnuplot is recommended for quick visualization of the results. Nature of problem: Direct numerical integration of stochastic differential equations is a computationally intensive problem, due to the necessity of calculating multiple independent realizations of the system. We exploit the inherent parallelism of this problem and perform the calculations on GPUs using the CUDA programming environment. The GPU's ability to execute hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU. Solution method: The stochastic Runge-Kutta method of the second order is applied to integrate the equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system. Unusual features: The numerical solution of the stochastic differential equations in question is performed on a GPU using the CUDA environment. Running time: < 1 minute

Lake eutrophication and environmental change: A viability framework for resilience, vulnerability and adaptive capacity

NASA Astrophysics Data System (ADS)

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

2013-04-01

We present a simple stochastic model of lake eutrophication to demonstrate how the mathematical framework of viability theory fosters operational definitions of resilience, vulnerability and adaptive capacity, and then helps understand which response one should bring to environmental changes. The model represents the phosphorus dynamics, given that high concentrations trigger a regime change from oligotrophic to eutrophic, and causes ecological but also economic losses, for instance from tourism. Phosphorus comes from agricultural inputs upstream of the lake, and we will consider a stochastic input. We consider the system made of both the lake and its upstream region, and explore how to maintain the desirable ecological and economic properties of this system. In the viability framework, we translate these desirable properties into state constraints, then examine how, given the dynamics of the model and the available policy options, the properties can be kept. The set of states for which there exists a policy to keep the properties is called the viability kernel. We extend this framework to both major perturbations and long-term environmental changes. In our model, since the phosphorus inputs and outputs from the lake depend on rainfall, we will focus on extreme rainfall events and long-term changes in the rainfall regime. They can be described as changes in the state of the system, and may displace it outside the viability kernel. Its response can then be described using the concepts of resilience, vulnerability and adaptive capacity. Resilience is the capacity to recover by getting back to the viability kernel where the dynamics keep the system safe, and in this work we assume it to be the first objective of management. Computed for a given trajectory, vulnerability is a measure of the consequence of violating a property. We propose a family of functions from which cost functions and other vulnerability indicators can be derived for any trajectory. There can be several vulnerability functions, representing for instance social, economic or ecological vulnerability, and each representing the violation of the associated property, but these functions need to be ultimately aggregated as a single indicator. Due to the stochastic nature of the system, there is a range of possible trajectories. Statistics can be derived from the probability distribution of the vulnerability of the trajectories. Dynamic programming methods can then yield the policies which, among available policies, minimize a given trajectory. Thus, this viability framework gives indication on both the possible consequences of a hazard or an environmental change, and on the policies that can mitigate or avert it. It also enables to assess the benefits of extending the set of available policy options, and we define adaptive capacity as the reduction in a given vulnerability statistic due to the introduction of new policy options.

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

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

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.

A stochastic model for the normal tissue complication probability (NTCP) and applicationss.

PubMed

Stocks, Theresa; Hillen, Thomas; Gong, Jiafen; Burger, Martin

2017-12-11

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

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

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

FAST: a framework for simulation and analysis of large-scale protein-silicon biosensor circuits.

PubMed

Gu, Ming; Chakrabartty, Shantanu

2013-08-01

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Using Probabilistic Information in Solving Resource Allocation Problems for a Decentralized Firm

DTIC Science & Technology

1978-09-01

deterministic equivalent form of HIQ’s problem (5) by an approach similar to the one used in stochastic programming with simple recourse. See Ziemba [38) or, in...1964). 38. Ziemba , W.T., "Stochastic Programs with Simple Recourse," Technical Report 72-15, Stanford University, Department of Operations Research

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.

Stochastic computing with biomolecular automata

PubMed Central

Adar, Rivka; Benenson, Yaakov; Linshiz, Gregory; Rosner, Amit; Tishby, Naftali; Shapiro, Ehud

2004-01-01

Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure. PMID:15215499

pth moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays.

PubMed

Wang, Fen; Chen, Yuanlong; Liu, Meichun

2018-02-01

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô's differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy-Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

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

PubMed

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

2015-03-17

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

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

PubMed Central

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

2015-01-01

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

The uncertainty of atmospheric processes in planning a hybrid renewable energy system for a non-connected island

NASA Astrophysics Data System (ADS)

Daniil, Vasiliki; Pouliasis, George; Zacharopoulou, Eleni; Demetriou, Evangelos; Manou, Georgia; Chalakatevaki, Maria; Parara, Iliana; Georganta, Xristina; Stamou, Paraskevi; Karali, Sophia; Hadjimitsis, Evanthis; Koudouris, Giannis; Moschos, Evangelos; Roussis, Dimitrios; Papoulakos, Konstantinos; Koskinas, Aristotelis; Pollakis, Giorgos; Gournari, Panagiota; Sakellari, Katerina; Moustakis, Yiannis

2017-04-01

Non-connected islands to the electric gird are often depending on oil-fueled power plants with high unit cost. A hybrid energy system with renewable resources such as wind and solar plants could reduce this cost and also offer more environmental friendly solutions. However, atmospheric processes are characterized by high uncertainty that does not permit harvesting and utilizing full of their potential. Therefore, a more sophisticated framework that somehow incorporates this uncertainty could improve the performance of the system. In this context, we describe several stochastic and financial aspects of this framework. Particularly, we investigate the cross-correlation between several atmospheric processes and the energy demand, the possibility of mixing renewable resources with the conventional ones and in what degree of reliability, and critical financial subsystems such as weather derivatives. A pilot application of the above framework is also presented for a remote island in the Aegean Sea. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly. *The "Stochastics in Energy Resources Management (NTUA)" Team: Nikos Mamasis, Andreas Efstratiadis, Hristos Tyralis, Panayiotis Dimitriadis, Theano Iliopoulou, Georgios Karakatsanis, Katerina Tzouka, Ilias Deligiannis, Vicky Tsoukala, Panos Papanicolaou and Demetris Koutsoyiannis

Fitting of full Cobb-Douglas and full VRTS cost frontiers by solving goal programming problem

NASA Astrophysics Data System (ADS)

Venkateswarlu, B.; Mahaboob, B.; Subbarami Reddy, C.; Madhusudhana Rao, B.

2017-11-01

The present research article first defines two popular production functions viz, Cobb-Douglas and VRTS production frontiers and their dual cost functions and then derives their cost limited maximal outputs. This paper tells us that the cost limited maximal output is cost efficient. Here the one side goal programming problem is proposed by which the full Cobb-Douglas cost frontier, full VRTS frontier can be fitted. This paper includes the framing of goal programming by which stochastic cost frontier and stochastic VRTS frontiers are fitted. Hasan et al. [1] used a parameter approach Stochastic Frontier Approach (SFA) to examine the technical efficiency of the Malaysian domestic banks listed in the Kuala Lumpur stock Exchange (KLSE) market over the period 2005-2010. AshkanHassani [2] exposed Cobb-Douglas Production Functions application in construction schedule crashing and project risk analysis related to the duration of construction projects. Nan Jiang [3] applied Stochastic Frontier analysis to a panel of New Zealand dairy forms in 1998/99-2006/2007.

PIPS-SBB: A Parallel Distributed-Memory Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

DOE PAGES

Munguia, Lluis-Miquel; Oxberry, Geoffrey; Rajan, Deepak

2016-05-01

Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. In order to overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We also show promising results on the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. Finally, we expect the performance of PIPS-SBB to improve furthermore » as more functionality is added in the future.« less

Extremal flows in Wasserstein space

NASA Astrophysics Data System (ADS)

Conforti, Giovanni; Pavon, Michele

2018-06-01

We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm's and Nelson's stochastic mechanics.

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

Malikopoulos, Andreas; Djouadi, Seddik M; Kuruganti, Teja

We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to thosemore » studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.« less

Can a microscopic stochastic model explain the emergence of pain cycles in patients?

NASA Astrophysics Data System (ADS)

Di Patti, Francesca; Fanelli, Duccio

2009-01-01

A stochastic model is introduced here to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: oscillations in the amount of bound receptors are spontaneously manifested, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations, and analytically, through a large size expansion. The claim that our findings could provide a consistent interpretative framework for explaining the emergence of cyclic behaviors in response to analgesic treatments is substantiated.

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2006-01-01

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2007-01-01

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

A theoretical stochastic control framework for adapting radiotherapy to hypoxia

NASA Astrophysics Data System (ADS)

Saberian, Fatemeh; Ghate, Archis; Kim, Minsun

2016-10-01

Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton’s method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course. Through these simulations, we also gain insights into when and why dynamic planning is likely to yield the largest benefits.

A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks

PubMed Central

Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed

2015-01-01

We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056

A modeling framework for optimal long-term care insurance purchase decisions in retirement planning.

PubMed

Gupta, Aparna; Li, Lepeng

2004-05-01

The level of need and costs of obtaining long-term care (LTC) during retired life require that planning for it is an integral part of retirement planning. In this paper, we divide retirement planning into two phases, pre-retirement and post-retirement. On the basis of four interrelated models for health evolution, wealth evolution, LTC insurance premium and coverage, and LTC cost structure, a framework for optimal LTC insurance purchase decisions in the pre-retirement phase is developed. Optimal decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums and coverage. Two-way branching models are used to model stochastic health events and asset returns. The resulting optimization problem is formulated as a dynamic programming problem. We compare the optimal decision under two insurance purchase scenarios: one assumes that insurance is purchased for good and other assumes it may be purchased, relinquished and re-purchased. Sensitivity analysis is performed for the retirement age.

AESS: Accelerated Exact Stochastic Simulation

NASA Astrophysics Data System (ADS)

Jenkins, David D.; Peterson, Gregory D.

2011-12-01

The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution method: The Accelerated Exact Stochastic Simulation (AESS) tool provides implementations of a wide variety of popular variations on the Gillespie method. Users can select the specific algorithm considered most appropriate. Comparisons between the methods and with other available implementations indicate that AESS provides the fastest known implementation of Gillespie's method for a variety of test models. Users may wish to execute ensembles of simulations to sweep parameters or to obtain better statistical results, so AESS supports acceleration of ensembles of simulation using parallel processing with MPI, SSE vector units on x86 processors, and/or using NVIDIA GPUs with CUDA.

Learning Weight Uncertainty with Stochastic Gradient MCMC for Shape Classification

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

Li, Chunyuan; Stevens, Andrew J.; Chen, Changyou

2016-08-10

Learning the representation of shape cues in 2D & 3D objects for recognition is a fundamental task in computer vision. Deep neural networks (DNNs) have shown promising performance on this task. Due to the large variability of shapes, accurate recognition relies on good estimates of model uncertainty, ignored in traditional training of DNNs, typically learned via stochastic optimization. This paper leverages recent advances in stochastic gradient Markov Chain Monte Carlo (SG-MCMC) to learn weight uncertainty in DNNs. It yields principled Bayesian interpretations for the commonly used Dropout/DropConnect techniques and incorporates them into the SG-MCMC framework. Extensive experiments on 2D &more » 3D shape datasets and various DNN models demonstrate the superiority of the proposed approach over stochastic optimization. Our approach yields higher recognition accuracy when used in conjunction with Dropout and Batch-Normalization.« less

On the physical realizability of quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

PubMed

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org.

RAVEN Theory Manual

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

Alfonsi, Andrea; Rabiti, Cristian; Mandelli, Diego

2016-06-01

RAVEN is a software framework able to perform parametric and stochastic analysis based on the response of complex system codes. The initial development was aimed at providing dynamic risk analysis capabilities to the thermohydraulic code RELAP-7, currently under development at Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose stochastic and uncertainty quantification platform, capable of communicating with any system code. In fact, the provided Application Programming Interfaces (APIs) allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by input filesmore » or via python interfaces. RAVEN is capable of investigating system response and explore input space using various sampling schemes such as Monte Carlo, grid, or Latin hypercube. However, RAVEN strength lies in its system feature discovery capabilities such as: constructing limit surfaces, separating regions of the input space leading to system failure, and using dynamic supervised learning techniques. The development of RAVEN started in 2012 when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework arose. RAVEN’s principal assignment is to provide the necessary software and algorithms in order to employ the concepts developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just to identify the frequency of an event potentially leading to a system failure, but the proximity (or lack thereof) to key safety-related events. Hence, the approach is interested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. peak pressure in a pipe) is exceeded under certain conditions. Most of the capabilities, implemented having RELAP-7 as a principal focus, are easily deployable to other system codes. For this reason, several side activates have been employed (e.g. RELAP5-3D, any MOOSE-based App, etc.) or are currently ongoing for coupling RAVEN with several different software. The aim of this document is to provide a set of commented examples that can help the user to become familiar with the RAVEN code usage.« less

NEVESIM: event-driven neural simulation framework with a Python interface.

PubMed

Pecevski, Dejan; Kappel, David; Jonke, Zeno

2014-01-01

NEVESIM is a software package for event-driven simulation of networks of spiking neurons with a fast simulation core in C++, and a scripting user interface in the Python programming language. It supports simulation of heterogeneous networks with different types of neurons and synapses, and can be easily extended by the user with new neuron and synapse types. To enable heterogeneous networks and extensibility, NEVESIM is designed to decouple the simulation logic of communicating events (spikes) between the neurons at a network level from the implementation of the internal dynamics of individual neurons. In this paper we will present the simulation framework of NEVESIM, its concepts and features, as well as some aspects of the object-oriented design approaches and simulation strategies that were utilized to efficiently implement the concepts and functionalities of the framework. We will also give an overview of the Python user interface, its basic commands and constructs, and also discuss the benefits of integrating NEVESIM with Python. One of the valuable capabilities of the simulator is to simulate exactly and efficiently networks of stochastic spiking neurons from the recently developed theoretical framework of neural sampling. This functionality was implemented as an extension on top of the basic NEVESIM framework. Altogether, the intended purpose of the NEVESIM framework is to provide a basis for further extensions that support simulation of various neural network models incorporating different neuron and synapse types that can potentially also use different simulation strategies.

NEVESIM: event-driven neural simulation framework with a Python interface

PubMed Central

Pecevski, Dejan; Kappel, David; Jonke, Zeno

2014-01-01

NEVESIM is a software package for event-driven simulation of networks of spiking neurons with a fast simulation core in C++, and a scripting user interface in the Python programming language. It supports simulation of heterogeneous networks with different types of neurons and synapses, and can be easily extended by the user with new neuron and synapse types. To enable heterogeneous networks and extensibility, NEVESIM is designed to decouple the simulation logic of communicating events (spikes) between the neurons at a network level from the implementation of the internal dynamics of individual neurons. In this paper we will present the simulation framework of NEVESIM, its concepts and features, as well as some aspects of the object-oriented design approaches and simulation strategies that were utilized to efficiently implement the concepts and functionalities of the framework. We will also give an overview of the Python user interface, its basic commands and constructs, and also discuss the benefits of integrating NEVESIM with Python. One of the valuable capabilities of the simulator is to simulate exactly and efficiently networks of stochastic spiking neurons from the recently developed theoretical framework of neural sampling. This functionality was implemented as an extension on top of the basic NEVESIM framework. Altogether, the intended purpose of the NEVESIM framework is to provide a basis for further extensions that support simulation of various neural network models incorporating different neuron and synapse types that can potentially also use different simulation strategies. PMID:25177291

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...

An inexact multistage fuzzy-stochastic programming for regional electric power system management constrained by environmental quality.

PubMed

Fu, Zhenghui; Wang, Han; Lu, Wentao; Guo, Huaicheng; Li, Wei

2017-12-01

Electric power system involves different fields and disciplines which addressed the economic system, energy system, and environment system. Inner uncertainty of this compound system would be an inevitable problem. Therefore, an inexact multistage fuzzy-stochastic programming (IMFSP) was developed for regional electric power system management constrained by environmental quality. A model which concluded interval-parameter programming, multistage stochastic programming, and fuzzy probability distribution was built to reflect the uncertain information and dynamic variation in the case study, and the scenarios under different credibility degrees were considered. For all scenarios under consideration, corrective actions were allowed to be taken dynamically in accordance with the pre-regulated policies and the uncertainties in reality. The results suggest that the methodology is applicable to handle the uncertainty of regional electric power management systems and help the decision makers to establish an effective development plan.

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 continuum dislocation dynamics framework for plasticity of polycrystalline materials

NASA Astrophysics Data System (ADS)

Askari, Hesam Aldin

The objective of this research is to investigate the mechanical response of polycrystals in different settings to identify the mechanisms that give rise to specific response observed in the deformation process. Particularly the large deformation of magnesium alloys and yield properties of copper in small scales are investigated. We develop a continuum dislocation dynamics framework based on dislocation mechanisms and interaction laws and implement this formulation in a viscoplastic self-consistent scheme to obtain the mechanical response in a polycrystalline system. The versatility of this method allows various applications in the study of problems involving large deformation, study of microstructure and its evolution, superplasticity, study of size effect in polycrystals and stochastic plasticity. The findings from the numerical solution are compared to the experimental results to validate the simulation results. We apply this framework to study the deformation mechanisms in magnesium alloys at moderate to fast strain rates and room temperature to 450 °C. Experiments for the same range of strain rates and temperatures were carried out to obtain the mechanical and material properties, and to compare with the numerical results. The numerical approach for magnesium is divided into four main steps; 1) room temperature unidirectional loading 2) high temperature deformation without grain boundary sliding 3) high temperature with grain boundary sliding mechanism 4) room temperature cyclic loading. We demonstrate the capability of our modeling approach in prediction of mechanical properties and texture evolution and discuss the improvement obtained by using the continuum dislocation dynamics method. The framework was also applied to nano-sized copper polycrystals to study the yield properties at small scales and address the observed yield scatter. By combining our developed method with a Monte Carlo simulation approach, the stochastic plasticity at small length scales was studied and the sources of the uncertainty in the polycrystalline structure are discussed. Our results suggest that the stochastic response is mainly because of a) stochastic plasticity due to dislocation substructure inside crystals and b) the microstructure of the polycrystalline material. The extent of the uncertainty is correlated to the "effective cell length" in the sampling procedure whether using simulations and experimental approach.

A stochastic context free grammar based framework for analysis of protein sequences

PubMed Central

Dyrka, Witold; Nebel, Jean-Christophe

2009-01-01

Background In the last decade, there have been many applications of formal language theory in bioinformatics such as RNA structure prediction and detection of patterns in DNA. However, in the field of proteomics, the size of the protein alphabet and the complexity of relationship between amino acids have mainly limited the application of formal language theory to the production of grammars whose expressive power is not higher than stochastic regular grammars. However, these grammars, like other state of the art methods, cannot cover any higher-order dependencies such as nested and crossing relationships that are common in proteins. In order to overcome some of these limitations, we propose a Stochastic Context Free Grammar based framework for the analysis of protein sequences where grammars are induced using a genetic algorithm. Results This framework was implemented in a system aiming at the production of binding site descriptors. These descriptors not only allow detection of protein regions that are involved in these sites, but also provide insight in their structure. Grammars were induced using quantitative properties of amino acids to deal with the size of the protein alphabet. Moreover, we imposed some structural constraints on grammars to reduce the extent of the rule search space. Finally, grammars based on different properties were combined to convey as much information as possible. Evaluation was performed on sites of various sizes and complexity described either by PROSITE patterns, domain profiles or a set of patterns. Results show the produced binding site descriptors are human-readable and, hence, highlight biologically meaningful features. Moreover, they achieve good accuracy in both annotation and detection. In addition, findings suggest that, unlike current state-of-the-art methods, our system may be particularly suited to deal with patterns shared by non-homologous proteins. Conclusion A new Stochastic Context Free Grammar based framework has been introduced allowing the production of binding site descriptors for analysis of protein sequences. Experiments have shown that not only is this new approach valid, but produces human-readable descriptors for binding sites which have been beyond the capability of current machine learning techniques. PMID:19814800

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.

A mathematical model for maximizing the value of phase 3 drug development portfolios incorporating budget constraints and risk.

PubMed

Patel, Nitin R; Ankolekar, Suresh; Antonijevic, Zoran; Rajicic, Natasa

2013-05-10

We describe a value-driven approach to optimizing pharmaceutical portfolios. Our approach incorporates inputs from research and development and commercial functions by simultaneously addressing internal and external factors. This approach differentiates itself from current practices in that it recognizes the impact of study design parameters, sample size in particular, on the portfolio value. We develop an integer programming (IP) model as the basis for Bayesian decision analysis to optimize phase 3 development portfolios using expected net present value as the criterion. We show how this framework can be used to determine optimal sample sizes and trial schedules to maximize the value of a portfolio under budget constraints. We then illustrate the remarkable flexibility of the IP model to answer a variety of 'what-if' questions that reflect situations that arise in practice. We extend the IP model to a stochastic IP model to incorporate uncertainty in the availability of drugs from earlier development phases for phase 3 development in the future. We show how to use stochastic IP to re-optimize the portfolio development strategy over time as new information accumulates and budget changes occur. Copyright © 2013 John Wiley & Sons, Ltd.

A reliability-based maintenance technicians' workloads optimisation model with stochastic consideration

NASA Astrophysics Data System (ADS)

Ighravwe, D. E.; Oke, S. A.; Adebiyi, K. A.

2016-06-01

The growing interest in technicians' workloads research is probably associated with the recent surge in competition. This was prompted by unprecedented technological development that triggers changes in customer tastes and preferences for industrial goods. In a quest for business improvement, this worldwide intense competition in industries has stimulated theories and practical frameworks that seek to optimise performance in workplaces. In line with this drive, the present paper proposes an optimisation model which considers technicians' reliability that complements factory information obtained. The information used emerged from technicians' productivity and earned-values using the concept of multi-objective modelling approach. Since technicians are expected to carry out routine and stochastic maintenance work, we consider these workloads as constraints. The influence of training, fatigue and experiential knowledge of technicians on workload management was considered. These workloads were combined with maintenance policy in optimising reliability, productivity and earned-values using the goal programming approach. Practical datasets were utilised in studying the applicability of the proposed model in practice. It was observed that our model was able to generate information that practicing maintenance engineers can apply in making more informed decisions on technicians' management.

Using Multi-Objective Genetic Programming to Synthesize Stochastic Processes

NASA Astrophysics Data System (ADS)

Ross, Brian; Imada, Janine

Genetic programming is used to automatically construct stochastic processes written in the stochastic π-calculus. Grammar-guided genetic programming constrains search to useful process algebra structures. The time-series behaviour of a target process is denoted with a suitable selection of statistical feature tests. Feature tests can permit complex process behaviours to be effectively evaluated. However, they must be selected with care, in order to accurately characterize the desired process behaviour. Multi-objective evaluation is shown to be appropriate for this application, since it permits heterogeneous statistical feature tests to reside as independent objectives. Multiple undominated solutions can be saved and evaluated after a run, for determination of those that are most appropriate. Since there can be a vast number of candidate solutions, however, strategies for filtering and analyzing this set are required.

