Hybrid approaches for multiple-species stochastic reaction–diffusion models

International Nuclear Information System (INIS)

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

2015-01-01

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

Hybrid approaches for multiple-species stochastic reaction–diffusion models

Energy Technology Data Exchange (ETDEWEB)

Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)

2015-10-15

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

Changing contributions of stochastic and deterministic processes in community assembly over a successional gradient.

Science.gov (United States)

Måren, Inger Elisabeth; Kapfer, Jutta; Aarrestad, Per Arild; Grytnes, John-Arvid; Vandvik, Vigdis

2018-01-01

Successional dynamics in plant community assembly may result from both deterministic and stochastic ecological processes. The relative importance of different ecological processes is expected to vary over the successional sequence, between different plant functional groups, and with the disturbance levels and land-use management regimes of the successional systems. We evaluate the relative importance of stochastic and deterministic processes in bryophyte and vascular plant community assembly after fire in grazed and ungrazed anthropogenic coastal heathlands in Northern Europe. A replicated series of post-fire successions (n = 12) were initiated under grazed and ungrazed conditions, and vegetation data were recorded in permanent plots over 13 years. We used redundancy analysis (RDA) to test for deterministic successional patterns in species composition repeated across the replicate successional series and analyses of co-occurrence to evaluate to what extent species respond synchronously along the successional gradient. Change in species co-occurrences over succession indicates stochastic successional dynamics at the species level (i.e., species equivalence), whereas constancy in co-occurrence indicates deterministic dynamics (successional niche differentiation). The RDA shows high and deterministic vascular plant community compositional change, especially early in succession. Co-occurrence analyses indicate stochastic species-level dynamics the first two years, which then give way to more deterministic replacements. Grazed and ungrazed successions are similar, but the early stage stochasticity is higher in ungrazed areas. Bryophyte communities in ungrazed successions resemble vascular plant communities. In contrast, bryophytes in grazed successions showed consistently high stochasticity and low determinism in both community composition and species co-occurrence. In conclusion, stochastic and individualistic species responses early in succession give way to more

Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

DEFF Research Database (Denmark)

Eldeberky, Y.; Madsen, Per A.

1999-01-01

and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

Deterministic Versus Stochastic Interpretation of Continuously Monitored Sewer Systems

DEFF Research Database (Denmark)

Harremoës, Poul; Carstensen, Niels Jacob

1994-01-01

An analysis has been made of the uncertainty of input parameters to deterministic models for sewer systems. The analysis reveals a very significant uncertainty, which can be decreased, but not eliminated and has to be considered for engineering application. Stochastic models have a potential for ...

Deterministic and Stochastic Study of Wind Farm Harmonic Currents

DEFF Research Database (Denmark)

Sainz, Luis; Mesas, Juan Jose; Teodorescu, Remus

2010-01-01

Wind farm harmonic emissions are a well-known power quality problem, but little data based on actual wind farm measurements are available in literature. In this paper, harmonic emissions of an 18 MW wind farm are investigated using extensive measurements, and the deterministic and stochastic char...

Chaotic transitions in deterministic and stochastic dynamical systems applications of Melnikov processes in engineering, physics, and neuroscience

CERN Document Server

Simiu, Emil

2002-01-01

The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to d...

Deterministic and stochastic trends in the Lee-Carter mortality model

DEFF Research Database (Denmark)

Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene

The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies to a random walk model...... that characterizes mortality data. We find empirical evidence that this feature of the Lee-Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find...... that the classical Lee-Carter model will otherwise over estimate the reduction of mortality for the younger age groups and will under estimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee-Carter model instead of a one-factor model should be formulated...

Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

Science.gov (United States)

Choustova, Olga

2007-02-01

We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

Stochastic Reachability Analysis of Hybrid Systems

CERN Document Server

Bujorianu, Luminita Manuela

2012-01-01

Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...

Functional Abstraction of Stochastic Hybrid Systems

NARCIS (Netherlands)

Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.

2006-01-01

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways

Deterministic and stochastic trends in the Lee-Carter mortality model

DEFF Research Database (Denmark)

Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene

2015-01-01

The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics load with identical weights when describing the development of age-specific mortality rates. Effectively this means that the main characteristics of the model simplify to a random walk model with age...... mortality data. We find empirical evidence that this feature of the Lee–Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee......–Carter model will otherwise overestimate the reduction of mortality for the younger age groups and will underestimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee–Carter model instead of a one-factor model should be formulated as a two- (or several...

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

Science.gov (United States)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Handbook of EOQ inventory problems stochastic and deterministic models and applications

CERN Document Server

Choi, Tsan-Ming

2013-01-01

This book explores deterministic and stochastic EOQ-model based problems and applications, presenting technical analyses of single-echelon EOQ model based inventory problems, and applications of the EOQ model for multi-echelon supply chain inventory analysis.

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

Science.gov (United States)

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.

Optimal power flow: a bibliographic survey II. Non-deterministic and hybrid methods

Energy Technology Data Exchange (ETDEWEB)

Frank, Stephen [Colorado School of Mines, Department of Electrical Engineering and Computer Science, Golden, CO (United States); Steponavice, Ingrida [Univ. of Jyvaskyla, Dept. of Mathematical Information Technology, Agora (Finland); Rebennack, Steffen [Colorado School of Mines, Division of Economics and Business, Golden, CO (United States)

2012-09-15

Over the past half-century, optimal power flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey (this article) examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF. (orig.)

Measures of thermodynamic irreversibility in deterministic and stochastic dynamics

International Nuclear Information System (INIS)

Ford, Ian J

2015-01-01

It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour. (paper)

Methods and models in mathematical biology deterministic and stochastic approaches

CERN Document Server

Müller, Johannes

2015-01-01

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

On the deterministic and stochastic use of hydrologic models

Science.gov (United States)

Farmer, William H.; Vogel, Richard M.

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

Scott Ferrenberg

2016-10-01

Full Text Available Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species and belowground (species active in organic and mineral soil layers arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community and modified Winkler funnels (belowground community and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the

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

Science.gov (United States)

Martinez, Alexander S.; Faist, Akasha M.

2016-01-01

Background Understanding patterns of biodiversity is a longstanding challenge in ecology. Similar to other biotic groups, arthropod community structure can be shaped by deterministic and stochastic processes, with limited understanding of what moderates the relative influence of these processes. Disturbances have been noted to alter the relative influence of deterministic and stochastic processes on community assembly in various study systems, implicating ecological disturbances as a potential moderator of these forces. Methods Using a disturbance gradient along a 5-year chronosequence of insect-induced tree mortality in a subalpine forest of the southern Rocky Mountains, Colorado, USA, we examined changes in community structure and relative influences of deterministic and stochastic processes in the assembly of aboveground (surface and litter-active species) and belowground (species active in organic and mineral soil layers) arthropod communities. Arthropods were sampled for all years of the chronosequence via pitfall traps (aboveground community) and modified Winkler funnels (belowground community) and sorted to morphospecies. Community structure of both communities were assessed via comparisons of morphospecies abundance, diversity, and composition. Assembly processes were inferred from a mixture of linear models and matrix correlations testing for community associations with environmental properties, and from null-deviation models comparing observed vs. expected levels of species turnover (Beta diversity) among samples. Results Tree mortality altered community structure in both aboveground and belowground arthropod communities, but null models suggested that aboveground communities experienced greater relative influences of deterministic processes, while the relative influence of stochastic processes increased for belowground communities. Additionally, Mantel tests and linear regression models revealed significant associations between the aboveground arthropod

Flow injection analysis simulations and diffusion coefficient determination by stochastic and deterministic optimization methods.

Science.gov (United States)

Kucza, Witold

2013-07-25

Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg-Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches. Copyright © 2013 The Author. Published by Elsevier B.V. All rights reserved.

Stochastic and deterministic causes of streamer branching in liquid dielectrics

International Nuclear Information System (INIS)

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

2013-01-01

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

Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

Science.gov (United States)

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.

Molecular dynamics with deterministic and stochastic numerical methods

CERN Document Server

Leimkuhler, Ben

2015-01-01

This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?

Science.gov (United States)

Kubota, Noriaki

2018-03-01

The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model

Science.gov (United States)

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-01

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Deterministic linear-optics quantum computing based on a hybrid approach

International Nuclear Information System (INIS)

Lee, Seung-Woo; Jeong, Hyunseok

2014-01-01

We suggest a scheme for all-optical quantum computation using hybrid qubits. It enables one to efficiently perform universal linear-optical gate operations in a simple and near-deterministic way using hybrid entanglement as off-line resources

Deterministic linear-optics quantum computing based on a hybrid approach

Energy Technology Data Exchange (ETDEWEB)

Lee, Seung-Woo; Jeong, Hyunseok [Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul, 151-742 (Korea, Republic of)

2014-12-04

We suggest a scheme for all-optical quantum computation using hybrid qubits. It enables one to efficiently perform universal linear-optical gate operations in a simple and near-deterministic way using hybrid entanglement as off-line resources.

The concerted calculation of the BN-600 reactor for the deterministic and stochastic codes

Science.gov (United States)

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.

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

Science.gov (United States)

Liu, Xiangdong; Li, Qingze; Pan, Jianxin

2018-06-01

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

Bayesian analysis of deterministic and stochastic prisoner's dilemma games

Directory of Open Access Journals (Sweden)

Howard Kunreuther

2009-08-01

Full Text Available This paper compares the behavior of individuals playing a classic two-person deterministic prisoner's dilemma (PD game with choice data obtained from repeated interdependent security prisoner's dilemma games with varying probabilities of loss and the ability to learn (or not learn about the actions of one's counterpart, an area of recent interest in experimental economics. This novel data set, from a series of controlled laboratory experiments, is analyzed using Bayesian hierarchical methods, the first application of such methods in this research domain. We find that individuals are much more likely to be cooperative when payoffs are deterministic than when the outcomes are probabilistic. A key factor explaining this difference is that subjects in a stochastic PD game respond not just to what their counterparts did but also to whether or not they suffered a loss. These findings are interpreted in the context of behavioral theories of commitment, altruism and reciprocity. The work provides a linkage between Bayesian statistics, experimental economics, and consumer psychology.

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

Science.gov (United States)

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.

Filtering and control of stochastic jump hybrid systems

CERN Document Server

Yao, Xiuming; Zheng, Wei Xing

2016-01-01

This book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analy...

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

NARCIS (Netherlands)

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

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

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

Science.gov (United States)

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

2014-08-01

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

Compositional Modelling of Stochastic Hybrid Systems

NARCIS (Netherlands)

Strubbe, S.N.

2005-01-01

In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete

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

Science.gov (United States)

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

2017-08-01

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

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

KAUST Repository

Ehrhardt, Matthias J.

2017-08-24

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

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

Science.gov (United States)

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Neutronics comparative analysis of plate-type research reactor using deterministic and stochastic methods

International Nuclear Information System (INIS)

Liu, Shichang; Wang, Guanbo; Wu, Gaochen; Wang, Kan

2015-01-01

Highlights: • DRAGON and DONJON are applied and verified in calculations of research reactors. • Continuous-energy Monte Carlo calculations by RMC are chosen as the references. • “ECCO” option of DRAGON is suitable for the calculations of research reactors. • Manual modifications of cross-sections are not necessary with DRAGON and DONJON. • DRAGON and DONJON agree well with RMC if appropriate treatments are applied. - Abstract: Simulation of the behavior of the plate-type research reactors such as JRR-3M and CARR poses a challenge for traditional neutronics calculation tools and schemes for power reactors, due to the characteristics of complex geometry, highly heterogeneity and large leakage of the research reactors. Two different theoretical approaches, the deterministic and the stochastic methods, are used for the neutronics analysis of the JRR-3M plate-type research reactor in this paper. For the deterministic method the neutronics codes DRAGON and DONJON are used, while the continuous-energy Monte Carlo code RMC (Reactor Monte Carlo code) is employed for the stochastic approach. The goal of this research is to examine the capability of the deterministic code system DRAGON and DONJON to reliably simulate the research reactors. The results indicate that the DRAGON and DONJON code system agrees well with the continuous-energy Monte Carlo simulation on both k eff and flux distributions if the appropriate treatments (such as the ECCO option) are applied

Deterministic and stochastic control of chimera states in delayed feedback oscillator

Energy Technology Data Exchange (ETDEWEB)

Semenov, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Maistrenko, Y. [Institute of Mathematics and Center for Medical and Biotechnical Research, NAS of Ukraine, Tereschenkivska Str. 3, 01601 Kyiv (Ukraine)

2016-06-08

Chimera states, characterized by the coexistence of regular and chaotic dynamics, are found in a nonlinear oscillator model with negative time-delayed feedback. The control of these chimera states by external periodic forcing is demonstrated by numerical simulations. Both deterministic and stochastic external periodic forcing are considered. It is shown that multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. The constructive role of noise in the formation of a chimera states is shown.

Exploring the stochastic and deterministic aspects of cyclic emission variability on a high speed spark-ignition engine

International Nuclear Information System (INIS)

Karvountzis-Kontakiotis, A.; Dimaratos, A.; Ntziachristos, L.; Samaras, Z.

2017-01-01

This study contributes to the understanding of cycle-to-cycle emissions variability (CEV) in premixed spark-ignition combustion engines. A number of experimental investigations of cycle-to-cycle combustion variability (CCV) exist in published literature; however only a handful of studies deal with CEV. This study experimentally investigates the impact of CCV on CEV of NO and CO, utilizing experimental results from a high-speed spark-ignition engine. Both CEV and CCV are shown to comprise a deterministic and a stochastic component. Results show that at maximum break torque (MBT) operation, the indicated mean effective pressure (IMEP) maximizes and its coefficient of variation (COV_I_M_E_P) minimizes, leading to minimum variation of NO. NO variability and hence mean NO levels can be reduced by more than 50% and 30%, respectively, at advanced ignition timing, by controlling the deterministic CCV using cycle resolved combustion control. The deterministic component of CEV increases at lean combustion (lambda = 1.12) and this overall increases NO variability. CEV was also found to decrease with engine load. At steady speed, increasing throttle position from 20% to 80%, decreased COV_I_M_E_P, COV_N_O and COV_C_O by 59%, 46%, and 6% respectively. Highly resolved engine control, by means of cycle-to-cycle combustion control, appears as key to limit the deterministic feature of cyclic variability and by that to overall reduce emission levels. - Highlights: • Engine emissions variability comprise both stochastic and deterministic components. • Lean and diluted combustion conditions increase emissions variability. • Advanced ignition timing enhances the deterministic component of variability. • Load increase decreases the deterministic component of variability. • The deterministic component can be reduced by highly resolved combustion control.