A Stochastic Framework for Evaluating Seizure Prediction Algorithms Using Hidden Markov Models

PubMed Central

Wong, Stephen; Gardner, Andrew B.; Krieger, Abba M.; Litt, Brian

2007-01-01

Responsive, implantable stimulation devices to treat epilepsy are now in clinical trials. New evidence suggests that these devices may be more effective when they deliver therapy before seizure onset. Despite years of effort, prospective seizure prediction, which could improve device performance, remains elusive. In large part, this is explained by lack of agreement on a statistical framework for modeling seizure generation and a method for validating algorithm performance. We present a novel stochastic framework based on a three-state hidden Markov model (HMM) (representing interictal, preictal, and seizure states) with the feature that periods of increased seizure probability can transition back to the interictal state. This notion reflects clinical experience and may enhance interpretation of published seizure prediction studies. Our model accommodates clipped EEG segments and formalizes intuitive notions regarding statistical validation. We derive equations for type I and type II errors as a function of the number of seizures, duration of interictal data, and prediction horizon length and we demonstrate the model’s utility with a novel seizure detection algorithm that appeared to predicted seizure onset. We propose this framework as a vital tool for designing and validating prediction algorithms and for facilitating collaborative research in this area. PMID:17021032

Designing a robust activity recognition framework for health and exergaming using wearable sensors.

PubMed

Alshurafa, Nabil; Xu, Wenyao; Liu, Jason J; Huang, Ming-Chun; Mortazavi, Bobak; Roberts, Christian K; Sarrafzadeh, Majid

2014-09-01

Detecting human activity independent of intensity is essential in many applications, primarily in calculating metabolic equivalent rates and extracting human context awareness. Many classifiers that train on an activity at a subset of intensity levels fail to recognize the same activity at other intensity levels. This demonstrates weakness in the underlying classification method. Training a classifier for an activity at every intensity level is also not practical. In this paper, we tackle a novel intensity-independent activity recognition problem where the class labels exhibit large variability, the data are of high dimensionality, and clustering algorithms are necessary. We propose a new robust stochastic approximation framework for enhanced classification of such data. Experiments are reported using two clustering techniques, K-Means and Gaussian Mixture Models. The stochastic approximation algorithm consistently outperforms other well-known classification schemes which validate the use of our proposed clustered data representation. We verify the motivation of our framework in two applications that benefit from intensity-independent activity recognition. The first application shows how our framework can be used to enhance energy expenditure calculations. The second application is a novel exergaming environment aimed at using games to reward physical activity performed throughout the day, to encourage a healthy lifestyle.

Solution Methods for Stochastic Dynamic Linear Programs.

DTIC Science & Technology

1980-12-01

16, No. 11, pp. 652-675, July 1970. [28] Glassey, C.R., "Dynamic linear programs for production scheduling", OR 19, pp. 45-56. 1971 . 129 Glassey, C.R...Huang, C.C., I. Vertinsky, W.T. Ziemba, ’Sharp bounds on the value of perfect information", OR 25, pp. 128-139, 1977. [37 Kall , P., ’Computational... 1971 . [701 Ziemba, W.T., *Computational algorithms for convex stochastic programs with simple recourse", OR 8, pp. 414-431, 1970. 131 UNCLASSI FIED

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

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

Liang, Faming; Cheng, Yichen; Lin, Guang

2014-06-13

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« 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.

StochKit2: software for discrete stochastic simulation of biochemical systems with events.

PubMed

Sanft, Kevin R; Wu, Sheng; Roh, Min; Fu, Jin; Lim, Rone Kwei; Petzold, Linda R

2011-09-01

StochKit2 is the first major upgrade of the popular StochKit stochastic simulation software package. StochKit2 provides highly efficient implementations of several variants of Gillespie's stochastic simulation algorithm (SSA), and tau-leaping with automatic step size selection. StochKit2 features include automatic selection of the optimal SSA method based on model properties, event handling, and automatic parallelism on multicore architectures. The underlying structure of the code has been completely updated to provide a flexible framework for extending its functionality. StochKit2 runs on Linux/Unix, Mac OS X and Windows. It is freely available under GPL version 3 and can be downloaded from http://sourceforge.net/projects/stochkit/. petzold@engineering.ucsb.edu.

A two-stage mixed-integer fuzzy programming with interval-valued membership functions approach for flood-diversion planning.

PubMed

Wang, S; Huang, G H

2013-03-15

Flood disasters have been extremely severe in recent decades, and they account for about one third of all natural catastrophes throughout the world. In this study, a two-stage mixed-integer fuzzy programming with interval-valued membership functions (TMFP-IMF) approach is developed for flood-diversion planning under uncertainty. TMFP-IMF integrates the fuzzy flexible programming, two-stage stochastic programming, and integer programming within a general framework. A concept of interval-valued fuzzy membership function is introduced to address complexities of system uncertainties. TMFP-IMF can not only deal with uncertainties expressed as fuzzy sets and probability distributions, but also incorporate pre-regulated water-diversion policies directly into its optimization process. TMFP-IMF is applied to a hypothetical case study of flood-diversion planning for demonstrating its applicability. Results indicate that reasonable solutions can be generated for binary and continuous variables. A variety of flood-diversion and capacity-expansion schemes can be obtained under four scenarios, which enable decision makers (DMs) to identify the most desired one based on their perceptions and attitudes towards the objective-function value and constraints. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Global identification of stochastic dynamical systems under different pseudo-static operating conditions: The functionally pooled ARMAX case

NASA Astrophysics Data System (ADS)

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

2017-01-01

The identification of a single global model for a stochastic dynamical system operating under various conditions is considered. Each operating condition is assumed to have a pseudo-static effect on the dynamics and be characterized by a single measurable scheduling variable. Identification is accomplished within a recently introduced Functionally Pooled (FP) framework, which offers a number of advantages over Linear Parameter Varying (LPV) identification techniques. The focus of the work is on the extension of the framework to include the important FP-ARMAX model case. Compared to their simpler FP-ARX counterparts, FP-ARMAX models are much more general and offer improved flexibility in describing various types of stochastic noise, but at the same time lead to a more complicated, non-quadratic, estimation problem. Prediction Error (PE), Maximum Likelihood (ML), and multi-stage estimation methods are postulated, and the PE estimator optimality, in terms of consistency and asymptotic efficiency, is analytically established. The postulated estimators are numerically assessed via Monte Carlo experiments, while the effectiveness of the approach and its superiority over its FP-ARX counterpart are demonstrated via an application case study pertaining to simulated railway vehicle suspension dynamics under various mass loading conditions.

The Influence of Turbulent Coherent Structure on Suspended Sediment Transport

NASA Astrophysics Data System (ADS)

Huang, S. H.; Tsai, C.

2017-12-01

The anomalous diffusion of turbulent sedimentation has received more and more attention in recent years. With the advent of new instruments and technologies, researchers have found that sediment behavior may deviate from Fickian assumptions when particles are heavier. In particle-laden flow, bursting phenomena affects instantaneous local concentrations, and seems to carry suspended particles for a longer distance. Instead of the pure diffusion process in an analogy to Brownian motion, Levy flight which allows particles to move in response to bursting phenomena is suspected to be more suitable for describing particle movement in turbulence. And the fractional differential equation is a potential candidate to improve the concentration profile. However, stochastic modeling (the Differential Chapmen-Kolmogorov Equation) also provides an alternative mathematical framework to describe system transits between different states through diffusion/the jump processes. Within this framework, the stochastic particle tracking model linked with advection diffusion equation is a powerful tool to simulate particle locations in the flow field. By including the jump process to this model, a more comprehensive description for suspended sediment transport can be provided with a better physical insight. This study also shows the adaptability and expandability of the stochastic particle tracking model for suspended sediment transport modeling.

Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes

PubMed Central

Dobos, László; Király, András; Abonyi, János

2012-01-01

Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. PMID:23213298

Stochastic information transfer from cochlear implant electrodes to auditory nerve fibers

NASA Astrophysics Data System (ADS)

Gao, Xiao; Grayden, David B.; McDonnell, Mark D.

2014-08-01

Cochlear implants, also called bionic ears, are implanted neural prostheses that can restore lost human hearing function by direct electrical stimulation of auditory nerve fibers. Previously, an information-theoretic framework for numerically estimating the optimal number of electrodes in cochlear implants has been devised. This approach relies on a model of stochastic action potential generation and a discrete memoryless channel model of the interface between the array of electrodes and the auditory nerve fibers. Using these models, the stochastic information transfer from cochlear implant electrodes to auditory nerve fibers is estimated from the mutual information between channel inputs (the locations of electrodes) and channel outputs (the set of electrode-activated nerve fibers). Here we describe a revised model of the channel output in the framework that avoids the side effects caused by an "ambiguity state" in the original model and also makes fewer assumptions about perceptual processing in the brain. A detailed comparison of how different assumptions on fibers and current spread modes impact on the information transfer in the original model and in the revised model is presented. We also mathematically derive an upper bound on the mutual information in the revised model, which becomes tighter as the number of electrodes increases. We found that the revised model leads to a significantly larger maximum mutual information and corresponding number of electrodes compared with the original model and conclude that the assumptions made in this part of the modeling framework are crucial to the model's overall utility.

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.

The ESPAT tool: a general-purpose DSS shell for solving stochastic optimization problems in complex river-aquifer systems

NASA Astrophysics Data System (ADS)

Macian-Sorribes, Hector; Pulido-Velazquez, Manuel; Tilmant, Amaury

2015-04-01

Stochastic programming methods are better suited to deal with the inherent uncertainty of inflow time series in water resource management. However, one of the most important hurdles in their use in practical implementations is the lack of generalized Decision Support System (DSS) shells, usually based on a deterministic approach. The purpose of this contribution is to present a general-purpose DSS shell, named Explicit Stochastic Programming Advanced Tool (ESPAT), able to build and solve stochastic programming problems for most water resource systems. It implements a hydro-economic approach, optimizing the total system benefits as the sum of the benefits obtained by each user. It has been coded using GAMS, and implements a Microsoft Excel interface with a GAMS-Excel link that allows the user to introduce the required data and recover the results. Therefore, no GAMS skills are required to run the program. The tool is divided into four modules according to its capabilities: 1) the ESPATR module, which performs stochastic optimization procedures in surface water systems using a Stochastic Dual Dynamic Programming (SDDP) approach; 2) the ESPAT_RA module, which optimizes coupled surface-groundwater systems using a modified SDDP approach; 3) the ESPAT_SDP module, capable of performing stochastic optimization procedures in small-size surface systems using a standard SDP approach; and 4) the ESPAT_DET module, which implements a deterministic programming procedure using non-linear programming, able to solve deterministic optimization problems in complex surface-groundwater river basins. The case study of the Mijares river basin (Spain) is used to illustrate the method. It consists in two reservoirs in series, one aquifer and four agricultural demand sites currently managed using historical (XIV century) rights, which give priority to the most traditional irrigation district over the XX century agricultural developments. Its size makes it possible to use either the SDP or the SDDP methods. The independent use of surface and groundwater can be examined with and without the aquifer. The ESPAT_DET, ESPATR and ESPAT_SDP modules were executed for the surface system, while the ESPAT_RA and the ESPAT_DET modules were run for the surface-groundwater system. The surface system's results show a similar performance between the ESPAT_SDP and ESPATR modules, with outperform the one showed by the current policies besides being outperformed by the ESPAT_DET results, which have the advantage of the perfect foresight. The surface-groundwater system's results show a robust situation in which the differences between the module's results and the current policies are lower due the use of pumped groundwater in the XX century crops when surface water is scarce. The results are realistic, with the deterministic optimization outperforming the stochastic one, which at the same time outperforms the current policies; showing that the tool is able to stochastically optimize river-aquifer water resources systems. We are currently working in the application of these tools in the analysis of changes in systems' operation under global change conditions. ACKNOWLEDGEMENT: This study has been partially supported by the IMPADAPT project (CGL2013-48424-C2-1-R) with Spanish MINECO (Ministerio de Economía y Competitividad) funds.

Stochastic multifractal forecasts: from theory to applications in radar meteorology

NASA Astrophysics Data System (ADS)

da Silva Rocha Paz, Igor; Tchiguirinskaia, Ioulia; Schertzer, Daniel

2017-04-01

Radar meteorology has been very inspiring for the development of multifractals. It has enabled to work on a 3D+1 field with many challenging applications, including predictability and stochastic forecasts, especially nowcasts that are particularly demanding in computation speed. Multifractals are indeed parsimonious stochastic models that require only a few physically meaningful parameters, e.g. Universal Multifractal (UM) parameters, because they are based on non-trivial symmetries of nonlinear equations. We first recall the physical principles of multifractal predictability and predictions, which are so closely related that the latter correspond to the most optimal predictions in the multifractal framework. Indeed, these predictions are based on the fundamental duality of a relatively slow decay of large scale structures and an injection of new born small scale structures. Overall, this triggers a mulfitractal inverse cascade of unpredictability. With the help of high resolution rainfall radar data (≈ 100 m), we detail and illustrate the corresponding stochastic algorithm in the framework of (causal) UM Fractionally Integrated Flux models (UM-FIF), where the rainfall field is obtained with the help of a fractional integration of a conservative multifractal flux, whose average is strictly scale invariant (like the energy flux in a dynamic cascade). Whereas, the introduction of small structures is rather straightforward, the deconvolution of the past of the field is more subtle, but nevertheless achievable, to obtain the past of the flux. Then, one needs to only fractionally integrate a multiplicative combination of past and future fluxes to obtain a nowcast realisation.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Evolution in fluctuating environments: decomposing selection into additive components of the Robertson-Price equation.

PubMed

Engen, Steinar; Saether, Bernt-Erik

2014-03-01

We analyze the stochastic components of the Robertson-Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.

K-Minimax Stochastic Programming Problems

NASA Astrophysics Data System (ADS)

Nedeva, C.

2007-10-01

The purpose of this paper is a discussion of a numerical procedure based on the simplex method for stochastic optimization problems with partially known distribution functions. The convergence of this procedure is proved by the condition on dual problems.

Next generation of weather generators on web service framework

NASA Astrophysics Data System (ADS)

Chinnachodteeranun, R.; Hung, N. D.; Honda, K.; Ines, A. V. M.

2016-12-01

Weather generator is a statistical model that synthesizes possible realization of long-term historical weather in future. It generates several tens to hundreds of realizations stochastically based on statistical analysis. Realization is essential information as a crop modeling's input for simulating crop growth and yield. Moreover, they can be contributed to analyzing uncertainty of weather to crop development stage and to decision support system on e.g. water management and fertilizer management. Performing crop modeling requires multidisciplinary skills which limit the usage of weather generator only in a research group who developed it as well as a barrier for newcomers. To improve the procedures of performing weather generators as well as the methodology to acquire the realization in a standard way, we implemented a framework for providing weather generators as web services, which support service interoperability. Legacy weather generator programs were wrapped in the web service framework. The service interfaces were implemented based on an international standard that was Sensor Observation Service (SOS) defined by Open Geospatial Consortium (OGC). Clients can request realizations generated by the model through SOS Web service. Hierarchical data preparation processes required for weather generator are also implemented as web services and seamlessly wired. Analysts and applications can invoke services over a network easily. The services facilitate the development of agricultural applications and also reduce the workload of analysts on iterative data preparation and handle legacy weather generator program. This architectural design and implementation can be a prototype for constructing further services on top of interoperable sensor network system. This framework opens an opportunity for other sectors such as application developers and scientists in other fields to utilize weather generators.

Optoelectronic analogs of self-programming neural nets - Architecture and methodologies for implementing fast stochastic learning by simulated annealing

NASA Technical Reports Server (NTRS)

Farhat, Nabil H.

1987-01-01

Self-organization and learning is a distinctive feature of neural nets and processors that sets them apart from conventional approaches to signal processing. It leads to self-programmability which alleviates the problem of programming complexity in artificial neural nets. In this paper architectures for partitioning an optoelectronic analog of a neural net into distinct layers with prescribed interconnectivity pattern to enable stochastic learning by simulated annealing in the context of a Boltzmann machine are presented. Stochastic learning is of interest because of its relevance to the role of noise in biological neural nets. Practical considerations and methodologies for appreciably accelerating stochastic learning in such a multilayered net are described. These include the use of parallel optical computing of the global energy of the net, the use of fast nonvolatile programmable spatial light modulators to realize fast plasticity, optical generation of random number arrays, and an adaptive noisy thresholding scheme that also makes stochastic learning more biologically plausible. The findings reported predict optoelectronic chips that can be used in the realization of optical learning machines.

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.

A New Mathematical Framework for Design Under Uncertainty

DTIC Science & Technology

2016-05-05

blending multiple information sources via auto-regressive stochastic modeling. A computationally efficient machine learning framework is developed based on...sion and machine learning approaches; see Fig. 1. This will lead to a comprehensive description of system performance with less uncertainty than in the...Bayesian optimization of super-cavitating hy- drofoils The goal of this study is to demonstrate the capabilities of statistical learning and

Conditional Stochastic Models in Reduced Space: Towards Efficient Simulation of Tropical Cyclone Precipitation Patterns

NASA Astrophysics Data System (ADS)

Dodov, B.

2017-12-01

Stochastic simulation of realistic and statistically robust patterns of Tropical Cyclone (TC) induced precipitation is a challenging task. It is even more challenging in a catastrophe modeling context, where tens of thousands of typhoon seasons need to be simulated in order to provide a complete view of flood risk. Ultimately, one could run a coupled global climate model and regional Numerical Weather Prediction (NWP) model, but this approach is not feasible in the catastrophe modeling context and, most importantly, may not provide TC track patterns consistent with observations. Rather, we propose to leverage NWP output for the observed TC precipitation patterns (in terms of downscaled reanalysis 1979-2015) collected on a Lagrangian frame along the historical TC tracks and reduced to the leading spatial principal components of the data. The reduced data from all TCs is then grouped according to timing, storm evolution stage (developing, mature, dissipating, ETC transitioning) and central pressure and used to build a dictionary of stationary (within a group) and non-stationary (for transitions between groups) covariance models. Provided that the stochastic storm tracks with all the parameters describing the TC evolution are already simulated, a sequence of conditional samples from the covariance models chosen according to the TC characteristics at a given moment in time are concatenated, producing a continuous non-stationary precipitation pattern in a Lagrangian framework. The simulated precipitation for each event is finally distributed along the stochastic TC track and blended with a non-TC background precipitation using a data assimilation technique. The proposed framework provides means of efficient simulation (10000 seasons simulated in a couple of days) and robust typhoon precipitation patterns consistent with observed regional climate and visually undistinguishable from high resolution NWP output. The framework is used to simulate a catalog of 10000 typhoon seasons implemented in a flood risk model for Japan.

A dynamical framework for integrated corridor management.

DOT National Transportation Integrated Search

2016-01-11

We develop analysis and control synthesis tools for dynamic traffic flow over networks. Our analysis : relies on exploiting monotonicity properties of the dynamics, and on adapting relevant tools from : stochastic queuing networks. We develop proport...

Hybrid modeling in biochemical systems theory by means of functional petri nets.

PubMed

Wu, Jialiang; Voit, Eberhard

2009-02-01

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

A robust nonparametric framework for reconstruction of stochastic differential equation models

NASA Astrophysics Data System (ADS)

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

2016-05-01

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

New Results on a Stochastic Duel Game with Each Force Consisting of Heterogeneous Units

DTIC Science & Technology

2013-02-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA NEW RESULTS ON A STOCHASTIC DUEL GAME WITH EACH FORCE CONSISTING OF...on a Stochastic Duel Game With Each Force Consisting of Heterogeneous Units 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...distribution is unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT Two forces engage in a duel , with each force initially consisting of several

FINITE-STATE APPROXIMATIONS TO DENUMERABLE-STATE DYNAMIC PROGRAMS,

DTIC Science & Technology

AIR FORCE OPERATIONS, LOGISTICS), (*INVENTORY CONTROL, DYNAMIC PROGRAMMING), (*DYNAMIC PROGRAMMING, APPROXIMATION(MATHEMATICS)), INVENTORY CONTROL, DECISION MAKING, STOCHASTIC PROCESSES, GAME THEORY, ALGORITHMS, CONVERGENCE

Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale

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

Zabaras, Nicolas J.

2016-11-08

Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.

Price dynamics of the financial markets using the stochastic differential equation for a potential double well

NASA Astrophysics Data System (ADS)

Lima, L. S.; Miranda, L. L. B.

2018-01-01

We have used the Itô's stochastic differential equation for the double well with additive white noise as a mathematical model for price dynamics of the financial market. We have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents, with respect to the facts of financial markets. We have obtained the mean price in terms of the β parameter that represents the force of the randomness term of the model.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Crossing the threshold

NASA Astrophysics Data System (ADS)

Bush, John; Tambasco, Lucas

2017-11-01

First, we summarize the circumstances in which chaotic pilot-wave dynamics gives rise to quantum-like statistical behavior. For ``closed'' systems, in which the droplet is confined to a finite domain either by boundaries or applied forces, quantum-like features arise when the persistence time of the waves exceeds the time required for the droplet to cross its domain. Second, motivated by the similarities between this hydrodynamic system and stochastic electrodynamics, we examine the behavior of a bouncing droplet above the Faraday threshold, where a stochastic element is introduced into the drop dynamics by virtue of its interaction with a background Faraday wave field. With a view to extending the dynamical range of pilot-wave systems to capture more quantum-like features, we consider a generalized theoretical framework for stochastic pilot-wave dynamics in which the relative magnitudes of the drop-generated pilot-wave field and a stochastic background field may be varied continuously. We gratefully acknowledge the financial support of the NSF through their CMMI and DMS divisions.

Stochastic DT-MRI connectivity mapping on the GPU.

PubMed

McGraw, Tim; Nadar, Mariappan

2007-01-01

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

Physical realizability of continuous-time quantum stochastic walks

NASA Astrophysics Data System (ADS)

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

2018-05-01

Quantum walks are a promising methodology that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution and the physical assumptions underpinning them. We show that general direct implementations would require the complete solution of the underlying unitary dynamics and sophisticated reservoir engineering, thus weakening the benefits of experimental implementation.

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-12-01

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

A new version of the CADNA library for estimating round-off error propagation in Fortran programs

NASA Astrophysics Data System (ADS)

Jézéquel, Fabienne; Chesneaux, Jean-Marie; Lamotte, Jean-Luc

2010-11-01

The CADNA library enables one to estimate, using a probabilistic approach, round-off error propagation in any simulation program. CADNA provides new numerical types, the so-called stochastic types, on which round-off errors can be estimated. Furthermore CADNA contains the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. On 64-bit processors, depending on the rounding mode chosen, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs. Therefore the CADNA library has been improved to enable the numerical validation of programs on 64-bit processors. New version program summaryProgram title: CADNA Catalogue identifier: AEAT_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 28 488 No. of bytes in distributed program, including test data, etc.: 463 778 Distribution format: tar.gz Programming language: Fortran NOTE: A C++ version of this program is available in the Library as AEGQ_v1_0 Computer: PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM Operating system: LINUX, UNIX Classification: 6.5 Catalogue identifier of previous version: AEAT_v1_0 Journal reference of previous version: Comput. Phys. Commun. 178 (2008) 933 Does the new version supersede the previous version?: Yes Nature of problem: A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time. Solution method: The CADNA library [1-3] implements Discrete Stochastic Arithmetic [4,5] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic. Reasons for new version: On 64-bit processors, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs with rounding towards -∞ and +∞, which the random rounding mode is based on. Therefore a particular definition of mathematical functions for stochastic arguments has been included in the CADNA library to enable its use with the GNU Fortran compiler on 64-bit processors. Summary of revisions: If CADNA is used on a 64-bit processor with the GNU Fortran compiler, mathematical functions are computed with rounding to the nearest, otherwise they are computed with the random rounding mode. It must be pointed out that the knowledge of the accuracy of the stochastic argument of a mathematical function is never lost. Restrictions: CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays. Additional comments: In the library archive, users are advised to read the INSTALL file first. The doc directory contains a user guide named ug.cadna.pdf which shows how to control the numerical accuracy of a program using CADNA, provides installation instructions and describes test runs. The source code, which is located in the src directory, consists of one assembly language file (cadna_rounding.s) and eighteen Fortran language files. cadna_rounding.s is a symbolic link to the assembly file corresponding to the processor and the Fortran compiler used. This assembly file contains routines which are frequently called in the CADNA Fortran files to change the rounding mode. The Fortran language files contain the definition of the stochastic types on which the control of accuracy can be performed, CADNA specific functions (for instance to enable or disable the detection of numerical instabilities), the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. The examples directory contains seven test runs which illustrate the use of the CADNA library and the benefits of Discrete Stochastic Arithmetic. Running time: The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected.