Combining deterministic and stochastic velocity fields in the analysis of deep crustal seismic data

Science.gov (United States)

Larkin, Steven Paul

Standard crustal seismic modeling obtains deterministic velocity models which ignore the effects of wavelength-scale heterogeneity, known to exist within the Earth's crust. Stochastic velocity models are a means to include wavelength-scale heterogeneity in the modeling. These models are defined by statistical parameters obtained from geologic maps of exposed crystalline rock, and are thus tied to actual geologic structures. Combining both deterministic and stochastic velocity models into a single model allows a realistic full wavefield (2-D) to be computed. By comparing these simulations to recorded seismic data, the effects of wavelength-scale heterogeneity can be investigated. Combined deterministic and stochastic velocity models are created for two datasets, the 1992 RISC seismic experiment in southeastern California and the 1986 PASSCAL seismic experiment in northern Nevada. The RISC experiment was located in the transition zone between the Salton Trough and the southern Basin and Range province. A high-velocity body previously identified beneath the Salton Trough is constrained to pinch out beneath the Chocolate Mountains to the northeast. The lateral extent of this body is evidence for the ephemeral nature of rifting loci as a continent is initially rifted. Stochastic modeling of wavelength-scale structures above this body indicate that little more than 5% mafic intrusion into a more felsic continental crust is responsible for the observed reflectivity. Modeling of the wide-angle RISC data indicates that coda waves following PmP are initially dominated by diffusion of energy out of the near-surface basin as the wavefield reverberates within this low-velocity layer. At later times, this coda consists of scattered body waves and P to S conversions. Surface waves do not play a significant role in this coda. Modeling of the PASSCAL dataset indicates that a high-gradient crust-mantle transition zone or a rough Moho interface is necessary to reduce precritical Pm

Hybrid framework for the simulation of stochastic chemical kinetics

International Nuclear Information System (INIS)

Duncan, Andrew; Erban, Radek; Zygalakis, Konstantinos

2016-01-01

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

Hybrid framework for the simulation of stochastic chemical kinetics

Science.gov (United States)

Duncan, Andrew; Erban, Radek; Zygalakis, Konstantinos

2016-12-01

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the "fast" reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

Hybrid framework for the simulation of stochastic chemical kinetics

Energy Technology Data Exchange (ETDEWEB)

Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk [Department of Mathematics, Imperial College, South Kensington Campus, London, SW7 2AZ (United Kingdom); Erban, Radek, E-mail: erban@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk [School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD (United Kingdom)

2016-12-01

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

A hybrid algorithm for stochastic single-source capacitated facility location problem with service level requirements

Directory of Open Access Journals (Sweden)

Hosseinali Salemi

2016-04-01

Full Text Available Facility location models are observed in many diverse areas such as communication networks, transportation, and distribution systems planning. They play significant role in supply chain and operations management and are one of the main well-known topics in strategic agenda of contemporary manufacturing and service companies accompanied by long-lasting effects. We define a new approach for solving stochastic single source capacitated facility location problem (SSSCFLP. Customers with stochastic demand are assigned to set of capacitated facilities that are selected to serve them. It is demonstrated that problem can be transformed to deterministic Single Source Capacitated Facility Location Problem (SSCFLP for Poisson demand distribution. A hybrid algorithm which combines Lagrangian heuristic with adjusted mixture of Ant colony and Genetic optimization is proposed to find lower and upper bounds for this problem. Computational results of various instances with distinct properties indicate that proposed solving approach is efficient.

Application of Hybrid Genetic Algorithm Routine in Optimizing Food and Bioengineering Processes

Directory of Open Access Journals (Sweden)

Jaya Shankar Tumuluru

2016-11-01

Full Text Available Optimization is a crucial step in the analysis of experimental results. Deterministic methods only converge on local optimums and require exponentially more time as dimensionality increases. Stochastic algorithms are capable of efficiently searching the domain space; however convergence is not guaranteed. This article demonstrates the novelty of the hybrid genetic algorithm (HGA, which combines both stochastic and deterministic routines for improved optimization results. The new hybrid genetic algorithm developed is applied to the Ackley benchmark function as well as case studies in food, biofuel, and biotechnology processes. For each case study, the hybrid genetic algorithm found a better optimum candidate than reported by the sources. In the case of food processing, the hybrid genetic algorithm improved the anthocyanin yield by 6.44%. Optimization of bio-oil production using HGA resulted in a 5.06% higher yield. In the enzyme production process, HGA predicted a 0.39% higher xylanase yield. Hybridization of the genetic algorithm with a deterministic algorithm resulted in an improved optimum compared to statistical methods.

Doses from aquatic pathways in CSA-N288.1: deterministic and stochastic predictions compared

Energy Technology Data Exchange (ETDEWEB)

Chouhan, S.L.; Davis, P

2002-04-01

The conservatism and uncertainty in the Canadian Standards Association (CSA) model for calculating derived release limits (DRLs) for aquatic emissions of radionuclides from nuclear facilities was investigated. The model was run deterministically using the recommended default values for its parameters, and its predictions were compared with the distributed doses obtained by running the model stochastically. Probability density functions (PDFs) for the model parameters for the stochastic runs were constructed using data reported in the literature and results from experimental work done by AECL. The default values recommended for the CSA model for some parameters were found to be lower than the central values of the PDFs in about half of the cases. Doses (ingestion, groundshine and immersion) calculated as the median of 400 stochastic runs were higher than the deterministic doses predicted using the CSA default values of the parameters for more than half (85 out of the 163) of the cases. Thus, the CSA model is not conservative for calculating DRLs for aquatic radionuclide emissions, as it was intended to be. The output of the stochastic runs was used to determine the uncertainty in the CSA model predictions. The uncertainty in the total dose was high, with the 95% confidence interval exceeding an order of magnitude for all radionuclides. A sensitivity study revealed that total ingestion doses to adults predicted by the CSA model are sensitive primarily to water intake rates, bioaccumulation factors for fish and marine biota, dietary intakes of fish and marine biota, the fraction of consumed food arising from contaminated sources, the irrigation rate, occupancy factors and the sediment solid/liquid distribution coefficient. To improve DRL models, further research into aquatic exposure pathways should concentrate on reducing the uncertainty in these parameters. The PDFs given here can he used by other modellers to test and improve their models and to ensure that DRLs

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution

Directory of Open Access Journals (Sweden)

Rice Sean H

2008-09-01

Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general

Integrated Deterministic-Probabilistic Safety Assessment Methodologies

Energy Technology Data Exchange (ETDEWEB)

Kudinov, P.; Vorobyev, Y.; Sanchez-Perea, M.; Queral, C.; Jimenez Varas, G.; Rebollo, M. J.; Mena, L.; Gomez-Magin, J.

2014-02-01

IDPSA (Integrated Deterministic-Probabilistic Safety Assessment) is a family of methods which use tightly coupled probabilistic and deterministic approaches to address respective sources of uncertainties, enabling Risk informed decision making in a consistent manner. The starting point of the IDPSA framework is that safety justification must be based on the coupling of deterministic (consequences) and probabilistic (frequency) considerations to address the mutual interactions between stochastic disturbances (e.g. failures of the equipment, human actions, stochastic physical phenomena) and deterministic response of the plant (i.e. transients). This paper gives a general overview of some IDPSA methods as well as some possible applications to PWR safety analyses. (Author)

Burnup-dependent core neutronics analysis of plate-type research reactor using deterministic and stochastic methods

International Nuclear Information System (INIS)

Liu, Shichang; Wang, Guanbo; Liang, Jingang; Wu, Gaochen; Wang, Kan

2015-01-01

Highlights: • DRAGON & DONJON were applied in burnup calculations of plate-type research reactors. • Continuous-energy Monte Carlo burnup calculations by RMC were chosen as references. • Comparisons of keff, isotopic densities and power distribution were performed. • Reasons leading to discrepancies between two different approaches were analyzed. • DRAGON & DONJON is capable of burnup calculations with appropriate treatments. - Abstract: The burnup-dependent core neutronics analysis of the plate-type research reactors such as JRR-3M poses a challenge for traditional neutronics calculational tools and schemes for power reactors, due to the characteristics of complex geometry, highly heterogeneity, large leakage and the particular neutron spectrum of the research reactors. Two different theoretical approaches, the deterministic and the stochastic methods, are used for the burnup-dependent core neutronics analysis of the JRR-3M plate-type research reactor in this paper. For the deterministic method the neutronics codes DRAGON & DONJON are used, while the continuous-energy Monte Carlo code RMC (Reactor Monte Carlo code) is employed for the stochastic one. In the first stage, the homogenizations of few-group cross sections by DRAGON and the full core diffusion calculations by DONJON have been verified by comparing with the detailed Monte Carlo simulations. In the second stage, the burnup-dependent calculations of both assembly level and the full core level were carried out, to examine the capability of the deterministic code system DRAGON & DONJON to reliably simulate the burnup-dependent behavior of research reactors. The results indicate that both RMC and DRAGON & DONJON code system are capable of burnup-dependent neutronics analysis of research reactors, provided that appropriate treatments are applied in both assembly and core levels for the deterministic codes

Hybrid stochastic simplifications for multiscale gene networks

Directory of Open Access Journals (Sweden)

Debussche Arnaud

2009-09-01

Full Text Available Abstract Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion 123 which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.

Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems

International Nuclear Information System (INIS)

Deco, Gustavo; Marti, Daniel

2007-01-01

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability

Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems

Science.gov (United States)

Deco, Gustavo; Martí, Daniel

2007-03-01

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.

Stochastic and deterministic models to evaluate the critical distance of a near surface repository for the disposal of intermediate and low level radioactive wastes

Energy Technology Data Exchange (ETDEWEB)

Alves, A.S.M., E-mail: asergi@eletronuclear.gov.br [Eletrobrás Termonuclear – Eletronuclear S.A. , Rua da Candelária 65, 7° andar, GSN.T, 20091-906 Rio de Janeiro, RJ (Brazil); Melo, P.F. Frutuoso e, E-mail: frutuoso@nuclear.ufrj.br [Graduate Program of Nuclear Engineering, COPPE, Federal University of Rio de Janeiro, Av. Horácio Macedo 2030, Bloco G, sala 206, 21941-914 Rio de Janeiro, RJ (Brazil); Passos, E.M., E-mail: epassos@eletronuclear.gov.br [Eletrobrás Termonuclear – Eletronuclear S.A. , Rua da Candelária 65, 7° andar, GSN.T, 20091-906 Rio de Janeiro, RJ (Brazil); Fontes, G.S., E-mail: gsfontes@hotmail.com [Instituto Militar de Engenharia – IME, Praça General Tibúrcio 80, 22290-270 Rio de Janeiro, RJ (Brazil)

2015-06-15

Highlights: • The water infiltration scenario is evaluated for a near surface repository. • The main objective is the determination of the critical distance of the repository. • The column liquid height in the repository is governed by an Ito stochastic equation. • Practical results are obtained for the Abadia de Goiás repository in Brazil. - Abstract: The aim of this paper is to present the stochastic and deterministic models developed for the evaluation of the critical distance of a near surface repository for the disposal of intermediate (ILW) and low level (LLW) radioactive wastes. The critical distance of a repository is defined as the distance between the repository and a well in which the water activity concentration is able to cause a radiological dose to a member of the public equal to the dose limit set by the regulatory body. The mathematical models are developed based on the Richards equation for the liquid flow in the porous media and on the solute transport equation in this medium. The release of radioactive material from the repository to the environment is considered through its base and its flow is determined by Darcy's Law. The deterministic model is obtained from the stochastic approach by neglecting the influence of the Gaussian white noise on the rainfall and the equations are solved analytically with the help of conventional calculus (non-stochastic calculus). The equations of the stochastic model are solved analytically based on the Ito stochastic calculus and numerically by using the Euler–Maruyama method. The impact on the value of the critical distance of the Abadia de Goiás repository is analyzed, taken as a study case, when the deterministic methodology is replaced by the stochastic one, considered more appropriate for modeling rainfall as a stochastic process.

Evolving Stochastic Learning Algorithm based on Tsallis entropic index

Science.gov (United States)

Anastasiadis, A. D.; Magoulas, G. D.

2006-03-01

In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and stochastic search steps by employing a different adaptive stepsize for each network weight, and applies a form of noise that is characterized by the nonextensive entropic index q, regulated by a weight decay term. The behavior of the learning algorithm can be made more stochastic or deterministic depending on the trade off between the temperature T and the q values. This is achieved by introducing a formula that defines a time-dependent relationship between these two important learning parameters. Our experimental study verifies that there are indeed improvements in the convergence speed of this new evolving stochastic learning algorithm, which makes learning faster than using the original Hybrid Learning Scheme (HLS). In addition, experiments are conducted to explore the influence of the entropic index q and temperature T on the convergence speed and stability of the proposed method.

The theory of hybrid stochastic algorithms

International Nuclear Information System (INIS)

Duane, S.; Kogut, J.B.

1986-01-01

The theory of hybrid stochastic algorithms is developed. A generalized Fokker-Planck equation is derived and is used to prove that the correct equilibrium distribution is generated by the algorithm. Systematic errors following from the discrete time-step used in the numerical implementation of the scheme are computed. Hybrid algorithms which simulate lattice gauge theory with dynamical fermions are presented. They are optimized in computer simulations and their systematic errors and efficiencies are studied. (orig.)