A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles

DOE PAGES

Malikopoulos, Andreas

2015-01-01

The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.more » Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.« less

A framework for modeling and optimizing dynamic systems under uncertainty

DOE PAGES

Nicholson, Bethany; Siirola, John

2017-11-11

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

A framework for modeling and optimizing dynamic systems under uncertainty

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

Nicholson, Bethany; Siirola, John

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

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

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

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

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 1: theoretical development

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian Fokker-Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Impact of deterministic and stochastic updates on network reciprocity in the prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Tanimoto, Jun

2014-08-01

In 2 × 2 prisoner's dilemma games, network reciprocity is one mechanism for adding social viscosity, which leads to cooperative equilibrium. This study introduced an intriguing framework for the strategy update rule that allows any combination of a purely deterministic method, imitation max (IM), and a purely probabilistic one, pairwise Fermi (Fermi-PW). A series of simulations covering the whole range from IM to Fermi-PW reveals that, as a general tendency, the larger fractions of stochastic updating reduce network reciprocity, so long as the underlying lattice contains no noise in the degree of distribution. However, a small amount of stochastic flavor added to an otherwise perfectly deterministic update rule was actually found to enhance network reciprocity. This occurs because a subtle stochastic effect in the update rule improves the evolutionary trail in games having more stag-hunt-type dilemmas, although the same stochastic effect degenerates evolutionary trails in games having more chicken-type dilemmas. We explain these effects by dividing evolutionary trails into the enduring and expanding periods defined by Shigaki et al. [Phys. Rev. E 86, 031141 (2012), 10.1103/PhysRevE.86.031141].

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.

Modelling ecosystem service flows under uncertainty with stochiastic SPAN

USGS Publications Warehouse

Johnson, Gary W.; Snapp, Robert R.; Villa, Ferdinando; Bagstad, Kenneth J.

2012-01-01

Ecosystem service models are increasingly in demand for decision making. However, the data required to run these models are often patchy, missing, outdated, or untrustworthy. Further, communication of data and model uncertainty to decision makers is often either absent or unintuitive. In this work, we introduce a systematic approach to addressing both the data gap and the difficulty in communicating uncertainty through a stochastic adaptation of the Service Path Attribution Networks (SPAN) framework. The SPAN formalism assesses ecosystem services through a set of up to 16 maps, which characterize the services in a study area in terms of flow pathways between ecosystems and human beneficiaries. Although the SPAN algorithms were originally defined deterministically, we present them here in a stochastic framework which combines probabilistic input data with a stochastic transport model in order to generate probabilistic spatial outputs. This enables a novel feature among ecosystem service models: the ability to spatially visualize uncertainty in the model results. The stochastic SPAN model can analyze areas where data limitations are prohibitive for deterministic models. Greater uncertainty in the model inputs (including missing data) should lead to greater uncertainty expressed in the model’s output distributions. By using Bayesian belief networks to fill data gaps and expert-provided trust assignments to augment untrustworthy or outdated information, we can account for uncertainty in input data, producing a model that is still able to run and provide information where strictly deterministic models could not. Taken together, these attributes enable more robust and intuitive modelling of ecosystem services under uncertainty.

Fast Geostatistical Inversion using Randomized Matrix Decompositions and Sketchings for Heterogeneous Aquifer Characterization

NASA Astrophysics Data System (ADS)

O'Malley, D.; Le, E. B.; Vesselinov, V. V.

2015-12-01

We present a fast, scalable, and highly-implementable stochastic inverse method for characterization of aquifer heterogeneity. The method utilizes recent advances in randomized matrix algebra and exploits the structure of the Quasi-Linear Geostatistical Approach (QLGA), without requiring a structured grid like Fast-Fourier Transform (FFT) methods. The QLGA framework is a more stable version of Gauss-Newton iterates for a large number of unknown model parameters, but provides unbiased estimates. The methods are matrix-free and do not require derivatives or adjoints, and are thus ideal for complex models and black-box implementation. We also incorporate randomized least-square solvers and data-reduction methods, which speed up computation and simulate missing data points. The new inverse methodology is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). Julia is an advanced high-level scientific programing language that allows for efficient memory management and utilization of high-performance computational resources. Inversion results based on series of synthetic problems with steady-state and transient calibration data are presented.

Impact of Coverage-Dependent Marginal Costs on Optimal HPV Vaccination Strategies

PubMed Central

Ryser, Marc D.; McGoff, Kevin; Herzog, David P.; Sivakoff, David J.; Myers, Evan R.

2015-01-01

The effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs. PMID:25979280

An open and extensible framework for spatially explicit land use change modelling: the lulcc R package

NASA Astrophysics Data System (ADS)

Moulds, S.; Buytaert, W.; Mijic, A.

2015-10-01

We present the lulcc software package, an object-oriented framework for land use change modelling written in the R programming language. The contribution of the work is to resolve the following limitations associated with the current land use change modelling paradigm: (1) the source code for model implementations is frequently unavailable, severely compromising the reproducibility of scientific results and making it impossible for members of the community to improve or adapt models for their own purposes; (2) ensemble experiments to capture model structural uncertainty are difficult because of fundamental differences between implementations of alternative models; and (3) additional software is required because existing applications frequently perform only the spatial allocation of change. The package includes a stochastic ordered allocation procedure as well as an implementation of the CLUE-S algorithm. We demonstrate its functionality by simulating land use change at the Plum Island Ecosystems site, using a data set included with the package. It is envisaged that lulcc will enable future model development and comparison within an open environment.

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.

1999-01-01

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

Maxwell's demon and the management of ignorance in stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Ford, Ian J.

2016-07-01

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.

Kinetics of Thermal Unimolecular Decomposition of Acetic Anhydride: An Integrated Deterministic and Stochastic Model.

PubMed

Mai, Tam V-T; Duong, Minh V; Nguyen, Hieu T; Lin, Kuang C; Huynh, Lam K

2017-04-27

An integrated deterministic and stochastic model within the master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) framework was first used to characterize temperature- and pressure-dependent behaviors of thermal decomposition of acetic anhydride in a wide range of conditions (i.e., 300-1500 K and 0.001-100 atm). Particularly, using potential energy surface and molecular properties obtained from high-level electronic structure calculations at CCSD(T)/CBS, macroscopic thermodynamic properties and rate coefficients of the title reaction were derived with corrections for hindered internal rotation and tunneling treatments. Being in excellent agreement with the scattered experimental data, the results from deterministic and stochastic frameworks confirmed and complemented each other to reveal that the main decomposition pathway proceeds via a 6-membered-ring transition state with the 0 K barrier of 35.2 kcal·mol -1 . This observation was further understood and confirmed by the sensitivity analysis on the time-resolved species profiles and the derived rate coefficients with respect to the ab initio barriers. Such an agreement suggests the integrated model can be confidently used for a wide range of conditions as a powerful postfacto and predictive tool in detailed chemical kinetic modeling and simulation for the title reaction and thus can be extended to complex chemical reactions.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

ASSESSING RESIDENTIAL EXPOSURE USING THE STOCHASTIC HUMAN EXPOSURE AND DOSE SIMULATION (SHEDS) MODEL

EPA Science Inventory

As part of a workshop sponsored by the Environmental Protection Agency's Office of Research and Development and Office of Pesticide Programs, the Aggregate Stochastic Human Exposure and Dose Simulation (SHEDS) Model was used to assess potential aggregate residential pesticide e...

Stochastic models of the Social Security trust funds.

PubMed

Burdick, Clark; Manchester, Joyce

Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.

Sparse learning of stochastic dynamical equations

NASA Astrophysics Data System (ADS)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Parallel stochastic simulation of macroscopic calcium currents.

PubMed

González-Vélez, Virginia; González-Vélez, Horacio

2007-06-01

This work introduces MACACO, a macroscopic calcium currents simulator. It provides a parameter-sweep framework which computes macroscopic Ca(2+) currents from the individual aggregation of unitary currents, using a stochastic model for L-type Ca(2+) channels. MACACO uses a simplified 3-state Markov model to simulate the response of each Ca(2+) channel to different voltage inputs to the cell. In order to provide an accurate systematic view for the stochastic nature of the calcium channels, MACACO is composed of an experiment generator, a central simulation engine and a post-processing script component. Due to the computational complexity of the problem and the dimensions of the parameter space, the MACACO simulation engine employs a grid-enabled task farm. Having been designed as a computational biology tool, MACACO heavily borrows from the way cell physiologists conduct and report their experimental work.

A common stochastic accumulator with effector-dependent noise can explain eye-hand coordination

PubMed Central

Gopal, Atul; Viswanathan, Pooja

2015-01-01

The computational architecture that enables the flexible coupling between otherwise independent eye and hand effector systems is not understood. By using a drift diffusion framework, in which variability of the reaction time (RT) distribution scales with mean RT, we tested the ability of a common stochastic accumulator to explain eye-hand coordination. Using a combination of behavior, computational modeling and electromyography, we show how a single stochastic accumulator to threshold, followed by noisy effector-dependent delays, explains eye-hand RT distributions and their correlation, while an alternate independent, interactive eye and hand accumulator model does not. Interestingly, the common accumulator model did not explain the RT distributions of the same subjects when they made eye and hand movements in isolation. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning. PMID:25568161

Differential form representation of stochastic electromagnetic fields

NASA Astrophysics Data System (ADS)

Haider, Michael; Russer, Johannes A.

2017-09-01

In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.

On stochastic control and optimal measurement strategies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kramer, L. C.

1971-01-01

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

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.

Removing Barriers for Effective Deployment of Intermittent Renewable Generation

NASA Astrophysics Data System (ADS)

Arabali, Amirsaman

The stochastic nature of intermittent renewable resources is the main barrier to effective integration of renewable generation. This problem can be studied from feeder-scale and grid-scale perspectives. Two new stochastic methods are proposed to meet the feeder-scale controllable load with a hybrid renewable generation (including wind and PV) and energy storage system. For the first method, an optimization problem is developed whose objective function is the cost of the hybrid system including the cost of renewable generation and storage subject to constraints on energy storage and shifted load. A smart-grid strategy is developed to shift the load and match the renewable energy generation and controllable load. Minimizing the cost function guarantees minimum PV and wind generation installation, as well as storage capacity selection for supplying the controllable load. A confidence coefficient is allocated to each stochastic constraint which shows to what degree the constraint is satisfied. In the second method, a stochastic framework is developed for optimal sizing and reliability analysis of a hybrid power system including renewable resources (PV and wind) and energy storage system. The hybrid power system is optimally sized to satisfy the controllable load with a specified reliability level. A load-shifting strategy is added to provide more flexibility for the system and decrease the installation cost. Load shifting strategies and their potential impacts on the hybrid system reliability/cost analysis are evaluated trough different scenarios. Using a compromise-solution method, the best compromise between the reliability and cost will be realized for the hybrid system. For the second problem, a grid-scale stochastic framework is developed to examine the storage application and its optimal placement for the social cost and transmission congestion relief of wind integration. Storage systems are optimally placed and adequately sized to minimize the sum of operation and congestion costs over a scheduling period. A technical assessment framework is developed to enhance the efficiency of wind integration and evaluate the economics of storage technologies and conventional gas-fired alternatives. The proposed method is used to carry out a cost-benefit analysis for the IEEE 24-bus system and determine the most economical technology. In order to mitigate the financial and technical concerns of renewable energy integration into the power system, a stochastic framework is proposed for transmission grid reinforcement studies in a power system with wind generation. A multi-stage multi-objective transmission network expansion planning (TNEP) methodology is developed which considers the investment cost, absorption of private investment and reliability of the system as the objective functions. A Non-dominated Sorting Genetic Algorithm (NSGA II) optimization approach is used in combination with a probabilistic optimal power flow (POPF) to determine the Pareto optimal solutions considering the power system uncertainties. Using a compromise-solution method, the best final plan is then realized based on the decision maker preferences. The proposed methodology is applied to the IEEE 24-bus Reliability Tests System (RTS) to evaluate the feasibility and practicality of the developed planning strategy.

A PROBABILISTIC MODELING FRAMEWORK FOR PREDICTING POPULATION EXPOSURES TO BENZENE

EPA Science Inventory

The US Environmental Protection Agency (EPA) is modifying their probabilistic Stochastic Human Exposure Dose Simulation (SHEDS) model to assess aggregate exposures to air toxics. Air toxics include urban Hazardous Air Pollutants (HAPS) such as benzene from mobile sources, part...

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

PubMed Central

Truccolo, Wilson

2017-01-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity. PMID:28234899

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

PubMed

Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

2017-02-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Stochastic Kuramoto oscillators with discrete phase states.

PubMed

Jörg, David J

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

Stochastic Kuramoto oscillators with discrete phase states

NASA Astrophysics Data System (ADS)

Jörg, David J.

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Simplex-stochastic collocation method with improved scalability

NASA Astrophysics Data System (ADS)

Edeling, W. N.; Dwight, R. P.; Cinnella, P.

2016-04-01

The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

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

Coleman, Justin; Slaughter, Andrew; Veeraraghavan, Swetha

Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) is a finite element application that aims at analyzing the response of 3-D soil-structure systems to natural and man-made hazards such as earthquakes, floods and fire. MASTODON currently focuses on the simulation of seismic events and has the capability to perform extensive ‘source-to-site’ simulations including earthquake fault rupture, nonlinear wave propagation and nonlinear soil-structure interaction (NLSSI) analysis. MASTODON is being developed to be a dynamic probabilistic risk assessment framework that enables analysts to not only perform deterministic analyses, but also easily perform probabilistic or stochastic simulations for the purpose of risk assessment.

Ignition probability of polymer-bonded explosives accounting for multiple sources of material stochasticity

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

Kim, S.; Barua, A.; Zhou, M., E-mail: min.zhou@me.gatech.edu

2014-05-07

Accounting for the combined effect of multiple sources of stochasticity in material attributes, we develop an approach that computationally predicts the probability of ignition of polymer-bonded explosives (PBXs) under impact loading. The probabilistic nature of the specific ignition processes is assumed to arise from two sources of stochasticity. The first source involves random variations in material microstructural morphology; the second source involves random fluctuations in grain-binder interfacial bonding strength. The effect of the first source of stochasticity is analyzed with multiple sets of statistically similar microstructures and constant interfacial bonding strength. Subsequently, each of the microstructures in the multiple setsmore » is assigned multiple instantiations of randomly varying grain-binder interfacial strengths to analyze the effect of the second source of stochasticity. Critical hotspot size-temperature states reaching the threshold for ignition are calculated through finite element simulations that explicitly account for microstructure and bulk and interfacial dissipation to quantify the time to criticality (t{sub c}) of individual samples, allowing the probability distribution of the time to criticality that results from each source of stochastic variation for a material to be analyzed. Two probability superposition models are considered to combine the effects of the multiple sources of stochasticity. The first is a parallel and series combination model, and the second is a nested probability function model. Results show that the nested Weibull distribution provides an accurate description of the combined ignition probability. The approach developed here represents a general framework for analyzing the stochasticity in the material behavior that arises out of multiple types of uncertainty associated with the structure, design, synthesis and processing of materials.« less

Holistic irrigation water management approach based on stochastic soil water dynamics

NASA Astrophysics Data System (ADS)

Alizadeh, H.; Mousavi, S. J.

2012-04-01

Appreciating the essential gap between fundamental unsaturated zone transport processes and soil and water management due to low effectiveness of some of monitoring and modeling approaches, this study presents a mathematical programming model for irrigation management optimization based on stochastic soil water dynamics. The model is a nonlinear non-convex program with an economic objective function to address water productivity and profitability aspects in irrigation management through optimizing irrigation policy. Utilizing an optimization-simulation method, the model includes an eco-hydrological integrated simulation model consisting of an explicit stochastic module of soil moisture dynamics in the crop-root zone with shallow water table effects, a conceptual root-zone salt balance module, and the FAO crop yield module. Interdependent hydrology of soil unsaturated and saturated zones is treated in a semi-analytical approach in two steps. At first step analytical expressions are derived for the expected values of crop yield, total water requirement and soil water balance components assuming fixed level for shallow water table, while numerical Newton-Raphson procedure is employed at the second step to modify value of shallow water table level. Particle Swarm Optimization (PSO) algorithm, combined with the eco-hydrological simulation model, has been used to solve the non-convex program. Benefiting from semi-analytical framework of the simulation model, the optimization-simulation method with significantly better computational performance compared to a numerical Mote-Carlo simulation-based technique has led to an effective irrigation management tool that can contribute to bridging the gap between vadose zone theory and water management practice. In addition to precisely assessing the most influential processes at a growing season time scale, one can use the developed model in large scale systems such as irrigation districts and agricultural catchments. Accordingly, 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. The area suffers from the water scarcity problem and therefore the trade-off between the level of deficit and economical profit should be assessed. Based on the results, while the maximum net benefit has been obtained for the stress-avoidance (SA) irrigation policy, the highest water profitability, defined by economical net benefit gained from unit irrigation water volume application, has been resulted when only about 60% of water used in the SA policy is applied.

Integration of progressive hedging and dual decomposition in stochastic integer programs

DOE PAGES

Watson, Jean -Paul; Guo, Ge; Hackebeil, Gabriel; ...

2015-04-07

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.

Probability-Based Recognition Framework for Underwater Landmarks Using Sonar Images †.

PubMed

Lee, Yeongjun; Choi, Jinwoo; Ko, Nak Yong; Choi, Hyun-Taek

2017-08-24

This paper proposes a probability-based framework for recognizing underwater landmarks using sonar images. Current recognition methods use a single image, which does not provide reliable results because of weaknesses of the sonar image such as unstable acoustic source, many speckle noises, low resolution images, single channel image, and so on. However, using consecutive sonar images, if the status-i.e., the existence and identity (or name)-of an object is continuously evaluated by a stochastic method, the result of the recognition method is available for calculating the uncertainty, and it is more suitable for various applications. Our proposed framework consists of three steps: (1) candidate selection, (2) continuity evaluation, and (3) Bayesian feature estimation. Two probability methods-particle filtering and Bayesian feature estimation-are used to repeatedly estimate the continuity and feature of objects in consecutive images. Thus, the status of the object is repeatedly predicted and updated by a stochastic method. Furthermore, we develop an artificial landmark to increase detectability by an imaging sonar, which we apply to the characteristics of acoustic waves, such as instability and reflection depending on the roughness of the reflector surface. The proposed method is verified by conducting basin experiments, and the results are presented.

Modelling the protocol stack in NCS with deterministic and stochastic petri net

NASA Astrophysics Data System (ADS)

Hui, Chen; Chunjie, Zhou; Weifeng, Zhu

2011-06-01

Protocol stack is the basis of the networked control systems (NCS). Full or partial reconfiguration of protocol stack offers both optimised communication service and system performance. Nowadays, field testing is unrealistic to determine the performance of reconfigurable protocol stack; and the Petri net formal description technique offers the best combination of intuitive representation, tool support and analytical capabilities. Traditionally, separation between the different layers of the OSI model has been a common practice. Nevertheless, such a layered modelling analysis framework of protocol stack leads to the lack of global optimisation for protocol reconfiguration. In this article, we proposed a general modelling analysis framework for NCS based on the cross-layer concept, which is to establish an efficiency system scheduling model through abstracting the time constraint, the task interrelation, the processor and the bus sub-models from upper and lower layers (application, data link and physical layer). Cross-layer design can help to overcome the inadequacy of global optimisation based on information sharing between protocol layers. To illustrate the framework, we take controller area network (CAN) as a case study. The simulation results of deterministic and stochastic Petri-net (DSPN) model can help us adjust the message scheduling scheme and obtain better system performance.

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

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

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr; Picarelli, Athena, E-mail: athena.picarelli@inria.fr; Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system ofmore » controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.« less

Search Planning Under Incomplete Information Using Stochastic Optimization and Regression

DTIC Science & Technology

2011-09-01

solve since they involve un- certainty and unknown parameters (see for example Shapiro et al., 2009; Wallace & Ziemba , 2005). One application area is...M16130.2E. 43 Wallace, S. W., & Ziemba , W. T. (2005). Applications of stochastic programming. Philadelphia, PA: Society for Industrial and Applied

Environmental Barrier Coating Fracture, Fatigue and High-Heat-Flux Durability Modeling and Stochastic Progressive Damage Simulation

NASA Technical Reports Server (NTRS)

Zhu, Dongming; Nemeth, Noel N.

2017-01-01

Advanced environmental barrier coatings will play an increasingly important role in future gas turbine engines because of their ability to protect emerging light-weight SiC/SiC ceramic matrix composite (CMC) engine components, further raising engine operating temperatures and performance. Because the environmental barrier coating systems are critical to the performance, reliability and durability of these hot-section ceramic engine components, a prime-reliant coating system along with established life design methodology are required for the hot-section ceramic component insertion into engine service. In this paper, we have first summarized some observations of high temperature, high-heat-flux environmental degradation and failure mechanisms of environmental barrier coating systems in laboratory simulated engine environment tests. In particular, the coating surface cracking morphologies and associated subsequent delamination mechanisms under the engine level high-heat-flux, combustion steam, and mechanical creep and fatigue loading conditions will be discussed. The EBC compostion and archtechture improvements based on advanced high heat flux environmental testing, and the modeling advances based on the integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program will also be highlighted. The stochastic progressive damage simulation successfully predicts mud flat damage pattern in EBCs on coated 3-D specimens, and a 2-D model of through-the-thickness cross-section. A 2-parameter Weibull distribution was assumed in characterizing the coating layer stochastic strength response and the formation of damage was therefore modeled. The damage initiation and coalescence into progressively smaller mudflat crack cells was demonstrated. A coating life prediction framework may be realized by examining the surface crack initiation and delamination propagation in conjunction with environmental degradation under high-heat-flux and environment load test conditions.

A Note on Feynman Path Integral for Electromagnetic External Fields

NASA Astrophysics Data System (ADS)

Botelho, Luiz C. L.

2017-08-01

We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under an external electromagnetic time-independent potential.

UNCERTAINTY IN LEACHING POTENTIAL OF NONPOINT SOURCE POLLUTANTS WITH APPLICATION TO GIS

EPA Science Inventory

This paper presents a stochastic framework for the assessment of groundwater pollution potential of nonpoint source pesticides. A conceptual relationship is presented that relates seasonally averaged groundwater recharge to soil properties and depths to the water table. The analy...

Optimization under variability and uncertainty: a case study for NOx emissions control for a gasification system.