Stochastic optimization methods

CERN Document Server

Marti, Kurt

2005-01-01

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Deterministic Graphical Games Revisited

DEFF Research Database (Denmark)

Andersson, Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro

2008-01-01

We revisit the deterministic graphical games of Washburn. A deterministic graphical game can be described as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving deterministic graphical...... games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a linear time comparison-based algorithm remains an open problem....

Stochastic hybrid systems with renewal transitions

NARCIS (Netherlands)

Guerreiro Tome Antunes, D.J.; Hespanha, J.P.; Silvestre, C.J.

2010-01-01

We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an analysis framework based on a set of Volterra renewal-type equations, which allows us to compute any statistical

Automated Controller Synthesis for non-Deterministic Piecewise-Affine Hybrid Systems

DEFF Research Database (Denmark)

Grunnet, Jacob Deleuran

formations. This thesis uses a hybrid systems model of a satellite formation with possible actuator faults as a motivating example for developing an automated control synthesis method for non-deterministic piecewise-affine hybrid systems (PAHS). The method does not only open an avenue for further research...... in fault tolerant satellite formation control, but can be used to synthesise controllers for a wide range of systems where external events can alter the system dynamics. The synthesis method relies on abstracting the hybrid system into a discrete game, finding a winning strategy for the game meeting...... game and linear optimisation solvers for controller refinement. To illustrate the efficacy of the method a reoccurring satellite formation example including actuator faults has been used. The end result is the application of PAHSCTRL on the example showing synthesis and simulation of a fault tolerant...

Relative importance of deterministic and stochastic processes in driving arbuscular mycorrhizal fungal assemblage during the spreading of a toxic plant.

Directory of Open Access Journals (Sweden)

Guoxi Shi

Full Text Available Both deterministic and stochastic processes are expected to drive the assemblages of arbuscular mycorrhizal (AM fungi, but little is known about the relative importance of these processes during the spreading of toxic plants. Here, the species composition and phylogenetic structure of AM fungal communities colonizing the roots of a toxic plant, Ligularia virgaurea, and its neighborhood plants, were analyzed in patches with different individual densities of L. virgaurea (represents the spreading degree. Community compositions of AM fungi in both root systems were changed significantly by the L. virgaurea spreading, and also these communities fitted the neutral model very well. AM fungal communities in patches with absence and presence of L. virgaurea were phylogenetically random and clustered, respectively, suggesting that the principal ecological process determining AM fungal assemblage shifted from stochastic process to environmental filtering when this toxic plant was present. Our results indicate that deterministic and stochastic processes together determine the assemblage of AM fungi, but the dominant process would be changed by the spreading of toxic plants, and suggest that the spreading of toxic plants in alpine meadow ecosystems might be involving the mycorrhizal symbionts.

Deterministic and stochastic methods of calculation of polarization characteristics of radiation in natural environment

Science.gov (United States)

Strelkov, S. A.; Sushkevich, T. A.; Maksakova, S. V.

2017-11-01

We are talking about russian achievements of the world level in the theory of radiation transfer, taking into account its polarization in natural media and the current scientific potential developing in Russia, which adequately provides the methodological basis for theoretically-calculated research of radiation processes and radiation fields in natural media using supercomputers and mass parallelism. A new version of the matrix transfer operator is proposed for solving problems of polarized radiation transfer in heterogeneous media by the method of influence functions, when deterministic and stochastic methods can be combined.

Techno-economic simulation data based deterministic and stochastic for product engineering research and development BATAN

International Nuclear Information System (INIS)

Petrus Zacharias; Abdul Jami

2010-01-01

Researches conducted by Batan's researchers have resulted in a number competences that can be used to produce goods and services, which will be applied to industrial sector. However, there are difficulties how to convey and utilize the R and D products into industrial sector. Evaluation results show that each research result should be completed with techno-economy analysis to obtain the feasibility of a product for industry. Further analysis on multy-product concept, in which one business can produce many main products, will be done. For this purpose, a software package simulating techno-economy I economic feasibility which uses deterministic and stochastic data (Monte Carlo method) was been carried out for multi-product including side product. The programming language used in Visual Basic Studio Net 2003 and SQL as data base processing software. This software applied sensitivity test to identify which investment criteria is sensitive for the prospective businesses. Performance test (trial test) has been conducted and the results are in line with the design requirement, such as investment feasibility and sensitivity displayed deterministically and stochastically. These result can be interpreted very well to support business decision. Validation has been performed using Microsoft Excel (for single product). The result of the trial test and validation show that this package is suitable for demands and is ready for use. (author)

Stochastic resonance in small-world neuronal networks with hybrid electrical–chemical synapses

International Nuclear Information System (INIS)

Wang, Jiang; Guo, Xinmeng; Yu, Haitao; Liu, Chen; Deng, Bin; Wei, Xile; Chen, Yingyuan

2014-01-01

Highlights: •We study stochastic resonance in small-world neural networks with hybrid synapses. •The resonance effect depends largely on the probability of chemical synapse. •An optimal chemical synapse probability exists to evoke network resonance. •Network topology affects the stochastic resonance in hybrid neuronal networks. - Abstract: The dependence of stochastic resonance in small-world neuronal networks with hybrid electrical–chemical synapses on the probability of chemical synapse and the rewiring probability is investigated. A subthreshold periodic signal is imposed on one single neuron within the neuronal network as a pacemaker. It is shown that, irrespective of the probability of chemical synapse, there exists a moderate intensity of external noise optimizing the response of neuronal networks to the pacemaker. Moreover, the effect of pacemaker driven stochastic resonance of the system depends largely on the probability of chemical synapse. A high probability of chemical synapse will need lower noise intensity to evoke the phenomenon of stochastic resonance in the networked neuronal systems. In addition, for fixed noise intensity, there is an optimal chemical synapse probability, which can promote the propagation of the localized subthreshold pacemaker across neural networks. And the optimal chemical synapses probability turns even larger as the coupling strength decreases. Furthermore, the small-world topology has a significant impact on the stochastic resonance in hybrid neuronal networks. It is found that increasing the rewiring probability can always enhance the stochastic resonance until it approaches the random network limit

Mode identification using stochastic hybrid models with applications to conflict detection and resolution

Science.gov (United States)

Naseri Kouzehgarani, Asal

2009-12-01

as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers. We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs.

Investment timing under hybrid stochastic and local volatility

International Nuclear Information System (INIS)

Kim, Jeong-Hoon; Lee, Min-Ku; Sohn, So Young

2014-01-01

Highlights: • The effects of hybrid stochastic volatility on real option prices are studied. • The stochastic volatility consists of a fast mean-reverting component and a CEV type one. • A fast mean-reverting factor lowers real option prices and investment thresholds. • The increase of elasticity raises real option prices and investment thresholds. • The effects of the addition of a slowly varying factor depend upon the project value. - Abstract: We consider an investment timing problem under a real option model where the instantaneous volatility of the project value is given by a combination of a hidden stochastic process and the project value itself. The stochastic volatility part is given by a function of a fast mean-reverting process as well as a slowly varying process and the local volatility part is a power (the elasticity parameter) of the project value itself. The elasticity parameter controls directly the correlation between the project value and the volatility. Knowing that the project value represents the market price of a real asset in many applications and the value of the elasticity parameter depends on the asset, the elasticity parameter should be treated with caution for investment decision problems. Based on the hybrid structure of volatility, we investigate the simultaneous impact of the elasticity and the stochastic volatility on the real option value as well as the investment threshold

Relative Roles of Deterministic and Stochastic Processes in Driving the Vertical Distribution of Bacterial Communities in a Permafrost Core from the Qinghai-Tibet Plateau, China.