PubMed

Chen, Jianjun; Frey, H Christopher

2004-12-15

Methods for optimization of process technologies considering the distinction between variability and uncertainty are developed and applied to case studies of NOx control for Integrated Gasification Combined Cycle systems. Existing methods of stochastic optimization (SO) and stochastic programming (SP) are demonstrated. A comparison of SO and SP results provides the value of collecting additional information to reduce uncertainty. For example, an expected annual benefit of 240,000 dollars is estimated if uncertainty can be reduced before a final design is chosen. SO and SP are typically applied to uncertainty. However, when applied to variability, the benefit of dynamic process control is obtained. For example, an annual savings of 1 million dollars could be achieved if the system is adjusted to changes in process conditions. When variability and uncertainty are treated distinctively, a coupled stochastic optimization and programming method and a two-dimensional stochastic programming method are demonstrated via a case study. For the case study, the mean annual benefit of dynamic process control is estimated to be 700,000 dollars, with a 95% confidence range of 500,000 dollars to 940,000 dollars. These methods are expected to be of greatest utility for problems involving a large commitment of resources, for which small differences in designs can produce large cost savings.

Stochastic Integration H∞ Filter for Rapid Transfer Alignment of INS.

PubMed

Zhou, Dapeng; Guo, Lei

2017-11-18

The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H ∞ filter (SIH ∞ F) for improving both the accuracy and robustness of RTA. In this new nonlinear H ∞ filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H ∞ filter for the first time, and the resulting SIH ∞ F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH ∞ F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H ∞ filter. Moreover, the SIH ∞ F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.

Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2016-11-01

Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.

Stochastic resonance effects reveal the neural mechanisms of transcranial magnetic stimulation

PubMed Central

Schwarzkopf, Dietrich Samuel; Silvanto, Juha; Rees, Geraint

2011-01-01

Transcranial magnetic stimulation (TMS) is a popular method for studying causal relationships between neural activity and behavior. However its mode of action remains controversial, and so far there is no framework to explain its wide range of facilitatory and inhibitory behavioral effects. While some theoretical accounts suggests that TMS suppresses neuronal processing, other competing accounts propose that the effects of TMS result from the addition of noise to neuronal processing. Here we exploited the stochastic resonance phenomenon to distinguish these theoretical accounts and determine how TMS affects neuronal processing. Specifically, we showed that online TMS can induce stochastic resonance in the human brain. At low intensity, TMS facilitated the detection of weak motion signals but with higher TMS intensities and stronger motion signals we found only impairment in detection. These findings suggest that TMS acts by adding noise to neuronal processing, at least in an online TMS protocol. Importantly, such stochastic resonance effects may also explain why TMS parameters that under normal circumstances impair behavior, can induce behavioral facilitations when the stimulated area is in an adapted or suppressed state. PMID:21368025

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.

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.

Health safety nets can break cycles of poverty and disease: a stochastic ecological model.

PubMed

Plucinski, Mateusz M; Ngonghala, Calistus N; Bonds, Matthew H

2011-12-07

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a 'safety net', defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

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

Climate-informed stochastic hydrological modeling: Incorporating decadal-scale variability using paleoclimate data

NASA Astrophysics Data System (ADS)

Henley, B. J.; Thyer, M. A.; Kuczera, G. A.

2012-12-01

A hierarchical framework for incorporating modes of climate variability into stochastic simulations of hydrological data is developed, termed the climate-informed multi-time scale stochastic (CIMSS) framework. To characterize long-term variability for the first level of the hierarchy, paleoclimate and instrumental data describing the Interdecadal Pacific Oscillation (IPO) and the Pacific Decadal Oscillation (PDO) are analyzed. A new paleo IPO-PDO time series dating back 440 yrs is produced, combining seven IPO-PDO paleo sources using an objective smoothing procedure to fit low-pass filters to individual records. The paleo data analysis indicates that wet/dry IPO-PDO states have a broad range of run-lengths, with 90% between 3 and 33 yr and a mean of 15 yr. Model selection techniques were used to determine a suitable stochastic model to simulate these run-lengths. The Markov chain model, previously used to simulate oscillating wet/dry climate states, was found to underestimate the probability of wet/dry periods >5 yr, and was rejected in favor of a gamma distribution. For the second level of the hierarchy, a seasonal rainfall model is conditioned on the simulated IPO-PDO state. Application to two high-quality rainfall sites close to water supply reservoirs found that mean seasonal rainfall in the IPO-PDO dry state was 15%-28% lower than the wet state. The model was able to replicate observed statistics such as seasonal and multi-year accumulated rainfall distributions and interannual autocorrelations for the case study sites. In comparison, an annual lag-one autoregressive AR(1) model was unable to adequately capture the observed rainfall distribution within separate IPO-PDO states. Furthermore, analysis of the impact of the CIMSS framework on drought risk analysis found that short-term drought risks conditional on IPO/PDO state were considerably higher than the traditional AR(1) model.hort-term conditional water supply drought risks for the CIMSS and AR(1) models for the dry IPO-PDO scenario with a range of initial storage levels expressed as a proportion of the annual demand (yield).

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

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

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Demographic noise can reverse the direction of deterministic selection

PubMed Central

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

2016-01-01

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

Impacts of a Stochastic Ice Mass-Size Relationship on Squall Line Ensemble Simulations

NASA Astrophysics Data System (ADS)

Stanford, M.; Varble, A.; Morrison, H.; Grabowski, W.; McFarquhar, G. M.; Wu, W.

2017-12-01

Cloud and precipitation structure, evolution, and cloud radiative forcing of simulated mesoscale convective systems (MCSs) are significantly impacted by ice microphysics parameterizations. Most microphysics schemes assume power law relationships with constant parameters for ice particle mass, area, and terminal fallspeed relationships as a function of size, despite observations showing that these relationships vary in both time and space. To account for such natural variability, a stochastic representation of ice microphysical parameters was developed using the Predicted Particle Properties (P3) microphysics scheme in the Weather Research and Forecasting model, guided by in situ aircraft measurements from a number of field campaigns. Here, the stochastic framework is applied to the "a" and "b" parameters of the unrimed ice mass-size (m-D) relationship (m=aDb) with co-varying "a" and "b" values constrained by observational distributions tested over a range of spatiotemporal autocorrelation scales. Diagnostically altering a-b pairs in three-dimensional (3D) simulations of the 20 May 2011 Midlatitude Continental Convective Clouds Experiment (MC3E) squall line suggests that these parameters impact many important characteristics of the simulated squall line, including reflectivity structure (particularly in the anvil region), surface rain rates, surface and top of atmosphere radiative fluxes, buoyancy and latent cooling distributions, and system propagation speed. The stochastic a-b P3 scheme is tested using two frameworks: (1) a large ensemble of two-dimensional idealized squall line simulations and (2) a smaller ensemble of 3D simulations of the 20 May 2011 squall line, for which simulations are evaluated using observed radar reflectivity and radial velocity at multiple wavelengths, surface meteorology, and surface and satellite measured longwave and shortwave radiative fluxes. Ensemble spreads are characterized and compared against initial condition ensemble spreads for a range of variables.

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.

A Computational Framework for Analyzing Stochasticity in Gene Expression

PubMed Central

Sherman, Marc S.; Cohen, Barak A.

2014-01-01

Stochastic fluctuations in gene expression give rise to distributions of protein levels across cell populations. Despite a mounting number of theoretical models explaining stochasticity in protein expression, we lack a robust, efficient, assumption-free approach for inferring the molecular mechanisms that underlie the shape of protein distributions. Here we propose a method for inferring sets of biochemical rate constants that govern chromatin modification, transcription, translation, and RNA and protein degradation from stochasticity in protein expression. We asked whether the rates of these underlying processes can be estimated accurately from protein expression distributions, in the absence of any limiting assumptions. To do this, we (1) derived analytical solutions for the first four moments of the protein distribution, (2) found that these four moments completely capture the shape of protein distributions, and (3) developed an efficient algorithm for inferring gene expression rate constants from the moments of protein distributions. Using this algorithm we find that most protein distributions are consistent with a large number of different biochemical rate constant sets. Despite this degeneracy, the solution space of rate constants almost always informs on underlying mechanism. For example, we distinguish between regimes where transcriptional bursting occurs from regimes reflecting constitutive transcript production. Our method agrees with the current standard approach, and in the restrictive regime where the standard method operates, also identifies rate constants not previously obtainable. Even without making any assumptions we obtain estimates of individual biochemical rate constants, or meaningful ratios of rate constants, in 91% of tested cases. In some cases our method identified all of the underlying rate constants. The framework developed here will be a powerful tool for deducing the contributions of particular molecular mechanisms to specific patterns of gene expression. PMID:24811315

Distance estimation and collision prediction for on-line robotic motion planning

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1992-01-01

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem is incorporated into the framework of an in-line motion-planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning, the deterministic problem where the information about the objects is assumed to be certain is examined. L(1) or L(infinity) norms are used to represent distance and the problem becomes a linear programming problem. The stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: First, filtering of the distance between the robot and the moving object at the present time. Second, prediction of the minimum distance in the future in order to predict the collision time.

NSR&D Program Fiscal Year 2015 Funded Research Stochastic Modeling of Radioactive Material Releases Final Report

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

Andrus, Jason P.; Pope, Chad; Toston, Mary

2016-12-01

Nonreactor nuclear facilities operating under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculatesmore » the radiation dose distribution associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. Users can also specify custom distributions through a user defined distribution option. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA, developed using the MATLAB coding framework, has a graphical user interface and can be installed on both Windows and Mac computers. SODA is a standalone software application and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC; rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The SODA development project was funded through a grant from the DOE Nuclear Safety Research and Development Program.« less

NSR&D Program Fiscal Year 2015 Funded Research Stochastic Modeling of Radioactive Material Releases Final Report

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

Andrus, Jason P.; Pope, Chad; Toston, Mary

Nonreactor nuclear facilities operating under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculatesmore » the radiation dose distribution associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. Users can also specify custom distributions through a user defined distribution option. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA, developed using the MATLAB coding framework, has a graphical user interface and can be installed on both Windows and Mac computers. SODA is a standalone software application and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC; rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The SODA development project was funded through a grant from the DOE Nuclear Safety Research and Development Program.« less

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.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

PubMed

Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

2017-03-14

Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

Entropy production of doubly stochastic quantum channels

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

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

Dynamic system classifier.

PubMed

Pumpe, Daniel; Greiner, Maksim; Müller, Ewald; Enßlin, Torsten A

2016-07-01

Stochastic differential equations describe well many physical, biological, and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time-dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of the DSC to oscillation processes with a time-dependent frequency ω(t) and damping factor γ(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The ω and γ time lines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.

UNCERTAINTY IN LEACHING POTENTIAL OF NONPOINT SOURCE POLLUTANTS WITH APPLICATION TO A GIS

EPA Science Inventory

This paper presents a stochastic framework for the assessment of groundwater pollution potential of nonpoint source pesticides. A conceptual relationship is presented that relates seasonally averaged groundwater recharge to soil properties and depths to the water table. The analy...

Parameter-based stochastic simulation of selection and breeding for multiple traits

Treesearch

Jennifer Myszewski; Thomas Byram; Floyd Bridgwater

2006-01-01

To increase the adaptability and economic value of plantations, tree improvement professionals often manage multiple traits in their breeding programs. When these traits are unfavorably correlated, breeders must weigh the economic importance of each trait and select for a desirable aggregate phenotype. Stochastic simulation allows breeders to test the effects of...

A framework to analyze the stochastic harmonics and resonance of wind energy grid interconnection

DOE PAGES

Cho, Youngho; Lee, Choongman; Hur, Kyeon; ...

2016-08-31

This study addresses a modeling and analysis methodology for investigating the stochastic harmonics and resonance concerns of wind power plants (WPPs). Wideband harmonics from modern wind turbines are observed to be stochastic, associated with real power production, and they may adversely interact with the grid impedance and cause unexpected harmonic resonance if not comprehensively addressed in the planning and commissioning of the WPPs. These issues should become more critical as wind penetration levels increase. We thus propose a planning study framework comprising the following functional steps: First, the best-fitted probability density functions (PDFs) of the harmonic components of interest inmore » the frequency domain are determined. In operations planning, maximum likelihood estimations followed by a chi-square test are used once field measurements or manufacturers' data are available. Second, harmonic currents from the WPP are represented by randomly-generating harmonic components based on their PDFs (frequency spectrum) and then synthesized for time-domain simulations via inverse Fourier transform. Finally, we conduct a comprehensive assessment by including the impacts of feeder configurations, harmonic filters, and the variability of parameters. We demonstrate the efficacy of the proposed study approach for a 100-MW offshore WPP consisting of 20 units of 5-MW full-converter turbines, a realistic benchmark system adapted from a WPP under development in Korea, and discuss lessons learned through this research.« less

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

PubMed

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Learning Probabilistic Logic Models from Probabilistic Examples

PubMed Central

Chen, Jianzhong; Muggleton, Stephen; Santos, José

2009-01-01

Abstract We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) time-trace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches - abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from non-probabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from non-probabilistic examples. PMID:19888348

Learning Probabilistic Logic Models from Probabilistic Examples.

PubMed

Chen, Jianzhong; Muggleton, Stephen; Santos, José

2008-10-01

We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) time-trace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches - abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from non-probabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from non-probabilistic examples.

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Optimal Strategy for Integrated Dynamic Inventory Control and Supplier Selection in Unknown Environment via Stochastic Dynamic Programming

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Solikhin

2016-06-01

In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.

Investigation and incorporation of water inflow uncertainties through stochastic modelling in a combined optimisation methodology for water allocation in Alfeios River (Greece)

NASA Astrophysics Data System (ADS)

Bekri, Eleni; Yannopoulos, Panayotis; Disse, Markus

2014-05-01

The Alfeios River plays a vital role for Western Peloponnisos in Greece from natural, ecological, social and economic aspect. The main river and its six tributaries, forming the longest watercourse and the highest streamflow rate of Peloponnisose, represent a significant source of water supply for the region, aiming at delivering and satisfying the expected demands from a variety of water users, including irrigation, drinking water supply, hydropower production and recreation. In the previous EGU General Assembly, a fuzzy-boundary-interval linear programming methodology, based on Li et al. (2010) and Bekri et al. (2012), has been presented for optimal water allocation under uncertain and vague system conditions in the Alfeios River Basin. Uncertainties associated with the benefit and cost coefficient in the objective function of the main water uses (hydropower production and irrigation) were expressed as probability distributions and fuzzy boundary intervals derived by associated α-cut levels. The uncertainty of the monthly water inflows was not incorporated in the previous initial application and the analysis of all other sources of uncertainty has been applied to two extreme hydrologic years represented by a selected wet and dry year. To manage and operate the river system, decision makers should be able to analyze and evaluate the impact of various hydrologic scenarios. In the present work, the critical uncertain parameter of water inflows is analyzed and its incorporation as an additional type of uncertainty in the suggested methodology is investigated, in order to enable the assessment of optimal water allocation for hydrologic and socio-economic scenarios based both on historical data and projected climate change conditions. For this purpose, stochastic simulation analysis for a part of the Alfeios river system is undertaken, testing various stochastic models from simple stationary ones (AR and ARMA), Thomas-Fiering, ARIMA as well as more sophisticated and complete such as CASTALIA. A short description and comparison of their assumptions, the differences between them and the presentation of the results are included. Li, Y.P., Huang, G.H. and S.L., Nie, (2010), Planning water resources management systems using a fuzzy boundary interval-stochastic programming method, Elsevier Ltd, Advances in Water Resources, 33: 1105-1117. doi:10.1016/j.advwatres.2010.06.015 Bekri, E.S., Disse, M. and P.C.,Yannopoulos, (2012), Methodological framework for correction of quick river discharge measurements using quality characteristics, Session of Environmental Hydraulics - Hydrodynamics, 2nd Common Conference of Hellenic Hydrotechnical Association and Greek Committee for Water Resources Management, Volume: 546-557 (in Greek).

A new approach for measuring power spectra and reconstructing time series in active galactic nuclei

NASA Astrophysics Data System (ADS)

Li, Yan-Rong; Wang, Jian-Min

2018-05-01

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parametrizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enables an acceptable time complexity for the approach.

Entropy Production and Fluctuation Theorems for Active Matter

NASA Astrophysics Data System (ADS)

Mandal, Dibyendu; Klymko, Katherine; DeWeese, Michael R.

2017-12-01

Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.

Stochastic effects in hybrid inflation

NASA Astrophysics Data System (ADS)

Martin, Jérôme; Vennin, Vincent

2012-02-01

Hybrid inflation is a two-field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in particular, the question of how the quantum diffusion can affect the observable predictions of hybrid inflation.

A framework for the direct evaluation of large deviations in non-Markovian processes

NASA Astrophysics Data System (ADS)

Cavallaro, Massimo; Harris, Rosemary J.

2016-11-01

We propose a general framework to simulate stochastic trajectories with arbitrarily long memory dependence and efficiently evaluate large deviation functions associated to time-extensive observables. This extends the ‘cloning’ procedure of Giardiná et al (2006 Phys. Rev. Lett. 96 120603) to non-Markovian systems. We demonstrate the validity of this method by testing non-Markovian variants of an ion-channel model and the totally asymmetric exclusion process, recovering results obtainable by other means.

A Parallel Stochastic Framework for Reservoir Characterization and History Matching

DOE PAGES

Thomas, Sunil G.; Klie, Hector M.; Rodriguez, Adolfo A.; ...

2011-01-01

The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Two-stage fuzzy-stochastic robust programming: a hybrid model for regional air quality management.

PubMed

Li, Yongping; Huang, Guo H; Veawab, Amornvadee; Nie, Xianghui; Liu, Lei

2006-08-01

In this study, a hybrid two-stage fuzzy-stochastic robust programming (TFSRP) model is developed and applied to the planning of an air-quality management system. As an extension of existing fuzzy-robust programming and two-stage stochastic programming methods, the TFSRP can explicitly address complexities and uncertainties of the study system without unrealistic simplifications. Uncertain parameters can be expressed as probability density and/or fuzzy membership functions, such that robustness of the optimization efforts can be enhanced. Moreover, economic penalties as corrective measures against any infeasibilities arising from the uncertainties are taken into account. This method can, thus, provide a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken. In its solution algorithm, the fuzzy decision space can be delimited through specification of the uncertainties using dimensional enlargement of the original fuzzy constraints. The developed model is applied to a case study of regional air quality management. The results indicate that reasonable solutions have been obtained. The solutions can be used for further generating pollution-mitigation alternatives with minimized system costs and for providing a more solid support for sound environmental decisions.

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 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

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.

Optimal land use management for soil erosion control by using an interval-parameter fuzzy two-stage stochastic programming approach.

PubMed

Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong

2013-09-01

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10(9) $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.

Optimal Land Use Management for Soil Erosion Control by Using an Interval-Parameter Fuzzy Two-Stage Stochastic Programming Approach

NASA Astrophysics Data System (ADS)

Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong

2013-09-01

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 109 was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.

Generation Expansion Planning With Large Amounts of Wind Power via Decision-Dependent Stochastic Programming

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

Zhan, Yiduo; Zheng, Qipeng P.; Wang, Jianhui

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets' planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of windmore » power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning.« less

Solving multistage stochastic programming models of portfolio selection with outstanding liabilities

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

Edirisinghe, C.

1994-12-31

Models for portfolio selection in the presence of an outstanding liability have received significant attention, for example, models for pricing options. The problem may be described briefly as follows: given a set of risky securities (and a riskless security such as a bond), and given a set of cash flows, i.e., outstanding liability, to be met at some future date, determine an initial portfolio and a dynamic trading strategy for the underlying securities such that the initial cost of the portfolio is within a prescribed wealth level and the expected cash surpluses arising from trading is maximized. While the tradingmore » strategy should be self-financing, there may also be other restrictions such as leverage and short-sale constraints. Usually the treatment is limited to binomial evolution of uncertainty (of stock price), with possible extensions for developing computational bounds for multinomial generalizations. Posing as stochastic programming models of decision making, we investigate alternative efficient solution procedures under continuous evolution of uncertainty, for discrete time economies. We point out an important moment problem arising in the portfolio selection problem, the solution (or bounds) on which provides the basis for developing efficient computational algorithms. While the underlying stochastic program may be computationally tedious even for a modest number of trading opportunities (i.e., time periods), the derived algorithms may used to solve problems whose sizes are beyond those considered within stochastic optimization.« less

Stochastic Education in Childhood: Examining the Learning of Teachers and Students

ERIC Educational Resources Information Center

de Souza, Antonio Carlos; Lopes, Celi Espasandin; de Oliveira, Débora

2014-01-01

This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic…

Stochastic Geomorphology: A Framework for Creating General Principles on Erosion and Sedimentation in River Basins (Invited)

NASA Astrophysics Data System (ADS)

Benda, L. E.

2009-12-01

Stochastic geomorphology refers to the interaction of the stochastic field of sediment supply with hierarchically branching river networks where erosion, sediment flux and sediment storage are described by their probability densities. There are a number of general principles (hypotheses) that stem from this conceptual and numerical framework that may inform the science of erosion and sedimentation in river basins. Rainstorms and other perturbations, characterized by probability distributions of event frequency and magnitude, stochastically drive sediment influx to channel networks. The frequency-magnitude distribution of sediment supply that is typically skewed reflects strong interactions among climate, topography, vegetation, and geotechnical controls that vary between regions; the distribution varies systematically with basin area and the spatial pattern of erosion sources. Probability densities of sediment flux and storage evolve from more to less skewed forms downstream in river networks due to the convolution of the population of sediment sources in a watershed that should vary with climate, network patterns, topography, spatial scale, and degree of erosion asynchrony. The sediment flux and storage distributions are also transformed downstream due to diffusion, storage, interference, and attrition. In stochastic systems, the characteristically pulsed sediment supply and transport can create translational or stationary-diffusive valley and channel depositional landforms, the geometries of which are governed by sediment flux-network interactions. Episodic releases of sediment to the network can also drive a system memory reflected in a Hurst Effect in sediment yields and thus in sedimentological records. Similarly, discreet events of punctuated erosion on hillslopes can lead to altered surface and subsurface properties of a population of erosion source areas that can echo through time and affect subsequent erosion and sediment flux rates. Spatial patterns of probability densities have implications for the frequency and magnitude of sediment transport and storage and thus for the formation of alluvial and colluvial landforms throughout watersheds. For instance, the combination and interference of probability densities of sediment flux at confluences creates patterns of riverine heterogeneity, including standing waves of sediment with associated age distributions of deposits that can vary from younger to older depending on network geometry and position. Although the watershed world of probability densities is rarified and typically confined to research endeavors, it has real world implications for the day-to-day work on hillslopes and in fluvial systems, including measuring erosion, sediment transport, mapping channel morphology and aquatic habitats, interpreting deposit stratigraphy, conducting channel restoration, and applying environmental regulations. A question for the geomorphology community is whether the stochastic framework is useful for advancing our understanding of erosion and sedimentation and whether it should stimulate research to further develop, refine and test these and other principles. For example, a changing climate should lead to shifts in probability densities of erosion, sediment flux, storage, and associated habitats and thus provide a useful index of climate change in earth science forecast models.

Impacts of renewable fuel regulation and production on agriculture, energy, and welfare

NASA Astrophysics Data System (ADS)

McPhail, Lihong Lu

The purpose of this dissertation is to study the impact of U.S. federal renewable fuel regulations on energy and agriculture commodity markets and welfare. We consider two federal ethanol policies: the Renewable Fuel Standard (RFS) contained in the Energy Security and Independence Act of 2007 and tax credits to ethanol blenders contained in the Food, Conservation, and Energy Act of 2008. My first essay estimates the distribution of short-run impacts of changing federal ethanol policies on U.S. energy prices, agricultural commodity prices, and welfare through a stochastic partial equilibrium model of U.S. corn, ethanol, and gasoline markets. My second essay focuses on studying the price behavior of the renewable fuel credit (RFC) market, which is the mechanism developed by the Environmental Protection Agency (EPA) to meet the RFS. RFCs are a tradable, bankable, and borrowable accounting mechanism to ensure that all obligated parties use a mandated level of renewable fuel. I first develop a conceptual framework to understand how the market works and then apply stochastic dynamic programming to simulate prices for RFCs, examine the sensitivity of prices to relevant shocks, and estimate RFC option premiums. My third essay assesses the impact of policy led U.S. ethanol on the markets of global crude oil and U.S. gasoline using a structural Vector Auto Regression model of global crude oil, U.S. gasoline and ethanol markets.

Post-transcriptional bursting in genes regulated by small RNA molecules

NASA Astrophysics Data System (ADS)

Rodrigo, Guillermo

2018-03-01

Gene expression programs in living cells are highly dynamic due to spatiotemporal molecular signaling and inherent biochemical stochasticity. Here we study a mechanism based on molecule-to-molecule variability at the RNA level for the generation of bursts of protein production, which can lead to heterogeneity in a cell population. We develop a mathematical framework to show numerically and analytically that genes regulated post transcriptionally by small RNA molecules can exhibit such bursts due to different states of translation activity (on or off), mostly revealed in a regime of few molecules. We exploit this framework to compare transcriptional and post-transcriptional bursting and also to illustrate how to tune the resulting protein distribution with additional post-transcriptional regulations. Moreover, because RNA-RNA interactions are predictable with an energy model, we define the kinetic constants of on-off switching as functions of the two characteristic free-energy differences of the system, activation and formation, with a nonequilibrium scheme. Overall, post-transcriptional bursting represents a distinctive principle linking gene regulation to gene expression noise, which highlights the importance of the RNA layer beyond the simple information transfer paradigm and significantly contributes to the understanding of the intracellular processes from a first-principles perspective.

Efficient computation of optimal actions.

PubMed

Todorov, Emanuel

2009-07-14

Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress--as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.

Theory Learning as Stochastic Search in the Language of Thought

ERIC Educational Resources Information Center

Ullman, Tomer D.; Goodman, Noah D.; Tenenbaum, Joshua B.

2012-01-01

We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While…

Harmony Theory: A Mathematical Framework for Stochastic Parallel Processing.

ERIC Educational Resources Information Center

Smolensky, Paul

This paper presents preliminary results of research founded on the hypothesis that in real environments there exist regularities that can be idealized as mathematical structures that are simple enough to be analyzed. The author considered three steps in analyzing the encoding of modularity of the environment. First, a general information…

Mastodon

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

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

First passage times in homogeneous nucleation: Dependence on the total number of particles

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

Yvinec, Romain; Bernard, Samuel; Pujo-Menjouet, Laurent

2016-01-21

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find thatmore » the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.« less

First passage times in homogeneous nucleation: Dependence on the total number of particles

NASA Astrophysics Data System (ADS)

Yvinec, Romain; Bernard, Samuel; Hingant, Erwan; Pujo-Menjouet, Laurent

2016-01-01

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.

Improved Bayesian Infrasonic Source Localization for regional infrasound

DOE PAGES

Blom, Philip S.; Marcillo, Omar; Arrowsmith, Stephen J.

2015-10-20

The Bayesian Infrasonic Source Localization (BISL) methodology is examined and simplified providing a generalized method of estimating the source location and time for an infrasonic event and the mathematical framework is used therein. The likelihood function describing an infrasonic detection used in BISL has been redefined to include the von Mises distribution developed in directional statistics and propagation-based, physically derived celerity-range and azimuth deviation models. Frameworks for constructing propagation-based celerity-range and azimuth deviation statistics are presented to demonstrate how stochastic propagation modelling methods can be used to improve the precision and accuracy of the posterior probability density function describing themore » source localization. Infrasonic signals recorded at a number of arrays in the western United States produced by rocket motor detonations at the Utah Test and Training Range are used to demonstrate the application of the new mathematical framework and to quantify the improvement obtained by using the stochastic propagation modelling methods. Moreover, using propagation-based priors, the spatial and temporal confidence bounds of the source decreased by more than 40 per cent in all cases and by as much as 80 per cent in one case. Further, the accuracy of the estimates remained high, keeping the ground truth within the 99 per cent confidence bounds for all cases.« less

Probability-Based Recognition Framework for Underwater Landmarks Using Sonar Images †

PubMed Central

Choi, Jinwoo; Choi, Hyun-Taek

2017-01-01

This paper proposes a probability-based framework for recognizing underwater landmarks using sonar images. Current recognition methods use a single image, which does not provide reliable results because of weaknesses of the sonar image such as unstable acoustic source, many speckle noises, low resolution images, single channel image, and so on. However, using consecutive sonar images, if the status—i.e., the existence and identity (or name)—of an object is continuously evaluated by a stochastic method, the result of the recognition method is available for calculating the uncertainty, and it is more suitable for various applications. Our proposed framework consists of three steps: (1) candidate selection, (2) continuity evaluation, and (3) Bayesian feature estimation. Two probability methods—particle filtering and Bayesian feature estimation—are used to repeatedly estimate the continuity and feature of objects in consecutive images. Thus, the status of the object is repeatedly predicted and updated by a stochastic method. Furthermore, we develop an artificial landmark to increase detectability by an imaging sonar, which we apply to the characteristics of acoustic waves, such as instability and reflection depending on the roughness of the reflector surface. The proposed method is verified by conducting basin experiments, and the results are presented. PMID:28837068

Investment portfolio of a pension fund: Stochastic model

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

Bosch-Princep, M.; Fontanals-Albiol, H.

1994-12-31

This paper presents a stochastic programming model that aims at getting the optimal investment portfolio of a Pension Funds. The model has been designed bearing in mind the liabilities of the Funds to its members. The essential characteristic of the objective function and the constraints is the randomness of the coefficients and the right hand side of the constraints, so it`s necessary to use techniques of stochastic mathematical programming to get information about the amount of money that should be assigned to each sort of investment. It`s important to know the risky attitude of the person that has to takemore » decisions towards running risks. It incorporates the relation between the different coefficients of the objective function and constraints of each period of temporal horizon, through lineal and discrete random processes. Likewise, it includes the hypotheses that are related to Spanish law concerning the subject of Pension Funds.« less

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.

An Asymptotic and Stochastic Theory for the Effects of Surface Gravity Waves on Currents and Infragravity Waves

NASA Astrophysics Data System (ADS)

McWilliams, J. C.; Lane, E.; Melville, K.; Restrepo, J.; Sullivan, P.

2004-12-01

Oceanic surface gravity waves are approximately irrotational, weakly nonlinear, and conservative, and they have a much shorter time scale than oceanic currents and longer waves (e.g., infragravity waves) --- except where the primary surface waves break. This provides a framework for an asymptotic theory, based on separation of time (and space) scales, of wave-averaged effects associated with the conservative primary wave dynamics combined with a stochastic representation of the momentum transfer and induced mixing associated with non-conservative wave breaking. Such a theory requires only modest information about the primary wave field from measurements or operational model forecasts and thus avoids the enormous burden of calculating the waves on their intrinsically small space and time scales. For the conservative effects, the result is a vortex force associated with the primary wave's Stokes drift; a wave-averaged Bernoulli head and sea-level set-up; and an incremental material advection by the Stokes drift. This can be compared to the "radiation stress" formalism of Longuet-Higgins, Stewart, and Hasselmann; it is shown to be a preferable representation since the radiation stress is trivial at its apparent leading order. For the non-conservative breaking effects, a population of stochastic impulses is added to the current and infragravity momentum equations with distribution functions taken from measurements. In offshore wind-wave equilibria, these impulses replace the conventional surface wind stress and cause significant differences in the surface boundary layer currents and entrainment rate, particularly when acting in combination with the conservative vortex force. In the surf zone, where breaking associated with shoaling removes nearly all of the primary wave momentum and energy, the stochastic forcing plays an analogous role as the widely used nearshore radiation stress parameterizations. This talk describes the theoretical framework and presents some preliminary solutions using it. McWilliams, J.C., J.M. Restrepo, & E.M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech. 511, 135-178. Sullivan, P.P., J.C. McWilliams, & W.K. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. J. Fluid Mech. 507, 143-174.

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.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

PubMed Central

2018-01-01

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site. PMID:29386401

Conserving the linear momentum in stochastic dynamics: Dissipative particle dynamics as a general strategy to achieve local thermostatization in molecular dynamics simulations.

PubMed

Passler, Peter P; Hofer, Thomas S

2017-02-15

Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short-coming has little impact on structural and short-time dynamic properties, it can be shown that dynamics in the long-time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD-region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard-Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose-Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self-diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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

NASA Astrophysics Data System (ADS)

Wheater, H. S.

2015-12-01

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

Impact of a Stochastic Parameterization Scheme on El Nino-Southern Oscillation in the Community Climate System Model

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Berner, J.; Sardeshmukh, P. D.

2017-12-01

Stochastic parameterizations have been used for more than a decade in atmospheric models. They provide a way to represent model uncertainty through representing the variability of unresolved sub-grid processes, and have been shown to have a beneficial effect on the spread and mean state for medium- and extended-range forecasts. There is increasing evidence that stochastic parameterization of unresolved processes can improve the bias in mean and variability, e.g. by introducing a noise-induced drift (nonlinear rectification), and by changing the residence time and structure of flow regimes. We present results showing the impact of including the Stochastically Perturbed Parameterization Tendencies scheme (SPPT) in coupled runs of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 4 (CAM4) with historical forcing. SPPT results in a significant improvement in the representation of the El Nino-Southern Oscillation in CAM4, improving the power spectrum, as well as both the inter- and intra-annual variability of tropical pacific sea surface temperatures. We use a Linear Inverse Modelling framework to gain insight into the mechanisms by which SPPT has improved ENSO-variability.

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

PubMed

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

2010-03-26

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

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

PubMed Central

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-01-01

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity). PMID:25976626

Evaluation of stochastic differential equation approximation of ion channel gating models.

PubMed

Bruce, Ian C

2009-04-01

Fox and Lu derived an algorithm based on stochastic differential equations for approximating the kinetics of ion channel gating that is simpler and faster than "exact" algorithms for simulating Markov process models of channel gating. However, the approximation may not be sufficiently accurate to predict statistics of action potential generation in some cases. The objective of this study was to develop a framework for analyzing the inaccuracies and determining their origin. Simulations of a patch of membrane with voltage-gated sodium and potassium channels were performed using an exact algorithm for the kinetics of channel gating and the approximate algorithm of Fox & Lu. The Fox & Lu algorithm assumes that channel gating particle dynamics have a stochastic term that is uncorrelated, zero-mean Gaussian noise, whereas the results of this study demonstrate that in many cases the stochastic term in the Fox & Lu algorithm should be correlated and non-Gaussian noise with a non-zero mean. The results indicate that: (i) the source of the inaccuracy is that the Fox & Lu algorithm does not adequately describe the combined behavior of the multiple activation particles in each sodium and potassium channel, and (ii) the accuracy does not improve with increasing numbers of channels.

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity.

PubMed

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-05-15

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

NASA Astrophysics Data System (ADS)

Agliari, Elena; Altavilla, Matteo; Barra, Adriano; Dello Schiavo, Lorenzo; Katz, Evgeny

2015-05-01

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Quantum stochastic walks on networks for decision-making.

PubMed

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-31

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

NASA Astrophysics Data System (ADS)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

PubMed Central

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-01-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making. PMID:27030372

Health safety nets can break cycles of poverty and disease: a stochastic ecological model

PubMed Central

Pluciński, Mateusz M.; Ngonghala, Calistus N.; Bonds, Matthew H.

2011-01-01

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a ‘safety net’, defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium. PMID:21593026

Perturbation expansions of stochastic wavefunctions for open quantum systems

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-11-01

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Trading strategies for distribution company with stochastic distributed energy resources

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

Zhang, Chunyu; Wang, Qi; Wang, Jianhui

2016-09-01

This paper proposes a methodology to address the trading strategies of a proactive distribution company (PDISCO) engaged in the transmission-level (TL) markets. A one-leader multi-follower bilevel model is presented to formulate the gaming framework between the PDISCO and markets. The lower-level (LL) problems include the TL day-ahead market and scenario-based real-time markets, respectively with the objectives of maximizing social welfare and minimizing operation cost. The upper-level (UL) problem is to maximize the PDISCO’s profit across these markets. The PDISCO’s strategic offers/bids interactively influence the outcomes of each market. Since the LL problems are linear and convex, while the UL problemmore » is non-linear and non-convex, an equivalent primal–dual approach is used to reformulate this bilevel model to a solvable mathematical program with equilibrium constraints (MPEC). The effectiveness of the proposed model is verified by case studies.« less

Distance estimation and collision prediction for on-line robotic motion planning

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1991-01-01

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem has been incorporated in the framework of an in-line motion planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning the deterministic problem, where the information about the objects is assumed to be certain is examined. If instead of the Euclidean norm, L(sub 1) or L(sub infinity) norms are used to represent distance, the problem becomes a linear programming problem. The stochastic problem is formulated, where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: (1) filtering of the minimum distance between the robot and the moving object, at the present time; and (2) prediction of the minimum distance in the future, in order to predict possible collisions with the moving obstacles and estimate the collision time.

A Generalized Formulation of Demand Response under Market Environments

NASA Astrophysics Data System (ADS)

Nguyen, Minh Y.; Nguyen, Duc M.

2015-06-01

This paper presents a generalized formulation of Demand Response (DR) under deregulated electricity markets. The problem is scheduling and controls the consumption of electrical loads according to the market price to minimize the energy cost over a day. Taking into account the modeling of customers' comfort (i.e., preference), the formulation can be applied to various types of loads including what was traditionally classified as critical loads (e.g., air conditioning, lights). The proposed DR scheme is based on Dynamic Programming (DP) framework and solved by DP backward algorithm in which the stochastic optimization is used to treat the uncertainty, if any occurred in the problem. The proposed formulation is examined with the DR problem of different loads, including Heat Ventilation and Air Conditioning (HVAC), Electric Vehicles (EVs) and a newly DR on the water supply systems of commercial buildings. The result of simulation shows significant saving can be achieved in comparison with their traditional (On/Off) scheme.

BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs

DOE PAGES

Barnett, Jason; Watson, Jean -Paul; Woodruff, David L.

2016-11-27

Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. Additionally, to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.

Programming Probabilistic Structural Analysis for Parallel Processing Computer

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Chen, Heh-Chyun; Twisdale, Lawrence A.; Chamis, Christos C.; Murthy, Pappu L. N.

1991-01-01

The ultimate goal of this research program is to make Probabilistic Structural Analysis (PSA) computationally efficient and hence practical for the design environment by achieving large scale parallelism. The paper identifies the multiple levels of parallelism in PSA, identifies methodologies for exploiting this parallelism, describes the development of a parallel stochastic finite element code, and presents results of two example applications. It is demonstrated that speeds within five percent of those theoretically possible can be achieved. A special-purpose numerical technique, the stochastic preconditioned conjugate gradient method, is also presented and demonstrated to be extremely efficient for certain classes of PSA problems.

Simulation-based planning for theater air warfare

NASA Astrophysics Data System (ADS)

Popken, Douglas A.; Cox, Louis A., Jr.

2004-08-01

Planning for Theatre Air Warfare can be represented as a hierarchy of decisions. At the top level, surviving airframes must be assigned to roles (e.g., Air Defense, Counter Air, Close Air Support, and AAF Suppression) in each time period in response to changing enemy air defense capabilities, remaining targets, and roles of opposing aircraft. At the middle level, aircraft are allocated to specific targets to support their assigned roles. At the lowest level, routing and engagement decisions are made for individual missions. The decisions at each level form a set of time-sequenced Courses of Action taken by opposing forces. This paper introduces a set of simulation-based optimization heuristics operating within this planning hierarchy to optimize allocations of aircraft. The algorithms estimate distributions for stochastic outcomes of the pairs of Red/Blue decisions. Rather than using traditional stochastic dynamic programming to determine optimal strategies, we use an innovative combination of heuristics, simulation-optimization, and mathematical programming. Blue decisions are guided by a stochastic hill-climbing search algorithm while Red decisions are found by optimizing over a continuous representation of the decision space. Stochastic outcomes are then provided by fast, Lanchester-type attrition simulations. This paper summarizes preliminary results from top and middle level models.

A Numerical Method for the Simulation of Skew Brownian Motion and its Application to Diffusive Shock Acceleration of Charged Particles

NASA Astrophysics Data System (ADS)

McEvoy, Erica L.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

Comparison of SVAT models for simulating and optimizing deficit irrigation systems in arid and semi-arid countries under climate variability

NASA Astrophysics Data System (ADS)

Kloss, Sebastian; Schuetze, Niels; Schmitz, Gerd H.

2010-05-01

The strong competition for fresh water in order to fulfill the increased demand for food worldwide has led to a renewed interest in techniques to improve water use efficiency (WUE) such as controlled deficit irrigation. Furthermore, as the implementation of crop models into complex decision support systems becomes more and more common, it is imperative to reliably predict the WUE as ratio of water consumption and yield. The objective of this paper is the assessment of the problems the crop models - such as FAO-33, DAISY, and APSIM in this study - face when maximizing the WUE. We applied these crop models for calculating the risk in yield reduction in view of different sources of uncertainty (e.g. climate) employing a stochastic framework for decision support for the planning of water supply in irrigation. The stochastic framework consists of: (i) a weather generator for simulating regional impacts of climate change; (ii) a new tailor-made evolutionary optimization algorithm for optimal irrigation scheduling with limited water supply; and (iii) the above mentioned models for simulating water transport and crop growth in a sound manner. The results present stochastic crop water production functions (SCWPF) for different crops which can be used as basic tools for assessing the impact of climate variability on the risk for the potential yield. Case studies from India, Oman, Malawi, and France are presented to assess the differences in modeling water stress and yield response for the different crop models.

Stochastic correlative firing for figure-ground segregation.

PubMed

Chen, Zhe

2005-03-01

Segregation of sensory inputs into separate objects is a central aspect of perception and arises in all sensory modalities. The figure-ground segregation problem requires identifying an object of interest in a complex scene, in many cases given binaural auditory or binocular visual observations. The computations required for visual and auditory figure-ground segregation share many common features and can be cast within a unified framework. Sensory perception can be viewed as a problem of optimizing information transmission. Here we suggest a stochastic correlative firing mechanism and an associative learning rule for figure-ground segregation in several classic sensory perception tasks, including the cocktail party problem in binaural hearing, binocular fusion of stereo images, and Gestalt grouping in motion perception.

Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

NASA Astrophysics Data System (ADS)

Marcozzi, Michael D.

2008-12-01

We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.

[Stochastic model of infectious diseases transmission].

PubMed

Ruiz-Ramírez, Juan; Hernández-Rodríguez, Gabriela Eréndira

2009-01-01

Propose a mathematic model that shows how population structure affects the size of infectious disease epidemics. This study was conducted during 2004 at the University of Colima. It used generalized small-world network topology to represent contacts that occurred within and between families. To that end, two programs in MATLAB were conducted to calculate the efficiency of the network. The development of a program in the C programming language was also required, that represents the stochastic susceptible-infectious-removed model, and simultaneous results were obtained for the number of infected people. An increased number of families connected by meeting sites impacted the size of the infectious diseases by roughly 400%. Population structure influences the rapid spread of infectious diseases, reaching epidemic effects.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Stochastic stability of sigma-point Unscented Predictive Filter.

PubMed

Cao, Lu; Tang, Yu; Chen, Xiaoqian; Zhao, Yong

2015-07-01

In this paper, the Unscented Predictive Filter (UPF) is derived based on unscented transformation for nonlinear estimation, which breaks the confine of conventional sigma-point filters by employing Kalman filter as subject investigated merely. In order to facilitate the new method, the algorithm flow of UPF is given firstly. Then, the theoretical analyses demonstrate that the estimate accuracy of the model error and system for the UPF is higher than that of the conventional PF. Moreover, the authors analyze the stochastic boundedness and the error behavior of Unscented Predictive Filter (UPF) for general nonlinear systems in a stochastic framework. In particular, the theoretical results present that the estimation error remains bounded and the covariance keeps stable if the system׳s initial estimation error, disturbing noise terms as well as the model error are small enough, which is the core part of the UPF theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Active stability augmentation of large space structures: A stochastic control problem

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1987-01-01

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

NASA Astrophysics Data System (ADS)

González Arenas, Zochil; Barci, Daniel G.

2012-12-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

Political model of social evolution

PubMed Central

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-01-01

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved. PMID:22198760

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.

Ion pickup, scattering, and stochastic acceleration in the cometary environment of P/Giacobini-Zinner

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1991-01-01

Observations and theory related to the scattering and acceleration of cometary pickup ions are reviewed with emphasis on Comet P/Giacobini-Zinner. A comparison of the regions upstream and downstream of the bow shock is made to assess the relative merits of each as a site for stochastic acceleration of ions above the pickup energy through interaction with low-frequency MHD waves. In the far upstream region the data are most consistent with a model where pickup ions generate a low level of MHD waves but remain relatively scatter-free. In the downstream region intense magnetic fluctuations gives rise to rapid isotropization of the ions and a second-order stochastic acceleration. The properties of the MHD power spectrum are related to the energetic ion spectrum in the framework of a leaky box model where the bulk of the acceleration occurs downstream of the shock throughout the cometosheath. Good agreement of the observations with theory is evident for both P/Giacobini-Zinner and P/Halley.

Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

NASA Astrophysics Data System (ADS)

Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

2017-08-01

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

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

Natural Erosion of Sandstone as Shape Optimisation.

PubMed

Ostanin, Igor; Safonov, Alexander; Oseledets, Ivan

2017-12-11

Natural arches, pillars and other exotic sandstone formations have always been attracting attention for their unusual shapes and amazing mechanical balance that leave a strong impression of intelligent design rather than the result of a stochastic process. It has been recently demonstrated that these shapes could have been the result of the negative feedback between stress and erosion that originates in fundamental laws of friction between the rock's constituent particles. Here we present a deeper analysis of this idea and bridge it with the approaches utilized in shape and topology optimisation. It appears that the processes of natural erosion, driven by stochastic surface forces and Mohr-Coulomb law of dry friction, can be viewed within the framework of local optimisation for minimum elastic strain energy. Our hypothesis is confirmed by numerical simulations of the erosion using the topological-shape optimisation model. Our work contributes to a better understanding of stochastic erosion and feasible landscape formations that could be found on Earth and beyond.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

NASA Astrophysics Data System (ADS)

Romanczuk, P.; Bär, M.; Ebeling, W.; Lindner, B.; Schimansky-Geier, L.

2012-03-01

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.

Political model of social evolution.

PubMed

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-12-27

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved.

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Shu, Ruiwen, E-mail: rshu2@math.wisc.edu

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operatormore » that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.« less

Integrated communication and control systems. II - Design considerations

NASA Technical Reports Server (NTRS)

Ray, Asok; Halevi, Yoram

1988-01-01

The ICCS design issues for nonperiodic and stochastic delays are addressed and the framework for alternative design procedures is outlined. The impact of network-induced delays on system stability is investigated and their physical significance is demonstrated using a simulation. The negative effects of vacant sampling and message rejection at the controller are demonstrated.

Markov Random Fields, Stochastic Quantization and Image Analysis

DTIC Science & Technology

1990-01-01

Markov random fields based on the lattice Z2 have been extensively used in image analysis in a Bayesian framework as a-priori models for the...of Image Analysis can be given some fundamental justification then there is a remarkable connection between Probabilistic Image Analysis , Statistical Mechanics and Lattice-based Euclidean Quantum Field Theory.