Science.gov (United States)

Hu, Weigang; Zhang, Qi; Tian, Tian; Li, Dingyao; Cheng, Gang; Mu, Jing; Wu, Qingbai; Niu, Fujun; Stegen, James C; An, Lizhe; Feng, Huyuan

2015-01-01

Understanding the processes that influence the structure of biotic communities is one of the major ecological topics, and both stochastic and deterministic processes are expected to be at work simultaneously in most communities. Here, we investigated the vertical distribution patterns of bacterial communities in a 10-m-long soil core taken within permafrost of the Qinghai-Tibet Plateau. To get a better understanding of the forces that govern these patterns, we examined the diversity and structure of bacterial communities, and the change in community composition along the vertical distance (spatial turnover) from both taxonomic and phylogenetic perspectives. Measures of taxonomic and phylogenetic beta diversity revealed that bacterial community composition changed continuously along the soil core, and showed a vertical distance-decay relationship. Multiple stepwise regression analysis suggested that bacterial alpha diversity and phylogenetic structure were strongly correlated with soil conductivity and pH but weakly correlated with depth. There was evidence that deterministic and stochastic processes collectively drived bacterial vertically-structured pattern. Bacterial communities in five soil horizons (two originated from the active layer and three from permafrost) of the permafrost core were phylogenetically random, indicator of stochastic processes. However, we found a stronger effect of deterministic processes related to soil pH, conductivity, and organic carbon content that were structuring the bacterial communities. We therefore conclude that the vertical distribution of bacterial communities was governed primarily by deterministic ecological selection, although stochastic processes were also at work. Furthermore, the strong impact of environmental conditions (for example, soil physicochemical parameters and seasonal freeze-thaw cycles) on these communities underlines the sensitivity of permafrost microorganisms to climate change and potentially subsequent

HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

International Nuclear Information System (INIS)

Marchetti, Luca; Priami, Corrado; Thanh, Vo Hong

2016-01-01

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

HRSSA – Efficient hybrid stochastic simulation for spatially homogeneous biochemical reaction networks

Energy Technology Data Exchange (ETDEWEB)

Marchetti, Luca, E-mail: marchetti@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); University of Trento, Department of Mathematics (Italy); Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy)

2016-07-15

This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

Science.gov (United States)

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still

Stochastic effects in hybrid inflation

Science.gov (United States)

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.

Stochastic background of gravitational waves from hybrid preheating.

Science.gov (United States)

García-Bellido, Juan; Figueroa, Daniel G

2007-02-09

The process of reheating the Universe after hybrid inflation is extremely violent. It proceeds through the nucleation and subsequent collision of large concentrations of energy density in bubblelike structures, which generate a significant fraction of energy in the form of gravitational waves. We study the power spectrum of the stochastic background of gravitational waves produced at reheating after hybrid inflation. We find that the amplitude could be significant for high-scale models, although the typical frequencies are well beyond what could be reached by planned gravitational wave observatories. On the other hand, low-scale models could still produce a detectable stochastic background at frequencies accessible to those detectors. The discovery of such a background would open a new window into the very early Universe.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Science.gov (United States)

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

2015-10-01

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

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

KAUST Repository

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

2015-01-01

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

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

KAUST Repository

Spill, Fabian

2015-10-01

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

Development and application of a deterministic-realistic hybrid methodology for LOCA licensing analysis

International Nuclear Information System (INIS)

Liang, Thomas K.S.; Chou, Ling-Yao; Zhang, Zhongwei; Hsueh, Hsiang-Yu; Lee, Min

2011-01-01

Highlights: → A new LOCA licensing methodology (DRHM, deterministic-realistic hybrid methodology) was developed. → DRHM involves conservative Appendix K physical models and statistical treatment of plant status uncertainties. → DRHM can generate 50-100 K PCT margin as compared to a traditional Appendix K methodology. - Abstract: It is well recognized that a realistic LOCA analysis with uncertainty quantification can generate greater safety margin as compared with classical conservative LOCA analysis using Appendix K evaluation models. The associated margin can be more than 200 K. To quantify uncertainty in BELOCA analysis, generally there are two kinds of uncertainties required to be identified and quantified, which involve model uncertainties and plant status uncertainties. Particularly, it will take huge effort to systematically quantify individual model uncertainty of a best estimate LOCA code, such as RELAP5 and TRAC. Instead of applying a full ranged BELOCA methodology to cover both model and plant status uncertainties, a deterministic-realistic hybrid methodology (DRHM) was developed to support LOCA licensing analysis. Regarding the DRHM methodology, Appendix K deterministic evaluation models are adopted to ensure model conservatism, while CSAU methodology is applied to quantify the effect of plant status uncertainty on PCT calculation. Generally, DRHM methodology can generate about 80-100 K margin on PCT as compared to Appendix K bounding state LOCA analysis.

Separation of Stochastic and Deterministic Information from Seismological Time Series with Nonlinear Dynamics and Maximum Entropy Methods

International Nuclear Information System (INIS)

Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias

2007-01-01

We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.

1982-12-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rainfall runoff model may lead in some cases to nonconservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 - 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

A stochastic-deterministic approach for evaluation of uncertainty in the predicted maximum fuel bundle enthalpy in a CANDU postulated LBLOCA event

Energy Technology Data Exchange (ETDEWEB)

Serghiuta, D.; Tholammakkil, J.; Shen, W., E-mail: Dumitru.Serghiuta@cnsc-ccsn.gc.ca [Canadian Nuclear Safety Commission, Ottawa, Ontario (Canada)

2014-07-01

A stochastic-deterministic approach based on representation of uncertainties by subjective probabilities is proposed for evaluation of bounding values of functional failure probability and assessment of probabilistic safety margins. The approach is designed for screening and limited independent review verification. Its application is illustrated for a postulated generic CANDU LBLOCA and evaluation of the possibility distribution function of maximum bundle enthalpy considering the reactor physics part of LBLOCA power pulse simulation only. The computer codes HELIOS and NESTLE-CANDU were used in a stochastic procedure driven by the computer code DAKOTA to simulate the LBLOCA power pulse using combinations of core neutronic characteristics randomly generated from postulated subjective probability distributions with deterministic constraints and fixed transient bundle-wise thermal hydraulic conditions. With this information, a bounding estimate of functional failure probability using the limit for the maximum fuel bundle enthalpy can be derived for use in evaluation of core damage frequency. (author)

Model-based stochastic-deterministic State and Force Estimation using Kalman filtering with Application to Hanko-1 Channel Marker

OpenAIRE

Petersen, Øyvind Wiig

2014-01-01

Force identification in structural dynamics is an inverse problem concerned with finding loads from measured structural response. The main objective of this thesis is to perform and study state (displacement and velocity) and force estimation by Kalman filtering. Theory on optimal control and state-space models are presented, adapted to linear structural dynamics. Accommodation for measurement noise and model inaccuracies are attained by stochastic-deterministic coupling. Explicit requirem...