Pricing Policy and the College Choice Process. AIR Forum Paper 1978.

ERIC Educational Resources Information Center

Chapman, Randall G.

A presentation of a conceptual framework for viewing the admissions management process in higher education institutions and a discussion of the pricing policy process, particularly of private colleges and universities, precedes an examination of the stochastic utility model, a statistical model of the college choice process. Using student choice…

Mixture Distributions for Modeling Lead Time Demand in Coordinated Supply Chains

DTIC Science & Technology

2014-04-30

International Journal of Production Economics , 101...backorder price discount. International Journal of Production Economics , 111, 118–128. McClain, J. O., & Thomas, L. J. (1985). Operations management...2008). Using the inventory-theoretic framework to determine cost-minimizing supply strategies in a stochastic setting. International Journal of Production Economics ,

A MODELING FRAMEWORK FOR ESTIMATING CHILDREN'S RESIDENTIAL EXPOSURE AND DOSE TO CHLORPYRIFOS VIA DERMAL RESIDUE CONTACT AND NON-DIETARY INGESTION

EPA Science Inventory

To help address the Food Quality Protection Act of 1996, a physically-based probabilistic model (Residential Stochastic Human Exposure and Dose Simulation Model for Pesticides; Residential-SHEDS) has been developed to quantify and analyze dermal and non-dietary ingestion exposu...

Development of a restricted state space stochastic differential equation model for bacterial growth in rich media.

PubMed

Møller, Jan Kloppenborg; Bergmann, Kirsten Riber; Christiansen, Lasse Engbo; Madsen, Henrik

2012-07-21

In the present study, bacterial growth in a rich media is analysed in a Stochastic Differential Equation (SDE) framework. It is demonstrated that the SDE formulation and smoothened state estimates provide a systematic framework for data driven model improvements, using random walk hidden states. Bacterial growth is limited by the available substrate and the inclusion of diffusion must obey this natural restriction. By inclusion of a modified logistic diffusion term it is possible to introduce a diffusion term flexible enough to capture both the growth phase and the stationary phase, while concentration is restricted to the natural state space (substrate and bacteria non-negative). The case considered is the growth of Salmonella and Enterococcus in a rich media. It is found that a hidden state is necessary to capture the lag phase of growth, and that a flexible logistic diffusion term is needed to capture the random behaviour of the growth model. Further, it is concluded that the Monod effect is not needed to capture the dynamics of bacterial growth in the data presented. Copyright © 2012 Elsevier Ltd. All rights reserved.

path integral approach to closed form pricing formulas in the Heston framework.

NASA Astrophysics Data System (ADS)

Lemmens, Damiaan; Wouters, Michiel; Tempere, Jacques; Foulon, Sven

2008-03-01

We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert).

Water resources planning and management : A stochastic dual dynamic programming approach

NASA Astrophysics Data System (ADS)

Goor, Q.; Pinte, D.; Tilmant, A.

2008-12-01

Allocating water between different users and uses, including the environment, is one of the most challenging task facing water resources managers and has always been at the heart of Integrated Water Resources Management (IWRM). As water scarcity is expected to increase over time, allocation decisions among the different uses will have to be found taking into account the complex interactions between water and the economy. Hydro-economic optimization models can capture those interactions while prescribing efficient allocation policies. Many hydro-economic models found in the literature are formulated as large-scale non linear optimization problems (NLP), seeking to maximize net benefits from the system operation while meeting operational and/or institutional constraints, and describing the main hydrological processes. However, those models rarely incorporate the uncertainty inherent to the availability of water, essentially because of the computational difficulties associated stochastic formulations. The purpose of this presentation is to present a stochastic programming model that can identify economically efficient allocation policies in large-scale multipurpose multireservoir systems. The model is based on stochastic dual dynamic programming (SDDP), an extension of traditional SDP that is not affected by the curse of dimensionality. SDDP identify efficient allocation policies while considering the hydrologic uncertainty. The objective function includes the net benefits from the hydropower and irrigation sectors, as well as penalties for not meeting operational and/or institutional constraints. To be able to implement the efficient decomposition scheme that remove the computational burden, the one-stage SDDP problem has to be a linear program. Recent developments improve the representation of the non-linear and mildly non- convex hydropower function through a convex hull approximation of the true hydropower function. This model is illustrated on a cascade of 14 reservoirs on the Nile river basin.

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

NASA Astrophysics Data System (ADS)

Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

2017-01-01

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

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.

A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2012-01-01

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2011-01-01

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

Enhancement of the Logistics Battle Command Model: Architecture Upgrades and Attrition Module Development

DTIC Science & Technology

2017-01-05

module. 15. SUBJECT TERMS Logistics, attrition, discrete event simulation, Simkit, LBC 16. SECURITY CLASSIFICATION OF: Unclassified 17. LIMITATION...stochastics, and discrete event model programmed in Java building largely on the Simkit library. The primary purpose of the LBC model is to support...equations makes them incompatible with the discrete event construct of LBC. Bullard further advances this methodology by developing a stochastic

Toward Control of Universal Scaling in Critical Dynamics

DTIC Science & Technology

2016-01-27

program that aims to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Uwe Tauber Uwe C. T? uber , Michel Pleimling, Daniel J. Stilwell 611102 c. THIS PAGE The public reporting burden...to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi-component systems, namely

Mathematical Sciences Division 1992 Programs

DTIC Science & Technology

1992-10-01

statistical theory that underlies modern signal analysis . There is a strong emphasis on stochastic processes and time series , particularly those which...include optimal resource planning and real- time scheduling of stochastic shop-floor processes. Scheduling systems will be developed that can adapt to...make forecasts for the length-of-service time series . Protocol analysis of these sessions will be used to idenify relevant contextual features and to

Dynamically Consistent Parameterization of Mesoscale Eddies This work aims at parameterization of eddy effects for use in non-eddy-resolving ocean models and focuses on the effect of the stochastic part of the eddy forcing that backscatters and induces eastward jet extension of the western boundary currents and its adjacent recirculation zones.

NASA Astrophysics Data System (ADS)

Berloff, P. S.

2016-12-01

This work aims at developing a framework for dynamically consistent parameterization of mesoscale eddy effects for use in non-eddy-resolving ocean circulation models. The proposed eddy parameterization framework is successfully tested on the classical, wind-driven double-gyre model, which is solved both with explicitly resolved vigorous eddy field and in the non-eddy-resolving configuration with the eddy parameterization replacing the eddy effects. The parameterization focuses on the effect of the stochastic part of the eddy forcing that backscatters and induces eastward jet extension of the western boundary currents and its adjacent recirculation zones. The parameterization locally approximates transient eddy flux divergence by spatially localized and temporally periodic forcing, referred to as the plunger, and focuses on the linear-dynamics flow solution induced by it. The nonlinear self-interaction of this solution, referred to as the footprint, characterizes and quantifies the induced eddy forcing exerted on the large-scale flow. We find that spatial pattern and amplitude of each footprint strongly depend on the underlying large-scale flow, and the corresponding relationships provide the basis for the eddy parameterization and its closure on the large-scale flow properties. Dependencies of the footprints on other important parameters of the problem are also systematically analyzed. The parameterization utilizes the local large-scale flow information, constructs and scales the corresponding footprints, and then sums them up over the gyres to produce the resulting eddy forcing field, which is interactively added to the model as an extra forcing. Thus, the assumed ensemble of plunger solutions can be viewed as a simple model for the cumulative effect of the stochastic eddy forcing. The parameterization framework is implemented in the simplest way, but it provides a systematic strategy for improving the implementation algorithm.

A fuzzy stochastic framework for managing hydro-environmental and socio-economic interactions under uncertainty

NASA Astrophysics Data System (ADS)

Subagadis, Yohannes Hagos; Schütze, Niels; Grundmann, Jens

2014-05-01

An amplified interconnectedness between a hydro-environmental and socio-economic system brings about profound challenges of water management decision making. In this contribution, we present a fuzzy stochastic approach to solve a set of decision making problems, which involve hydrologically, environmentally, and socio-economically motivated criteria subjected to uncertainty and ambiguity. The proposed methodological framework combines objective and subjective criteria in a decision making procedure for obtaining an acceptable ranking in water resources management alternatives under different type of uncertainty (subjective/objective) and heterogeneous information (quantitative/qualitative) simultaneously. The first step of the proposed approach involves evaluating the performance of alternatives with respect to different types of criteria. The ratings of alternatives with respect to objective and subjective criteria are evaluated by simulation-based optimization and fuzzy linguistic quantifiers, respectively. Subjective and objective uncertainties related to the input information are handled through linking fuzziness and randomness together. Fuzzy decision making helps entail the linguistic uncertainty and a Monte Carlo simulation process is used to map stochastic uncertainty. With this framework, the overall performance of each alternative is calculated using an Order Weighted Averaging (OWA) aggregation operator accounting for decision makers' experience and opinions. Finally, ranking is achieved by conducting pair-wise comparison of management alternatives. This has been done on the basis of the risk defined by the probability of obtaining an acceptable ranking and mean difference in total performance for the pair of management alternatives. The proposed methodology is tested in a real-world hydrosystem, to find effective and robust intervention strategies for the management of a coastal aquifer system affected by saltwater intrusion due to excessive groundwater extraction for irrigated agriculture and municipal use. The results show that the approach gives useful support for robust decision-making and is sensitive to the decision makers' degree of optimism.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Decentralized stochastic control

NASA Technical Reports Server (NTRS)

Speyer, J. L.

1980-01-01

Decentralized stochastic control is characterized by being decentralized in that the information to one controller is not the same as information to another controller. The system including the information has a stochastic or uncertain component. This complicates the development of decision rules which one determines under the assumption that the system is deterministic. The system is dynamic which means the present decisions affect future system responses and the information in the system. This circumstance presents a complex problem where tools like dynamic programming are no longer applicable. These difficulties are discussed from an intuitive viewpoint. Particular assumptions are introduced which allow a limited theory which produces mechanizable affine decision rules.

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

PubMed

Avanzini, Francesco; Moro, Giorgio J

2018-03-15

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

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

Lin, Yen Ting; Buchler, Nicolas E.

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

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

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

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

The role of stochastic storms on hillslope runoff generation and connectivity in a dryland basin

NASA Astrophysics Data System (ADS)

Michaelides, K.; Singer, M. B.; Mudd, S. M.

2016-12-01

Despite low annual rainfall, dryland basins can generate significant surface runoff during certain rainstorms, which can cause flash flooding and high rates of erosion. However, it remains challenging to anticipate the nature and frequency of runoff generation in hydrological systems which are driven by spatially and temporally stochastic rainstorms. In particular, the stochasticity of rainfall presents challenges to simulating the hydrological response of dryland basins and understanding flow connectivity from hillslopes to the channel. Here we simulate hillslope runoff generation using rainfall characteristics produced by a simple stochastic rainfall generator, which is based on a rich rainfall dataset from the Walnut Gulch Experimental Watershed (WGEW) in Arizona, USA. We assess hillslope runoff generation using the hydrological model, COUP2D, driven by a subset of characteristic output from multiple ensembles of decadal monsoonal rainfall from the stochastic rainfall generator. The rainfall generator operates across WGEW by simulating storms with areas smaller than the basin and enables explicit characterization of rainfall characteristics at any location. We combine the characteristics of rainfall intensity and duration with data on rainstorm area and location to model the surface runoff properties (depth, velocity, duration, distance downslope) on a range of hillslopes within the basin derived from LiDAR analysis. We also analyze connectivity of flow from hillslopes to the channel for various combinations of hillslopes and storms. This approach provides a framework for understanding spatial and temporal dynamics of runoff generation and connectivity that is faithful to the hydrological characteristics of dryland environments.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

DOE PAGES

Lin, Yen Ting; Buchler, Nicolas E.

2018-01-31

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

Stochastic tools hidden behind the empirical dielectric relaxation laws

NASA Astrophysics Data System (ADS)

Stanislavsky, Aleksander; Weron, Karina

2017-03-01

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of ‘structures with variations’ (Goldenfield and Kadanoff 1999 Science 284 87-9) require application of such mathematical tools—by means of which their random nature can be analyzed and, independently of the details distinguishing various systems (dipolar materials, glasses, semiconductors, liquid crystals, polymers, etc), the empirical universal kinetic patterns can be derived. We begin with a brief survey of the historical background of the dielectric relaxation study. After a short outline of the theoretical ideas providing the random tools applicable to modeling of relaxation phenomena, we present probabilistic implications for the study of the relaxation-rate distribution models. In the framework of the probability distribution of relaxation rates we consider description of complex systems, in which relaxing entities form random clusters interacting with each other and single entities. Then we focus on stochastic mechanisms of the relaxation phenomenon. We discuss the diffusion approach and its usefulness for understanding of anomalous dynamics of relaxing systems. We also discuss extensions of the diffusive approach to systems under tempered random processes. Useful relationships among different stochastic approaches to the anomalous dynamics of complex systems allow us to get a fresh look at this subject. The paper closes with a final discussion on achievements of stochastic tools describing the anomalous time evolution of complex systems.

An enhanced export coefficient based optimization model for supporting agricultural nonpoint source pollution mitigation under uncertainty.

PubMed

Rong, Qiangqiang; Cai, Yanpeng; Chen, Bing; Yue, Wencong; Yin, Xin'an; Tan, Qian

2017-02-15

In this research, an export coefficient based dual inexact two-stage stochastic credibility constrained programming (ECDITSCCP) model was developed through integrating an improved export coefficient model (ECM), interval linear programming (ILP), fuzzy credibility constrained programming (FCCP) and a fuzzy expected value equation within a general two stage programming (TSP) framework. The proposed ECDITSCCP model can effectively address multiple uncertainties expressed as random variables, fuzzy numbers, pure and dual intervals. Also, the model can provide a direct linkage between pre-regulated management policies and the associated economic implications. Moreover, the solutions under multiple credibility levels can be obtained for providing potential decision alternatives for decision makers. The proposed model was then applied to identify optimal land use structures for agricultural NPS pollution mitigation in a representative upstream subcatchment of the Miyun Reservoir watershed in north China. Optimal solutions of the model were successfully obtained, indicating desired land use patterns and nutrient discharge schemes to get a maximum agricultural system benefits under a limited discharge permit. Also, numerous results under multiple credibility levels could provide policy makers with several options, which could help get an appropriate balance between system benefits and pollution mitigation. The developed ECDITSCCP model can be effectively applied to addressing the uncertain information in agricultural systems and shows great applicability to the land use adjustment for agricultural NPS pollution mitigation. Copyright © 2016 Elsevier B.V. All rights reserved.

Regionally Adaptable Ground Motion Prediction Equation (GMPE) from Empirical Models of Fourier and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, Sanjay; Scherbaum, Frank; Kuehn, Nicolas; Stafford, Peter; Edwards, Benjamin

2016-04-01

The current practice of deriving empirical ground motion prediction equations (GMPEs) involves using ground motions recorded at multiple sites. However, in applications like site-specific (e.g., critical facility) hazard ground motions obtained from the GMPEs are need to be adjusted/corrected to a particular site/site-condition under investigation. This study presents a complete framework for developing a response spectral GMPE, within which the issue of adjustment of ground motions is addressed in a manner consistent with the linear system framework. The present approach is a two-step process in which the first step consists of deriving two separate empirical models, one for Fourier amplitude spectra (FAS) and the other for a random vibration theory (RVT) optimized duration (Drvto) of ground motion. In the second step the two models are combined within the RVT framework to obtain full response spectral amplitudes. Additionally, the framework also involves a stochastic model based extrapolation of individual Fourier spectra to extend the useable frequency limit of the empirically derived FAS model. The stochastic model parameters were determined by inverting the Fourier spectral data using an approach similar to the one as described in Edwards and Faeh (2013). Comparison of median predicted response spectra from present approach with those from other regional GMPEs indicates that the present approach can also be used as a stand-alone model. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, the Middle East and the Mediterranean region.

Simple stochastic model for El Niño with westerly wind bursts

PubMed Central

Thual, Sulian; Majda, Andrew J.; Chen, Nan; Stechmann, Samuel N.

2016-01-01

Atmospheric wind bursts in the tropics play a key role in the dynamics of the El Niño Southern Oscillation (ENSO). A simple modeling framework is proposed that summarizes this relationship and captures major features of the observational record while remaining physically consistent and amenable to detailed analysis. Within this simple framework, wind burst activity evolves according to a stochastic two-state Markov switching–diffusion process that depends on the strength of the western Pacific warm pool, and is coupled to simple ocean–atmosphere processes that are otherwise deterministic, stable, and linear. A simple model with this parameterization and no additional nonlinearities reproduces a realistic ENSO cycle with intermittent El Niño and La Niña events of varying intensity and strength as well as realistic buildup and shutdown of wind burst activity in the western Pacific. The wind burst activity has a direct causal effect on the ENSO variability: in particular, it intermittently triggers regular El Niño or La Niña events, super El Niño events, or no events at all, which enables the model to capture observed ENSO statistics such as the probability density function and power spectrum of eastern Pacific sea surface temperatures. The present framework provides further theoretical and practical insight on the relationship between wind burst activity and the ENSO. PMID:27573821

Wheat forecast economics effect study. [value of improved information on crop inventories, production, imports and exports

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Rouhani, R.; Jones, S.; Schick, I.

1980-01-01

A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

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.

Condition-dependent mate choice: A stochastic dynamic programming approach.

PubMed

Frame, Alicia M; Mills, Alex F

2014-09-01

We study how changing female condition during the mating season and condition-dependent search costs impact female mate choice, and what strategies a female could employ in choosing mates to maximize her own fitness. We address this problem via a stochastic dynamic programming model of mate choice. In the model, a female encounters males sequentially and must choose whether to mate or continue searching. As the female searches, her own condition changes stochastically, and she incurs condition-dependent search costs. The female attempts to maximize the quality of the offspring, which is a function of the female's condition at mating and the quality of the male with whom she mates. The mating strategy that maximizes the female's net expected reward is a quality threshold. We compare the optimal policy with other well-known mate choice strategies, and we use simulations to examine how well the optimal policy fares under imperfect information. Copyright © 2014 Elsevier Inc. All rights reserved.

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

A supplier selection and order allocation problem with stochastic demands

NASA Astrophysics Data System (ADS)

Zhou, Yun; Zhao, Lei; Zhao, Xiaobo; Jiang, Jianhua

2011-08-01

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Stochastic simulation of enzyme-catalyzed reactions with disparate timescales.

PubMed

Barik, Debashis; Paul, Mark R; Baumann, William T; Cao, Yang; Tyson, John J

2008-10-01

Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of protein interactions (e.g., complex formation may occur in fractions of a second, whereas catalytic conversions may take minutes). Exact stochastic simulation may be very inefficient under these circumstances, and methods for speeding up the simulation without sacrificing accuracy have been widely studied. We show that the "total quasi-steady-state approximation" for enzyme-catalyzed reactions provides a useful framework for efficient and accurate stochastic simulations. The method is applied to three examples: a simple enzyme-catalyzed reaction where enzyme and substrate have comparable abundances, a Goldbeter-Koshland switch, where a kinase and phosphatase regulate the phosphorylation state of a common substrate, and coupled Goldbeter-Koshland switches that exhibit bistability. Simulations based on the total quasi-steady-state approximation accurately capture the steady-state probability distributions of all components of these reaction networks. In many respects, the approximation also faithfully reproduces time-dependent aspects of the fluctuations. The method is accurate even under conditions of poor timescale separation.

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed

Capitán, José A; Cuenda, Sara; Alonso, David

2015-09-06

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. © 2015 The Author(s).

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

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

Mlynarczyk, Paul J.; Pullen, Robert H.; Abel, Steven M., E-mail: abel@utk.edu

2016-01-07

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations.more » Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.« less

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

How similar can co-occurring species be in the presence of competition and ecological drift?

PubMed Central

Capitán, José A.; Cuenda, Sara; Alonso, David

2015-01-01

If two species live on a single resource, the one with a slight advantage will out-compete the other: complete competitors cannot coexist. This is known as the competitive exclusion principle. If no extinction occurs, it is because evolutionary adaptation to slightly different niches takes place. Therefore, it is widely accepted that ecological communities are assembled by evolutionary differentiation and progressive adaptation of species to different niches. However, some ecologists have recently challenged this classic paradigm highlighting the importance of chance and stochasticity. Using a synthetic framework for community dynamics, here we show that, while deterministic descriptors predict coexistence, species similarity is limited in a more restrictive way in the presence of stochasticity. We analyse the stochastic extinction phenomenon, showing that extinction occurs as competitive overlap increases above a certain threshold well below its deterministic counterpart. We also prove that the extinction threshold cannot be ascribed only to demographic fluctuations around small population sizes. The more restrictive limit to species similarity is, therefore, a consequence of the complex interplay between competitive interactions and ecological drift. As a practical implication, we show that the existence of a stochastic limit to similarity has important consequences in the recovery of fragmented habitats. PMID:26269234

Chemical Memory Reactions Induced Bursting Dynamics in Gene Expression

PubMed Central

Tian, Tianhai

2013-01-01

Memory is a ubiquitous phenomenon in biological systems in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many memorial phenomena are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict to the extant stochastic approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. To tackle the challenge, I proposed a novel theory consisting of the memory chemical master equations and memory stochastic simulation algorithm. A stochastic model for single-gene expression was proposed to illustrate the key function of memory reactions in inducing bursting dynamics of gene expression that has been observed in experiments recently. The importance of memory reactions has been further validated by the stochastic model of the p53-MDM2 core module. Simulations showed that memory reactions is a major mechanism for realizing both sustained oscillations of p53 protein numbers in single cells and damped oscillations over a population of cells. These successful applications of the memory modeling framework suggested that this innovative theory is an effective and powerful tool to study memory process and conditional chemical reactions in a wide range of complex biological systems. PMID:23349679

Chemical memory reactions induced bursting dynamics in gene expression.

PubMed

Tian, Tianhai

2013-01-01

Memory is a ubiquitous phenomenon in biological systems in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. Specifically, many memorial phenomena are characterized by chemical memory reactions that may fire under particular system conditions. These conditional chemical reactions contradict to the extant stochastic approaches for modeling chemical kinetics and have increasingly posed significant challenges to mathematical modeling and computer simulation. To tackle the challenge, I proposed a novel theory consisting of the memory chemical master equations and memory stochastic simulation algorithm. A stochastic model for single-gene expression was proposed to illustrate the key function of memory reactions in inducing bursting dynamics of gene expression that has been observed in experiments recently. The importance of memory reactions has been further validated by the stochastic model of the p53-MDM2 core module. Simulations showed that memory reactions is a major mechanism for realizing both sustained oscillations of p53 protein numbers in single cells and damped oscillations over a population of cells. These successful applications of the memory modeling framework suggested that this innovative theory is an effective and powerful tool to study memory process and conditional chemical reactions in a wide range of complex biological systems.

Data Analysis Approaches for the Risk-Informed Safety Margins Characterization Toolkit

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

Mandelli, Diego; Alfonsi, Andrea; Maljovec, Daniel P.

2016-09-01

In the past decades, several numerical simulation codes have been employed to simulate accident dynamics (e.g., RELAP5-3D, RELAP-7, MELCOR, MAAP). In order to evaluate the impact of uncertainties into accident dynamics, several stochastic methodologies have been coupled with these codes. These stochastic methods range from classical Monte-Carlo and Latin Hypercube sampling to stochastic polynomial methods. Similar approaches have been introduced into the risk and safety community where stochastic methods (such as RAVEN, ADAPT, MCDET, ADS) have been coupled with safety analysis codes in order to evaluate the safety impact of timing and sequencing of events. These approaches are usually calledmore » Dynamic PRA or simulation-based PRA methods. These uncertainties and safety methods usually generate a large number of simulation runs (database storage may be on the order of gigabytes or higher). The scope of this paper is to present a broad overview of methods and algorithms that can be used to analyze and extract information from large data sets containing time dependent data. In this context, “extracting information” means constructing input-output correlations, finding commonalities, and identifying outliers. Some of the algorithms presented here have been developed or are under development within the RAVEN statistical framework.« less

Stochastic Modeling of Radioactive Material Releases

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

Andrus, Jason; Pope, Chad

2015-09-01

Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculatesmore » the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was funded through a grant from the DOE Nuclear Safety Research and Development Program.« less

Stochastic flow shop scheduling of overlapping jobs on tandem machines in application to optimizing the US Army's deliberate nuclear, biological, and chemical decontamination process, (final report). Master's thesis

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

Novikov, V.

1991-05-01

The U.S. Army's detailed equipment decontamination process is a stochastic flow shop which has N independent non-identical jobs (vehicles) which have overlapping processing times. This flow shop consists of up to six non-identical machines (stations). With the exception of one station, the processing times of the jobs are random variables. Based on an analysis of the processing times, the jobs for the 56 Army heavy division companies were scheduled according to the best shortest expected processing time - longest expected processing time (SEPT-LEPT) sequence. To assist in this scheduling the Gap Comparison Heuristic was developed to select the best SEPT-LEPTmore » schedule. This schedule was then used in balancing the detailed equipment decon line in order to find the best possible site configuration subject to several constraints. The detailed troop decon line, in which all jobs are independent and identically distributed, was then balanced. Lastly, an NBC decon optimization computer program was developed using the scheduling and line balancing results. This program serves as a prototype module for the ANBACIS automated NBC decision support system.... Decontamination, Stochastic flow shop, Scheduling, Stochastic scheduling, Minimization of the makespan, SEPT-LEPT Sequences, Flow shop line balancing, ANBACIS.« less

A New Control Paradigm for Stochastic Differential Equations

NASA Astrophysics Data System (ADS)

Schmid, Matthias J. A.

This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension to scalar systems subject to state-dependent noise and to systems of higher order. The suggested control paradigm is further advanced when a sequential application of MLD control is considered. This technique yields a nominal path corresponding to the minimum total deviation probability on the entire time domain. It is demonstrated that this sequential optimization concept can be unified in a single objective function which is revealed to be the Jacobi field performance index on the entire domain subject to an endpoint deviation. The emerging closed-form term replaces the previously required nested optimization and, thus, results in a highly efficient application-ready control design. This effectively substantiates Minimum Path Deviation (MPD) control. The proposed control paradigm allows the specific problem of stochastic cost control to be addressed as a special case. This new technique is employed within this study for the stochastic cost problem giving rise to Cost Constrained MPD (CCMPD) as well as to Minimum Quadratic Cost Deviation (MQCD) control. An exemplary treatment of a generic scalar nonlinear system subject to quadratic costs is performed for MQCD control to demonstrate the elementary expandability of the new control paradigm. This work concludes with a numerical evaluation of both MPD and CCMPD control for three exemplary benchmark problems. Numerical issues associated with the simulation of SDEs are briefly discussed and illustrated. The numerical examples furnish proof of the successful design. This study is complemented by a thorough review of statistical control methods, stochastic processes, Large Deviations techniques and the Freidlin-Wentzell theory, providing a comprehensive, self-contained account. The presentation of the mathematical tools and concepts is of a unique character, specifically addressing an engineering audience.

Solving complex maintenance planning optimization problems using stochastic simulation and multi-criteria fuzzy decision making

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

Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei

One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms ofmore » a suggested framework model based on discrete event simulation.« less

Synchrony and entrainment properties of robust circadian oscillators

PubMed Central

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

2008-01-01

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

Granger-causality maps of diffusion processes.

PubMed

Wahl, Benjamin; Feudel, Ulrike; Hlinka, Jaroslav; Wächter, Matthias; Peinke, Joachim; Freund, Jan A

2016-02-01

Granger causality is a statistical concept devised to reconstruct and quantify predictive information flow between stochastic processes. Although the general concept can be formulated model-free it is often considered in the framework of linear stochastic processes. Here we show how local linear model descriptions can be employed to extend Granger causality into the realm of nonlinear systems. This novel treatment results in maps that resolve Granger causality in regions of state space. Through examples we provide a proof of concept and illustrate the utility of these maps. Moreover, by integration we convert the local Granger causality into a global measure that yields a consistent picture for a global Ornstein-Uhlenbeck process. Finally, we recover invariance transformations known from the theory of autoregressive processes.

A Second-Order Conditionally Linear Mixed Effects Model with Observed and Latent Variable Covariates

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Kohli, Nidhi; Silverman, Rebecca D.; Speece, Deborah L.

2012-01-01

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

A Simulation-Based Comparison of Several Stochastic Linear Regression Methods in the Presence of Outliers.

ERIC Educational Resources Information Center

Rule, David L.

Several regression methods were examined within the framework of weighted structural regression (WSR), comparing their regression weight stability and score estimation accuracy in the presence of outlier contamination. The methods compared are: (1) ordinary least squares; (2) WSR ridge regression; (3) minimum risk regression; (4) minimum risk 2;…

Displacement data assimilation

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

Rosenthal, W. Steven; Venkataramani, Shankar; Mariano, Arthur J.

We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices.

Assessing the expected effects of wildfire on vegetation condition on the Bridger-Teton National Forest, Wyoming, USA

Treesearch

J. H. Scott; D. J. Helmbrecht; M. P. Thompson

2014-01-01

Characterizing wildfire risk to a fire-adapted ecosystem presents particular challenges due to its broad spatial extent, inherent complexity, and the difficulty in defining wildfire-induced losses and benefits. Our approach couples stochastic wildfire simulation with a vegetation condition assessment framework to estimate the conditional and expected response of...

Risk of spacecraft on-orbit obsolescence: Novel framework, stochastic modeling, and implications

NASA Astrophysics Data System (ADS)

Dubos, Gregory F.; Saleh, Joseph H.

2010-07-01

The Government Accountability Office (GAO) has repeatedly noted the difficulties encountered by the Department of Defense (DOD) in keeping its acquisition of space systems on schedule and within budget. Among the recommendations provided by GAO, a minimum Technology Readiness Level (TRL) for technologies to be included in the development of a space system is advised. The DOD considers this recommendation impractical arguing that if space systems were designed with only mature technologies (high TRL), they would likely become obsolete on-orbit fairly quickly. The risk of on-orbit obsolescence is a key argument in the DOD's position for dipping into low technology maturity for space acquisition programs, but this policy unfortunately often results in the cost growth and schedule slippage criticized by the GAO. The concept of risk of on-orbit obsolescence has remained qualitative to date. In this paper, we formulate a theory of risk of on-orbit obsolescence by building on the traditional notion of obsolescence and adapting it to the specificities of space systems. We develop a stochastic model for quantifying and analyzing the risk of on-orbit obsolescence, and we assess, in its light, the appropriateness of DOD's rationale for maintaining low TRL technologies in its acquisition of space assets as a strategy for mitigating on-orbit obsolescence. Our model and results contribute one step towards the resolution of the conceptual stalemate on this matter between the DOD and the GAO, and we hope will inspire academics to further investigate the risk of on-orbit obsolescence.

Optimal operating rules definition in complex water resource systems combining fuzzy logic, expert criteria and stochastic programming

NASA Astrophysics Data System (ADS)

Macian-Sorribes, Hector; Pulido-Velazquez, Manuel

2016-04-01

This contribution presents a methodology for defining optimal seasonal operating rules in multireservoir systems coupling expert criteria and stochastic optimization. Both sources of information are combined using fuzzy logic. The structure of the operating rules is defined based on expert criteria, via a joint expert-technician framework consisting in a series of meetings, workshops and surveys carried out between reservoir managers and modelers. As a result, the decision-making process used by managers can be assessed and expressed using fuzzy logic: fuzzy rule-based systems are employed to represent the operating rules and fuzzy regression procedures are used for forecasting future inflows. Once done that, a stochastic optimization algorithm can be used to define optimal decisions and transform them into fuzzy rules. Finally, the optimal fuzzy rules and the inflow prediction scheme are combined into a Decision Support System for making seasonal forecasts and simulate the effect of different alternatives in response to the initial system state and the foreseen inflows. The approach presented has been applied to the Jucar River Basin (Spain). Reservoir managers explained how the system is operated, taking into account the reservoirs' states at the beginning of the irrigation season and the inflows previewed during that season. According to the information given by them, the Jucar River Basin operating policies were expressed via two fuzzy rule-based (FRB) systems that estimate the amount of water to be allocated to the users and how the reservoir storages should be balanced to guarantee those deliveries. A stochastic optimization model using Stochastic Dual Dynamic Programming (SDDP) was developed to define optimal decisions, which are transformed into optimal operating rules embedding them into the two FRBs previously created. As a benchmark, historical records are used to develop alternative operating rules. A fuzzy linear regression procedure was employed to foresee future inflows depending on present and past hydrological and meteorological variables actually used by the reservoir managers to define likely inflow scenarios. A Decision Support System (DSS) was created coupling the FRB systems and the inflow prediction scheme in order to give the user a set of possible optimal releases in response to the reservoir states at the beginning of the irrigation season and the fuzzy inflow projections made using hydrological and meteorological information. The results show that the optimal DSS created using the FRB operating policies are able to increase the amount of water allocated to the users in 20 to 50 Mm3 per irrigation season with respect to the current policies. Consequently, the mechanism used to define optimal operating rules and transform them into a DSS is able to increase the water deliveries in the Jucar River Basin, combining expert criteria and optimization algorithms in an efficient way. This study has been partially supported by the IMPADAPT project (CGL2013-48424-C2-1-R) with Spanish MINECO (Ministerio de Economía y Competitividad) and FEDER funds. It also has received funding from the European Union's Horizon 2020 research and innovation programme under the IMPREX project (grant agreement no: 641.811).

Using Stochastic Spiking Neural Networks on SpiNNaker to Solve Constraint Satisfaction Problems

PubMed Central

Fonseca Guerra, Gabriel A.; Furber, Steve B.

2017-01-01

Constraint satisfaction problems (CSP) are at the core of numerous scientific and technological applications. However, CSPs belong to the NP-complete complexity class, for which the existence (or not) of efficient algorithms remains a major unsolved question in computational complexity theory. In the face of this fundamental difficulty heuristics and approximation methods are used to approach instances of NP (e.g., decision and hard optimization problems). The human brain efficiently handles CSPs both in perception and behavior using spiking neural networks (SNNs), and recent studies have demonstrated that the noise embedded within an SNN can be used as a computational resource to solve CSPs. Here, we provide a software framework for the implementation of such noisy neural solvers on the SpiNNaker massively parallel neuromorphic hardware, further demonstrating their potential to implement a stochastic search that solves instances of P and NP problems expressed as CSPs. This facilitates the exploration of new optimization strategies and the understanding of the computational abilities of SNNs. We demonstrate the basic principles of the framework by solving difficult instances of the Sudoku puzzle and of the map color problem, and explore its application to spin glasses. The solver works as a stochastic dynamical system, which is attracted by the configuration that solves the CSP. The noise allows an optimal exploration of the space of configurations, looking for the satisfiability of all the constraints; if applied discontinuously, it can also force the system to leap to a new random configuration effectively causing a restart. PMID:29311791

A Correlation-based Framework for Evaluating Postural Control Stochastic Dynamics

PubMed Central

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

2016-01-01

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

Stochastic hyperfine interactions modeling library

NASA Astrophysics Data System (ADS)

Zacate, Matthew O.; Evenson, William E.

2011-04-01

The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When interactions fluctuate at rates comparable to the time scale of a hyperfine method, there is a loss in signal coherence, and spectra are damped. The degree of damping can be used to determine fluctuation rates, provided that theoretical expressions for spectra can be derived for relevant physical models of the fluctuations. SHIML provides routines to help researchers quickly develop code to incorporate stochastic models of fluctuating hyperfine interactions in calculations of hyperfine spectra. Solution method: Calculations are based on the method for modeling stochastic hyperfine interactions for PAC by Winkler and Gerdau [5]. The method is extended to include other hyperfine methods following the work of Dattagupta [6]. The code provides routines for reading model information from text files, allowing researchers to develop new models quickly without the need to modify computer code for each new model to be considered. Restrictions: In the present version of the code, only methods that measure the hyperfine interaction on one probe spin state, such as PAC, μSR, and NMR, are supported. Running time: Varies

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.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

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

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.

Mapping intra-urban transmission risk of dengue fever with big hourly cellphone data.

PubMed

Mao, Liang; Yin, Ling; Song, Xiaoqing; Mei, Shujiang

2016-10-01

Cellphone tracking has been recently integrated into risk assessment of disease transmission, because travel behavior of disease carriers can be depicted in unprecedented details. Still in its infancy, such an integration has been limited to: 1) risk assessment only at national and provincial scales, where intra-urban human movements are neglected, and 2) using irregularly logged cellphone data that miss numerous user movements. Furthermore, few risk assessments have considered positional uncertainty of cellphone data. This study proposed a new framework for mapping intra-urban disease risk with regularly logged cellphone tracking data, taking the dengue fever in Shenzhen city as an example. Hourly tracking records of 5.85 million cellphone users, combined with the random forest classification and mosquito activities, were utilized to estimate the local transmission risk of dengue fever and the importation risk through travels. Stochastic simulations were further employed to quantify the uncertainty of risk. The resultant maps suggest targeted interventions to maximally reduce dengue cases exported to other places, as well as appropriate interventions to contain risk in places that import them. Given the popularity of cellphone use in urbanized areas, this framework can be adopted by other cities to design spatio-temporally resolved programs for disease control. Copyright © 2016 Elsevier B.V. All rights reserved.

Shielding Calculations on Waste Packages - The Limits and Possibilities of different Calculation Methods by the example of homogeneous and inhomogeneous Waste Packages

NASA Astrophysics Data System (ADS)

Adams, Mike; Smalian, Silva

2017-09-01

For nuclear waste packages the expected dose rates and nuclide inventory are beforehand calculated. Depending on the package of the nuclear waste deterministic programs like MicroShield® provide a range of results for each type of packaging. Stochastic programs like "Monte-Carlo N-Particle Transport Code System" (MCNP®) on the other hand provide reliable results for complex geometries. However this type of program requires a fully trained operator and calculations are time consuming. The problem here is to choose an appropriate program for a specific geometry. Therefore we compared the results of deterministic programs like MicroShield® and stochastic programs like MCNP®. These comparisons enable us to make a statement about the applicability of the various programs for chosen types of containers. As a conclusion we found that for thin-walled geometries deterministic programs like MicroShield® are well suited to calculate the dose rate. For cylindrical containers with inner shielding however, deterministic programs hit their limits. Furthermore we investigate the effect of an inhomogeneous material and activity distribution on the results. The calculations are still ongoing. Results will be presented in the final abstract.

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.

The ADEPT Framework for Intelligent Autonomy

NASA Technical Reports Server (NTRS)

Ricard, Michael; Kolitz, Stephan

2003-01-01

This paper describes the design and implementation of Draper Laboratory's All-Domain Execution and Planning Technology (ADEPT) architecture for intelligent autonomy. Intelligent autonomy is the ability to plan and execute complex activities in a manner that provides rapid, effective response to stochastic and dynamic mission events. Thus, intelligent autonomy enables the high-level reasoning and adaptive behavior for an unmanned vehicle that is provided by an operator in man-in-the-loop systems. Draper s intelligent autonomy has architecture evolved over a decade and a half beginning in the mid 1980's culminating in an operational experiment funded under DARPA's Autonomous Minehunting and Mapping Technologies (AMMT) unmanned undersea vehicle program. ADEPT continues to be refined through its application to current programs that involve air vehicles, satellites and higher-level planning used to direct multiple vehicles. The objective of ADEPT is to solidify a proven, dependable software approach that can be quickly applied to new vehicles and domains. The architecture can be viewed as a hierarchical extension of the sense-think-act paradigm of intelligence and has strong parallels with the military's Observe-Orient-Decide-Act (OODA) loop. The key elements of the architecture are planning and decision-making nodes comprising modules for situation assessment, plan generation, plan implementation and coordination. A reusable, object-oriented software framework has been developed that implements these functions. As the architecture is applied to new areas, only the application specific software needs to be developed. This paper describes the core architecture in detail and discusses how this has been applied in the undersea, air, ground and space domains.

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

NASA Astrophysics Data System (ADS)

Devra, Amit; Prabhu, Prithviraj; Singh, Harpreet; Arvind; Dorai, Kavita

2018-03-01

We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled-NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. We devised a new selection mechanism within the genetic algorithm framework to select individuals from a population. We call this mechanism the "Luck-Choose" mechanism and were able to achieve faster convergence to a solution using this mechanism, as compared to existing selection mechanisms. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes and other numerical optimization methods.

Evaluation of traffic signal timing optimization methods using a stochastic and microscopic simulation program.

DOT National Transportation Integrated Search

2003-01-01

This study evaluated existing traffic signal optimization programs including Synchro,TRANSYT-7F, and genetic algorithm optimization using real-world data collected in Virginia. As a first step, a microscopic simulation model, VISSIM, was extensively ...

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

An Approach for Dynamic Optimization of Prevention Program Implementation in Stochastic Environments

NASA Astrophysics Data System (ADS)

Kang, Yuncheol; Prabhu, Vittal

The science of preventing youth problems has significantly advanced in developing evidence-based prevention program (EBP) by using randomized clinical trials. Effective EBP can reduce delinquency, aggression, violence, bullying and substance abuse among youth. Unfortunately the outcomes of EBP implemented in natural settings usually tend to be lower than in clinical trials, which has motivated the need to study EBP implementations. In this paper we propose to model EBP implementations in natural settings as stochastic dynamic processes. Specifically, we propose Markov Decision Process (MDP) for modeling and dynamic optimization of such EBP implementations. We illustrate these concepts using simple numerical examples and discuss potential challenges in using such approaches in practice.

Digital program for solving the linear stochastic optimal control and estimation problem

NASA Technical Reports Server (NTRS)

Geyser, L. C.; Lehtinen, B.

1975-01-01

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

Multiscale Hy3S: hybrid stochastic simulation for supercomputers.

PubMed

Salis, Howard; Sotiropoulos, Vassilios; Kaznessis, Yiannis N

2006-02-24

Stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI; special discrete events, such as transcriptional and translation elongation and cell division; mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use of NetCDF optimized binary format to quickly read and write large datasets; and a simple graphical user interface, written in Matlab, to help users create biological systems and analyze data. We demonstrate the accuracy and efficiency of Hy3S with examples, including a large-scale system benchmark and a complex bistable biochemical network with positive feedback. The software itself is open-sourced under the GPL license and is modular, allowing users to modify it for their own purposes. Hy3S is a powerful suite of simulation programs for simulating the stochastic dynamics of networks of biochemical reactions. Its first public version enables computational biologists to more efficiently investigate the dynamics of realistic biological systems.

Stochastic fluctuations and the detectability limit of network communities.

PubMed

Floretta, Lucio; Liechti, Jonas; Flammini, Alessandro; De Los Rios, Paolo

2013-12-01

We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and every instance of the benchmark, we come to the conclusion that the native, putative partition of the network is completely lost even before the in-degree/out-degree ratio becomes equal to that of a structureless Erdös-Rényi network. We develop a simple iterative scheme, analytically well described by an infinite branching process, to provide an estimate of the true detectability limit. Using various algorithms based on modularity optimization, we show that all of them behave (semiquantitatively) in the same way, with the same functional form of the detectability threshold as a function of the network parameters. Because the same behavior has also been found by further modularity-optimization methods and for methods based on different heuristics implementations, we conclude that indeed a correct definition of the detectability limit must take into account the stochastic fluctuations of the network construction.

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Identifying variably saturated water-flow patterns in a steep hillslope under intermittent heavy rainfall

USGS Publications Warehouse

El-Kadi, A. I.; Torikai, J.D.

2001-01-01

The objective of this paper is to identify water-flow patterns in part of an active landslide, through the use of numerical simulations and data obtained during a field study. The approaches adopted include measuring rainfall events and pore-pressure responses in both saturated and unsaturated soils at the site. To account for soil variability, the Richards equation is solved within deterministic and stochastic frameworks. The deterministic simulations considered average water-retention data, adjusted retention data to account for stones or cobbles, retention functions for a heterogeneous pore structure, and continuous retention functions for preferential flow. The stochastic simulations applied the Monte Carlo approach which considers statistical distribution and autocorrelation of the saturated conductivity and its cross correlation with the retention function. Although none of the models is capable of accurately predicting field measurements, appreciable improvement in accuracy was attained using stochastic, preferential flow, and heterogeneous pore-structure models. For the current study, continuum-flow models provide reasonable accuracy for practical purposes, although they are expected to be less accurate than multi-domain preferential flow models.

Multi-criteria multi-stakeholder decision analysis using a fuzzy-stochastic approach for hydrosystem management

NASA Astrophysics Data System (ADS)

Subagadis, Y. H.; Schütze, N.; Grundmann, J.

2014-09-01

The conventional methods used to solve multi-criteria multi-stakeholder problems are less strongly formulated, as they normally incorporate only homogeneous information at a time and suggest aggregating objectives of different decision-makers avoiding water-society interactions. In this contribution, Multi-Criteria Group Decision Analysis (MCGDA) using a fuzzy-stochastic approach has been proposed to rank a set of alternatives in water management decisions incorporating heterogeneous information under uncertainty. The decision making framework takes hydrologically, environmentally, and socio-economically motivated conflicting objectives into consideration. The criteria related to the performance of the physical system are optimized using multi-criteria simulation-based optimization, and fuzzy linguistic quantifiers have been used to evaluate subjective criteria and to assess stakeholders' degree of optimism. The proposed methodology is applied to find effective and robust intervention strategies for the management of a coastal hydrosystem affected by saltwater intrusion due to excessive groundwater extraction for irrigated agriculture and municipal use. Preliminary results show that the MCGDA based on a fuzzy-stochastic approach gives useful support for robust decision-making and is sensitive to the decision makers' degree of optimism.

multiUQ: An intrusive uncertainty quantification tool for gas-liquid multiphase flows

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2017-11-01

Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gas-liquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While non-intrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gas-liquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gas-liquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A least-squares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. NSF Grant #1511325.

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

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

SASS: A symmetry adapted stochastic search algorithm exploiting site symmetry

NASA Astrophysics Data System (ADS)

Wheeler, Steven E.; Schleyer, Paul v. R.; Schaefer, Henry F.