Testing the robustness of deterministic models of optimal dynamic pricing and lot-sizing for deteriorating items under stochastic conditions

DEFF Research Database (Denmark)

Ghoreishi, Maryam

2018-01-01

Many models within the field of optimal dynamic pricing and lot-sizing models for deteriorating items assume everything is deterministic and develop a differential equation as the core of analysis. Two prominent examples are the papers by Rajan et al. (Manag Sci 38:240–262, 1992) and Abad (Manag......, we will try to expose the model by Abad (1996) and Rajan et al. (1992) to stochastic inputs; however, designing these stochastic inputs such that they as closely as possible are aligned with the assumptions of those papers. We do our investigation through a numerical test where we test the robustness...... of the numerical results reported in Rajan et al. (1992) and Abad (1996) in a simulation model. Our numerical results seem to confirm that the results stated in these papers are indeed robust when being imposed to stochastic inputs....

The theory of hybrid stochastic algorithms

International Nuclear Information System (INIS)

Kennedy, A.D.

1989-01-01

These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory. After explaining the basic concepts of Monte Carlo integration we discuss the properties of Markov processes and one particularly useful example of them: the Metropolis algorithm. Building upon this framework we consider the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method; and thus we are led to consider Molecular Dynamics using the Leapfrog algorithm. The lectures conclude by reviewing recent progress in these areas, explaining higher-order integration schemes, the asymptotic large-volume behaviour of the various algorithms, and some simple exact results obtained by applying them to free field theory. It is attempted throughout to give simple yet correct proofs of the various results encountered. 38 refs

Robustness Analysis of Hybrid Stochastic Neural Networks with Neutral Terms and Time-Varying Delays

Directory of Open Access Journals (Sweden)

Chunmei Wu

2015-01-01

Full Text Available We analyze the robustness of global exponential stability of hybrid stochastic neural networks subject to neutral terms and time-varying delays simultaneously. Given globally exponentially stable hybrid stochastic neural networks, we characterize the upper bounds of contraction coefficients of neutral terms and time-varying delays by using the transcendental equation. Moreover, we prove theoretically that, for any globally exponentially stable hybrid stochastic neural networks, if additive neutral terms and time-varying delays are smaller than the upper bounds arrived, then the perturbed neural networks are guaranteed to also be globally exponentially stable. Finally, a numerical simulation example is given to illustrate the presented criteria.

Stochastic linear hybrid systems: Modeling, estimation, and application

Science.gov (United States)

Seah, Chze Eng

Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS

Bayesian inference for hybrid discrete-continuous stochastic kinetic models

International Nuclear Information System (INIS)

Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

2014-01-01

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

A Study on Efficiency Improvement of the Hybrid Monte Carlo/Deterministic Method for Global Transport Problems

International Nuclear Information System (INIS)

Kim, Jong Woo; Woo, Myeong Hyeon; Kim, Jae Hyun; Kim, Do Hyun; Shin, Chang Ho; Kim, Jong Kyung

2017-01-01

In this study hybrid Monte Carlo/Deterministic method is explained for radiation transport analysis in global system. FW-CADIS methodology construct the weight window parameter and it useful at most global MC calculation. However, Due to the assumption that a particle is scored at a tally, less particles are transported to the periphery of mesh tallies. For compensation this space-dependency, we modified the module in the ADVANTG code to add the proposed method. We solved the simple test problem for comparing with result from FW-CADIS methodology, it was confirmed that a uniform statistical error was secured as intended. In the future, it will be added more practical problems. It might be useful to perform radiation transport analysis using the Hybrid Monte Carlo/Deterministic method in global transport problems.

Dynamic Placement of Virtual Machines with Both Deterministic and Stochastic Demands for Green Cloud Computing

Directory of Open Access Journals (Sweden)

Wenying Yue

2014-01-01

Full Text Available Cloud computing has come to be a significant commercial infrastructure offering utility-oriented IT services to users worldwide. However, data centers hosting cloud applications consume huge amounts of energy, leading to high operational cost and greenhouse gas emission. Therefore, green cloud computing solutions are needed not only to achieve high level service performance but also to minimize energy consumption. This paper studies the dynamic placement of virtual machines (VMs with deterministic and stochastic demands. In order to ensure a quick response to VM requests and improve the energy efficiency, a two-phase optimization strategy has been proposed, in which VMs are deployed in runtime and consolidated into servers periodically. Based on an improved multidimensional space partition model, a modified energy efficient algorithm with balanced resource utilization (MEAGLE and a live migration algorithm based on the basic set (LMABBS are, respectively, developed for each phase. Experimental results have shown that under different VMs’ stochastic demand variations, MEAGLE guarantees the availability of stochastic resources with a defined probability and reduces the number of required servers by 2.49% to 20.40% compared with the benchmark algorithms. Also, the difference between the LMABBS solution and Gurobi solution is fairly small, but LMABBS significantly excels in computational efficiency.

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.; Asmis, G.J.K.

1983-01-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rain fall runoff model may lead in some cases to non-conservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 to 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

Stochasticity and determinism in models of hematopoiesis.

Science.gov (United States)

Kimmel, Marek

2014-01-01

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

Stochastic switching in biology: from genotype to phenotype

International Nuclear Information System (INIS)

Bressloff, Paul C

2017-01-01

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

Deterministic geologic processes and stochastic modeling

International Nuclear Information System (INIS)

Rautman, C.A.; Flint, A.L.

1992-01-01

This paper reports that recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. consideration of the spatial variability indicates that her are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. Because the geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling

Recursive stochastic effects in valley hybrid inflation

Science.gov (United States)

Levasseur, Laurence Perreault; Vennin, Vincent; Brandenberger, Robert

2013-10-01

Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88, 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution.

On ray stochasticity during lower hybrid current drive in tokamaks

International Nuclear Information System (INIS)

Bizarro, J.P.; Moreau, D.

1992-08-01

A comprehensive and detailed analysis is presented on the importance of toroidally induced ray stochasticity for the modelling of lower hybrid current drive and for the dynamics of the launched power spectrum. A combined ray tracing and Fokker-Planck code is used and the injected lower hybrid power distribution in poloidal angle and in parallel wave index is accurately represented by taking into account the poloidal extent of the antenna ad by efficiently covering the full range of its radiated spectrum. The importance of the balance between the wave damping and the exponential divergence of nearby ray trajectories in determining the shape of the predicted lower hybrid power deposition profiles is emphasized. When a sufficiently large number of rays is used to densely cover the region of the launched power spectrum which is affected by stochastic effects, code predictions are shown to be stable with respect to small changes in initial conditions and plasma parameters and to be consistent with experimental data

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

International Nuclear Information System (INIS)

Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert E.