2007-03-01

A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

On the reach of perturbative descriptions for dark matter displacement fields

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

Baldauf, Tobias; Zaldarriaga, Matias; Schaan, Emmanuel, E-mail: baldauf@ias.edu, E-mail: eschaan@astro.princeton.edu, E-mail: matiasz@ias.edu

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding N-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors ormore » transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a 1% error on the non-linear power spectrum at k = 0.2 h{sup −1}Mpc at z = 0. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.« less

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Bonds with index-linked stochastic coupons in quantum finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal Ehsan

2018-06-01

An index-linked coupon bond is defined that pays coupons whose values are stochastic, depending on a market defined index. This is an asset class distinct from the existing coupon bonds. The index-linked coupon bond is an example of a sukuk, which is an instrument that implements one of the cornerstones of Islamic finance (Askari et al., 2012): that an investor must share in the risk of the issuer in order to earn profits from the investment. The index-linked coupon bond is defined using the mathematical framework of quantum finance (Baaquie, 2004, 2010). The coupons are stochastic, with the quantum of coupon payments depending on a publicly traded index that is chosen to reflect the primary drivers of the revenues of the issuer of the bond. The index ensures there is information symmetry - regarding the quantum of coupon being paid - between issuer and investor. The dependence of the coupon on the index is designed so that the variation of the index mirrors the changing fortunes of the issuer, with the coupon's quantum increasing for increasing values of the index and conversely, decreasing with a fall of the index.

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

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.

The impacts of electricity dispatch protocols on the emission reductions due to wind power and carbon tax.

PubMed

Yu, Yang; Rajagopal, Ram

2015-02-17

Two dispatch protocols have been adopted by electricity markets to deal with the uncertainty of wind power but the effects of the selection between the dispatch protocols have not been comprehensively analyzed. We establish a framework to compare the impacts of adopting different dispatch protocols on the efficacy of using wind power and implementing a carbon tax to reduce emissions. We suggest that a market has high potential to achieve greater emission reduction by adopting the stochastic dispatch protocol instead of the static protocol when the wind energy in the market is highly uncertain or the market has enough adjustable generators, such as gas-fired combustion generators. Furthermore, the carbon-tax policy is more cost-efficient for reducing CO2 emission when the market operates according to the stochastic protocol rather than the static protocol. An empirical study, which is calibrated according to the data from the Electric Reliability Council of Texas market, confirms that using wind energy in the Texas market results in a 12% CO2 emission reduction when the market uses the stochastic dispatch protocol instead of the 8% emission reduction associated with the static protocol. In addition, if a 6$/ton carbon tax is implemented in the Texas market operated according to the stochastic protocol, the CO2 emission is similar to the emission level from the same market with a 16$/ton carbon tax operated according to the static protocol. Correspondingly, the 16$/ton carbon tax associated with the static protocol costs 42.6% more than the 6$/ton carbon tax associated with the stochastic protocol.

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

Stochastic Online Learning in Dynamic Networks under Unknown Models

DTIC Science & Technology

2016-08-02

Repeated Game with Incomplete Information, IEEE International Conference on Acoustics, Speech, and Signal Processing. 20-MAR-16, Shanghai, China...in a game theoretic framework for the application of multi-seller dynamic pricing with unknown demand models. We formulated the problem as an...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning

Cost-Effectiveness of Adolescent Pertussis Vaccination for The Netherlands: Using an Individual-Based Dynamic Model

PubMed Central

de Vries, Robin; Kretzschmar, Mirjam; Schellekens, Joop F. P.; Versteegh, Florens G. A.; Westra, Tjalke A.; Roord, John J.; Postma, Maarten J.

2010-01-01

Background Despite widespread immunization programs, a clear increase in pertussis incidence is apparent in many developed countries during the last decades. Consequently, additional immunization strategies are considered to reduce the burden of disease. The aim of this study is to design an individual-based stochastic dynamic framework to model pertussis transmission in the population in order to predict the epidemiologic and economic consequences of the implementation of universal booster vaccination programs. Using this framework, we estimate the cost-effectiveness of universal adolescent pertussis booster vaccination at the age of 12 years in the Netherlands. Methods/Principal Findings We designed a discrete event simulation (DES) model to predict the epidemiological and economic consequences of implementing universal adolescent booster vaccination. We used national age-specific notification data over the period 1996–2000—corrected for underreporting—to calibrate the model assuming a steady state situation. Subsequently, booster vaccination was introduced. Input parameters of the model were derived from literature, national data sources (e.g. costing data, incidence and hospitalization data) and expert opinions. As there is no consensus on the duration of immunity acquired by natural infection, we considered two scenarios for this duration of protection (i.e. 8 and 15 years). In both scenarios, total pertussis incidence decreased as a result of adolescent vaccination. From a societal perspective, the cost-effectiveness was estimated at €4418/QALY (range: 3205–6364 € per QALY) and €6371/QALY (range: 4139–9549 € per QALY) for the 8- and 15-year protection scenarios, respectively. Sensitivity analyses revealed that the outcomes are most sensitive to the quality of life weights used for pertussis disease. Conclusions/Significance To our knowledge we designed the first individual-based dynamic framework to model pertussis transmission in the population. This study indicates that adolescent pertussis vaccination is likely to be a cost-effective intervention for The Netherlands. The model is suited to investigate further pertussis booster vaccination strategies. PMID:20976213

A stochastic differential equation model of diurnal cortisol patterns

NASA Technical Reports Server (NTRS)

Brown, E. N.; Meehan, P. M.; Dempster, A. P.

2001-01-01

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

Periodic benefit-risk assessment using Bayesian stochastic multi-criteria acceptability analysis

PubMed Central

Li, Kan; Yuan, Shuai Sammy; Wang, William; Wan, Shuyan Sabrina; Ceesay, Paulette; Heyse, Joseph F.; Mt-Isa, Shahrul; Luo, Sheng

2018-01-01

Benefit-risk (BR) assessment is essential to ensure the best decisions are made for a medical product in the clinical development process, regulatory marketing authorization, post-market surveillance, and coverage and reimbursement decisions. One challenge of BR assessment in practice is that the benefit and risk profile may keep evolving while new evidence is accumulating. Regulators and the International Conference on Harmonization (ICH) recommend performing periodic benefit-risk evaluation report (PBRER) through the product's lifecycle. In this paper, we propose a general statistical framework for periodic benefit-risk assessment, in which Bayesian meta-analysis and stochastic multi-criteria acceptability analysis (SMAA) will be combined to synthesize the accumulating evidence. The proposed approach allows us to compare the acceptability of different drugs dynamically and effectively and accounts for the uncertainty of clinical measurements and imprecise or incomplete preference information of decision makers. We apply our approaches to two real examples in a post-hoc way for illustration purpose. The proposed method may easily be modified for other pre and post market settings, and thus be an important complement to the current structured benefit-risk assessment (sBRA) framework to improve the transparent and consistency of the decision-making process. PMID:29505866

A Framework to Analyze the Performance of Load Balancing Schemes for Ensembles of Stochastic Simulations

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

Ahn, Tae-Hyuk; Sandu, Adrian; Watson, Layne T.

2015-08-01

Ensembles of simulations are employed to estimate the statistics of possible future states of a system, and are widely used in important applications such as climate change and biological modeling. Ensembles of runs can naturally be executed in parallel. However, when the CPU times of individual simulations vary considerably, a simple strategy of assigning an equal number of tasks per processor can lead to serious work imbalances and low parallel efficiency. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms for ensembles of simulations where many tasks are mapped onto each processor, andmore » where the individual compute times vary considerably among tasks. Four load balancing strategies are discussed: most-dividing, all-redistribution, random-polling, and neighbor-redistribution. Simulation results with a stochastic budding yeast cell cycle model are consistent with the theoretical analysis. It is especially significant that there is a provable global decrease in load imbalance for the local rebalancing algorithms due to scalability concerns for the global rebalancing algorithms. The overall simulation time is reduced by up to 25 %, and the total processor idle time by 85 %.« less

Modeling disease transmission near eradication: An equation free approach

NASA Astrophysics Data System (ADS)

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

2015-01-01

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

Variation of Time Domain Failure Probabilities of Jack-up with Wave Return Periods

NASA Astrophysics Data System (ADS)

Idris, Ahmad; Harahap, Indra S. H.; Ali, Montassir Osman Ahmed

2018-04-01

This study evaluated failure probabilities of jack up units on the framework of time dependent reliability analysis using uncertainty from different sea states representing different return period of the design wave. Surface elevation for each sea state was represented by Karhunen-Loeve expansion method using the eigenfunctions of prolate spheroidal wave functions in order to obtain the wave load. The stochastic wave load was propagated on a simplified jack up model developed in commercial software to obtain the structural response due to the wave loading. Analysis of the stochastic response to determine the failure probability in excessive deck displacement in the framework of time dependent reliability analysis was performed by developing Matlab codes in a personal computer. Results from the study indicated that the failure probability increases with increase in the severity of the sea state representing a longer return period. Although the results obtained are in agreement with the results of a study of similar jack up model using time independent method at higher values of maximum allowable deck displacement, it is in contrast at lower values of the criteria where the study reported that failure probability decreases with increase in the severity of the sea state.

Evaluation of Electric Power Procurement Strategies by Stochastic Dynamic Programming

NASA Astrophysics Data System (ADS)

Saisho, Yuichi; Hayashi, Taketo; Fujii, Yasumasa; Yamaji, Kenji

In deregulated electricity markets, the role of a distribution company is to purchase electricity from the wholesale electricity market at randomly fluctuating prices and to provide it to its customers at a given fixed price. Therefore the company has to take risk stemming from the uncertainties of electricity prices and/or demand fluctuation instead of the customers. The way to avoid the risk is to make a bilateral contact with generating companies or install its own power generation facility. This entails the necessity to develop a certain method to make an optimal strategy for electric power procurement. In such a circumstance, this research has the purpose for proposing a mathematical method based on stochastic dynamic programming and additionally considering the characteristics of the start-up cost of electric power generation facility to evaluate strategies of combination of the bilateral contract and power auto-generation with its own facility for procuring electric power in deregulated electricity market. In the beginning we proposed two approaches to solve the stochastic dynamic programming, and they are a Monte Carlo simulation method and a finite difference method to derive the solution of a partial differential equation of the total procurement cost of electric power. Finally we discussed the influences of the price uncertainty on optimal strategies of power procurement.

Consistent Simulation Framework for Efficient Mass Discharge and Source Depletion Time Predictions of DNAPL Contaminants in Heterogeneous Aquifers Under Uncertainty

NASA Astrophysics Data System (ADS)

Nowak, W.; Koch, J.

2014-12-01

Predicting DNAPL fate and transport in heterogeneous aquifers is challenging and subject to an uncertainty that needs to be quantified. Models for this task needs to be equipped with an accurate source zone description, i.e., the distribution of mass of all partitioning phases (DNAPL, water, and soil) in all possible states ((im)mobile, dissolved, and sorbed), mass-transfer algorithms, and the simulation of transport processes in the groundwater. Such detailed models tend to be computationally cumbersome when used for uncertainty quantification. Therefore, a selective choice of the relevant model states, processes, and scales are both sensitive and indispensable. We investigate the questions: what is a meaningful level of model complexity and how to obtain an efficient model framework that is still physically and statistically consistent. In our proposed model, aquifer parameters and the contaminant source architecture are conceptualized jointly as random space functions. The governing processes are simulated in a three-dimensional, highly-resolved, stochastic, and coupled model that can predict probability density functions of mass discharge and source depletion times. We apply a stochastic percolation approach as an emulator to simulate the contaminant source formation, a random walk particle tracking method to simulate DNAPL dissolution and solute transport within the aqueous phase, and a quasi-steady-state approach to solve for DNAPL depletion times. Using this novel model framework, we test whether and to which degree the desired model predictions are sensitive to simplifications often found in the literature. With this we identify that aquifer heterogeneity, groundwater flow irregularity, uncertain and physically-based contaminant source zones, and their mutual interlinkages are indispensable components of a sound model framework.

Multi-tasking arbitration and behaviour design for human-interactive robots

NASA Astrophysics Data System (ADS)

Kobayashi, Yuichi; Onishi, Masaki; Hosoe, Shigeyuki; Luo, Zhiwei

2013-05-01

Robots that interact with humans in household environments are required to handle multiple real-time tasks simultaneously, such as carrying objects, collision avoidance and conversation with human. This article presents a design framework for the control and recognition processes to meet these requirements taking into account stochastic human behaviour. The proposed design method first introduces a Petri net for synchronisation of multiple tasks. The Petri net formulation is converted to Markov decision processes and processed in an optimal control framework. Three tasks (safety confirmation, object conveyance and conversation) interact and are expressed by the Petri net. Using the proposed framework, tasks that normally tend to be designed by integrating many if-then rules can be designed in a systematic manner in a state estimation and optimisation framework from the viewpoint of the shortest time optimal control. The proposed arbitration method was verified by simulations and experiments using RI-MAN, which was developed for interactive tasks with humans.

Overarching framework for data-based modelling

NASA Astrophysics Data System (ADS)

Schelter, Björn; Mader, Malenka; Mader, Wolfgang; Sommerlade, Linda; Platt, Bettina; Lai, Ying-Cheng; Grebogi, Celso; Thiel, Marco

2014-02-01

One of the main modelling paradigms for complex physical systems are networks. When estimating the network structure from measured signals, typically several assumptions such as stationarity are made in the estimation process. Violating these assumptions renders standard analysis techniques fruitless. We here propose a framework to estimate the network structure from measurements of arbitrary non-linear, non-stationary, stochastic processes. To this end, we propose a rigorous mathematical theory that underlies this framework. Based on this theory, we present a highly efficient algorithm and the corresponding statistics that are immediately sensibly applicable to measured signals. We demonstrate its performance in a simulation study. In experiments of transitions between vigilance stages in rodents, we infer small network structures with complex, time-dependent interactions; this suggests biomarkers for such transitions, the key to understand and diagnose numerous diseases such as dementia. We argue that the suggested framework combines features that other approaches followed so far lack.

Stochastic search in structural optimization - Genetic algorithms and simulated annealing

NASA Technical Reports Server (NTRS)

Hajela, Prabhat

1993-01-01

An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.

Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Mital, Subodh K.; Murthy, Pappu L. N.; Bednarcyk, Brett A.; Pineda, Evan J.; Bhatt, Ramakrishna T.; Arnold, Steven M.

2016-01-01

The Finite Element Analysis-Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to characterize and predict the progressive damage response of silicon-carbide-fiber-reinforced reaction-bonded silicon nitride matrix (SiC/RBSN) composite laminate tensile specimens. Studied were unidirectional laminates [0] (sub 8), [10] (sub 8), [45] (sub 8), and [90] (sub 8); cross-ply laminates [0 (sub 2) divided by 90 (sub 2),]s; angled-ply laminates [plus 45 (sub 2) divided by -45 (sub 2), ]s; doubled-edge-notched [0] (sub 8), laminates; and central-hole laminates. Results correlated well with the experimental data. This work was performed as a validation and benchmarking exercise of the FEAMAC/CARES program. FEAMAC/CARES simulates stochastic-based discrete-event progressive damage of ceramic matrix composite and polymer matrix composite material structures. It couples three software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life), and (3) the Abaqus finite element analysis program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating-unit-cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC, and Abaqus is used to model the overall composite structure. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events that incrementally progress until ultimate structural failure.

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

PubMed

Smith, R L; Al-Mamun, M A; Gröhn, Y T

2017-03-01

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

Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

Stochastic investigation of temperature process for climatic variability identification

NASA Astrophysics Data System (ADS)

Lerias, Eleutherios; Kalamioti, Anna; Dimitriadis, Panayiotis; Markonis, Yannis; Iliopoulou, Theano; Koutsoyiannis, Demetris

2016-04-01

The temperature process is considered as the most characteristic hydrometeorological process and has been thoroughly examined in the climate-change framework. We use a dataset comprising hourly temperature and dew point records to identify statistical variability with emphasis on the last period. Specifically, we investigate the occurrence of mean, maximum and minimum values and we estimate statistical properties such as marginal probability distribution function and the type of decay of the climacogram (i.e., mean process variance vs. scale) for various time periods. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

Stochastic dark energy from inflationary quantum fluctuations

NASA Astrophysics Data System (ADS)

Glavan, Dražen; Prokopec, Tomislav; Starobinsky, Alexei A.

2018-05-01

We study the quantum backreaction from inflationary fluctuations of a very light, non-minimally coupled spectator scalar and show that it is a viable candidate for dark energy. The problem is solved by suitably adapting the formalism of stochastic inflation. This allows us to self-consistently account for the backreaction on the background expansion rate of the Universe where its effects are large. This framework is equivalent to that of semiclassical gravity in which matter vacuum fluctuations are included at the one loop level, but purely quantum gravitational fluctuations are neglected. Our results show that dark energy in our model can be characterized by a distinct effective equation of state parameter (as a function of redshift) which allows for testing of the model at the level of the background.

Complete description of all self-similar models driven by Lévy stable noise

NASA Astrophysics Data System (ADS)

Weron, Aleksander; Burnecki, Krzysztof; Mercik, Szymon; Weron, Karina

2005-01-01

A canonical decomposition of H -self-similar Lévy symmetric α -stable processes is presented. The resulting components completely described by both deterministic kernels and the corresponding stochastic integral with respect to the Lévy symmetric α -stable motion are shown to be related to the dissipative and conservative parts of the dynamics. This result provides stochastic analysis tools for study the anomalous diffusion phenomena in the Langevin equation framework. For example, a simple computer test for testing the origins of self-similarity is implemented for four real empirical time series recorded from different physical systems: an ionic current flow through a single channel in a biological membrane, an energy of solar flares, a seismic electric signal recorded during seismic Earth activity, and foreign exchange rate daily returns.

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.

Do rational numbers play a role in selection for stochasticity?

PubMed

Sinclair, Robert

2014-01-01

When a given tissue must, to be able to perform its various functions, consist of different cell types, each fairly evenly distributed and with specific probabilities, then there are at least two quite different developmental mechanisms which might achieve the desired result. Let us begin with the case of two cell types, and first imagine that the proportion of numbers of cells of these types should be 1:3. Clearly, a regular structure composed of repeating units of four cells, three of which are of the dominant type, will easily satisfy the requirements, and a deterministic mechanism may lend itself to the task. What if, however, the proportion should be 10:33? The same simple, deterministic approach would now require a structure of repeating units of 43 cells, and this certainly seems to require a far more complex and potentially prohibitive deterministic developmental program. Stochastic development, replacing regular units with random distributions of given densities, might not be evolutionarily competitive in comparison with the deterministic program when the proportions should be 1:3, but it has the property that, whatever developmental mechanism underlies it, its complexity does not need to depend very much upon target cell densities at all. We are immediately led to speculate that proportions which correspond to fractions with large denominators (such as the 33 of 10/33) may be more easily achieved by stochastic developmental programs than by deterministic ones, and this is the core of our thesis: that stochastic development may tend to occur more often in cases involving rational numbers with large denominators. To be imprecise: that simple rationality and determinism belong together, as do irrationality and randomness.

Stochastic abstract policies: generalizing knowledge to improve reinforcement learning.

PubMed

Koga, Marcelo L; Freire, Valdinei; Costa, Anna H R

2015-01-01

Reinforcement learning (RL) enables an agent to learn behavior by acquiring experience through trial-and-error interactions with a dynamic environment. However, knowledge is usually built from scratch and learning to behave may take a long time. Here, we improve the learning performance by leveraging prior knowledge; that is, the learner shows proper behavior from the beginning of a target task, using the knowledge from a set of known, previously solved, source tasks. In this paper, we argue that building stochastic abstract policies that generalize over past experiences is an effective way to provide such improvement and this generalization outperforms the current practice of using a library of policies. We achieve that contributing with a new algorithm, AbsProb-PI-multiple and a framework for transferring knowledge represented as a stochastic abstract policy in new RL tasks. Stochastic abstract policies offer an effective way to encode knowledge because the abstraction they provide not only generalizes solutions but also facilitates extracting the similarities among tasks. We perform experiments in a robotic navigation environment and analyze the agent's behavior throughout the learning process and also assess the transfer ratio for different amounts of source tasks. We compare our method with the transfer of a library of policies, and experiments show that the use of a generalized policy produces better results by more effectively guiding the agent when learning a target task.

The concerted calculation of the BN-600 reactor for the deterministic and stochastic codes

NASA Astrophysics Data System (ADS)

Bogdanova, E. V.; Kuznetsov, A. N.

2017-01-01

The solution of the problem of increasing the safety of nuclear power plants implies the existence of complete and reliable information about the processes occurring in the core of a working reactor. Nowadays the Monte-Carlo method is the most general-purpose method used to calculate the neutron-physical characteristic of the reactor. But it is characterized by large time of calculation. Therefore, it may be useful to carry out coupled calculations with stochastic and deterministic codes. This article presents the results of research for possibility of combining stochastic and deterministic algorithms in calculation the reactor BN-600. This is only one part of the work, which was carried out in the framework of the graduation project at the NRC “Kurchatov Institute” in cooperation with S. S. Gorodkov and M. A. Kalugin. It is considering the 2-D layer of the BN-600 reactor core from the international benchmark test, published in the report IAEA-TECDOC-1623. Calculations of the reactor were performed with MCU code and then with a standard operative diffusion algorithm with constants taken from the Monte - Carlo computation. Macro cross-section, diffusion coefficients, the effective multiplication factor and the distribution of neutron flux and power were obtained in 15 energy groups. The reasonable agreement between stochastic and deterministic calculations of the BN-600 is observed.

Proper orthogonal decomposition-based spectral higher-order stochastic estimation

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

Baars, Woutijn J., E-mail: wbaars@unimelb.edu.au; Tinney, Charles E.

A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimationmore » (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.« less

Systematic Evaluation of Stochastic Methods in Power System Scheduling and Dispatch with Renewable Energy

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

Wang, Yishen; Zhou, Zhi; Liu, Cong

2016-08-01

As more wind power and other renewable resources are being integrated into the electric power grid, the forecast uncertainty brings operational challenges for the power system operators. In this report, different operational strategies for uncertainty management are presented and evaluated. A comprehensive and consistent simulation framework is developed to analyze the performance of different reserve policies and scheduling techniques under uncertainty in wind power. Numerical simulations are conducted on a modified version of the IEEE 118-bus system with a 20% wind penetration level, comparing deterministic, interval, and stochastic unit commitment strategies. The results show that stochastic unit commitment provides amore » reliable schedule without large increases in operational costs. Moreover, decomposition techniques, such as load shift factor and Benders decomposition, can help in overcoming the computational obstacles to stochastic unit commitment and enable the use of a larger scenario set to represent forecast uncertainty. In contrast, deterministic and interval unit commitment tend to give higher system costs as more reserves are being scheduled to address forecast uncertainty. However, these approaches require a much lower computational effort Choosing a proper lower bound for the forecast uncertainty is important for balancing reliability and system operational cost in deterministic and interval unit commitment. Finally, we find that the introduction of zonal reserve requirements improves reliability, but at the expense of higher operational costs.« less

Uncertainty quantification for personalized analyses of human proximal femurs.

PubMed

Wille, Hagen; Ruess, Martin; Rank, Ernst; Yosibash, Zohar

2016-02-29

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (ϵ1 and ϵ3) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coefficients of variation of ≈40%. Between 60 and 80% of the variance in ϵ1 and ϵ3 are attributable to the uncertainty in the E-ρ relationship, while ≈10% are caused by the load magnitude and 5-30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (pf<0.001). In summary, uncertainty quantification with PC has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs. Copyright © 2015 Elsevier Ltd. All rights reserved.

Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

PubMed

Mangel, Marc

2015-05-01

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming.

PubMed

Alvarado, Michelle; Ntaimo, Lewis

2018-03-01

Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.

Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

NASA Astrophysics Data System (ADS)

Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

2015-03-01

We present Π4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

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

Adams, Brian M.; Ebeida, Mohamed Salah; Eldred, Michael S.

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components requiredmore » for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.« less