2015-01-01

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

Probabilistic Analysis Methods for Hybrid Ventilation

DEFF Research Database (Denmark)

Brohus, Henrik; Frier, Christian; Heiselberg, Per

This paper discusses a general approach for the application of probabilistic analysis methods in the design of ventilation systems. The aims and scope of probabilistic versus deterministic methods are addressed with special emphasis on hybrid ventilation systems. A preliminary application...... of stochastic differential equations is presented comprising a general heat balance for an arbitrary number of loads and zones in a building to determine the thermal behaviour under random conditions....

A hybrid multiscale kinetic Monte Carlo method for simulation of copper electrodeposition

International Nuclear Information System (INIS)

Zheng Zheming; Stephens, Ryan M.; Braatz, Richard D.; Alkire, Richard C.; Petzold, Linda R.

2008-01-01

A hybrid multiscale kinetic Monte Carlo (HMKMC) method for speeding up the simulation of copper electrodeposition is presented. The fast diffusion events are simulated deterministically with a heterogeneous diffusion model which considers site-blocking effects of additives. Chemical reactions are simulated by an accelerated (tau-leaping) method for discrete stochastic simulation which adaptively selects exact discrete stochastic simulation for the appropriate reaction whenever that is necessary. The HMKMC method is seen to be accurate and highly efficient

Sequential neural models with stochastic layers

DEFF Research Database (Denmark)

Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich

2016-01-01

How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...

Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses

International Nuclear Information System (INIS)

Li, Liang; You, Sixiong; Yang, Chao; Yan, Bingjie; Song, Jian; Chen, Zheng

2016-01-01

Highlights: • The novel approximated global optimal energy management strategy has been proposed for hybrid powertrains. • Eight typical driving behaviors have been classified with K-means to deal with the multiplicative traffic conditions. • The stochastic driver models of different driving behaviors were established based on the Markov chains. • ECMS was used to modify the SMPC-based energy management strategy to improve its fuel economy. • The approximated global optimal energy management strategy for plug-in hybrid electric buses has been verified and analyzed. - Abstract: Driving cycles of a city bus is statistically characterized by some repetitive features, which makes the predictive energy management strategy very desirable to obtain approximate optimal fuel economy of a plug-in hybrid electric bus. But dealing with the complicated traffic conditions and finding an approximated global optimal strategy which is applicable to the plug-in hybrid electric bus still remains a challenging technique. To solve this problem, a novel driving-behavior-aware modified stochastic model predictive control method is proposed for the plug-in hybrid electric bus. Firstly, the K-means is employed to classify driving behaviors, and the driver models based on Markov chains is obtained under different kinds of driving behaviors. While the obtained driver behaviors are regarded as stochastic disturbance inputs, the local minimum fuel consumption might be obtained with a traditional stochastic model predictive control at each step, taking tracking the reference battery state of charge trajectory into consideration in the finite predictive horizons. However, this technique is still accompanied by some working points with reduced/worsened fuel economy. Thus, the stochastic model predictive control is modified with the equivalent consumption minimization strategy to eliminate these undesirable working points. The results in real-world city bus routines show that the

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II. Bayesian analyses

International Nuclear Information System (INIS)

Allen, Bruce; Creighton, Jolien D.E.; Flanagan, Eanna E.; Romano, Joseph D.

2003-01-01

In a previous paper (paper I), we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating or clipping sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in the limit of weak signals. For stochastic signals, the resulting statistic consisted of a sum of an autocorrelation term and a cross-correlation term; it was necessary to discard 'by hand' the autocorrelation term in order to arrive at the correct, generalized cross-correlation statistic. In the present paper, we present an alternative derivation of the same signal detection techniques from within the Bayesian framework. We compute, for both deterministic and stochastic signals, the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the signal is nevertheless strong enough to be detected (integrated signal-to-noise ratio large compared to 1), and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in paper I. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic autocorrelation term

Stochastic climate theory

NARCIS (Netherlands)

Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.

2017-01-01

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of

Piecewise deterministic processes in biological models

CERN Document Server

Rudnicki, Ryszard

2017-01-01

This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

Science.gov (United States)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

Science.gov (United States)

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

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

International Nuclear Information System (INIS)

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

2017-01-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge

Automated Flight Routing Using Stochastic Dynamic Programming

Science.gov (United States)

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.

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

Science.gov (United States)

Harrison, Jonathan U; Yates, Christian A

2016-09-01

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

Optimal power flow: a bibliographic survey I. Formulations and deterministic methods

Energy Technology Data Exchange (ETDEWEB)

Frank, Stephen [Colorado School of Mines, Department of Electrical Engineering and Computer Science, Golden, CO (United States); Steponavice, Ingrida [University of Jyvaskyla, Department of Mathematical Information Technology, Agora (Finland); Rebennack, Steffen [Colorado School of Mines, Division of Economics and Business, Golden, CO (United States)

2012-09-15

Over the past half-century, optimal power flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF. (orig.)

Risk-sensitive control of stochastic hybrid systems on infinite time horizon

Directory of Open Access Journals (Sweden)

Runolfsson Thordur

1999-01-01

Full Text Available A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive and H ∞ control in the nonhybrid case does not hold for stochastic hybrid systems.

The influence of deterministic and stochastic waiting time for triggering mortality and colonization events on the coexistence of cooperators and defectors in an evolutionary game model

Directory of Open Access Journals (Sweden)

YouHua Chen

2014-06-01

Full Text Available In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability. The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc. As such, when WT (WTm and/or WTc is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40] and colonization (WTc-[0.1,40] was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3, extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic

Applied stochastic modelling

CERN Document Server

Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P

2008-01-01

Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...

Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.

KAUST Repository

Bressloff, Paul C

2011-05-03

We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.

STOCHASTIC METHODS IN RISK ANALYSIS

Directory of Open Access Journals (Sweden)

Vladimíra OSADSKÁ

2017-06-01

Full Text Available In this paper, we review basic stochastic methods which can be used to extend state-of-the-art deterministic analytical methods for risk analysis. We can conclude that the standard deterministic analytical methods highly depend on the practical experience and knowledge of the evaluator and therefore, the stochastic methods should be introduced. The new risk analysis methods should consider the uncertainties in input values. We present how large is the impact on the results of the analysis solving practical example of FMECA with uncertainties modelled using Monte Carlo sampling.

RES: Regularized Stochastic BFGS Algorithm

Science.gov (United States)

Mokhtari, Aryan; Ribeiro, Alejandro

2014-12-01

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

A critical evaluation of deterministic methods in size optimisation of reliable and cost effective standalone hybrid renewable energy systems

International Nuclear Information System (INIS)

Maheri, Alireza

2014-01-01

Reliability of a hybrid renewable energy system (HRES) strongly depends on various uncertainties affecting the amount of power produced by the system. In the design of systems subject to uncertainties, both deterministic and nondeterministic design approaches can be adopted. In a deterministic design approach, the designer considers the presence of uncertainties and incorporates them indirectly into the design by applying safety factors. It is assumed that, by employing suitable safety factors and considering worst-case-scenarios, reliable systems can be designed. In fact, the multi-objective optimisation problem with two objectives of reliability and cost is reduced to a single-objective optimisation problem with the objective of cost only. In this paper the competence of deterministic design methods in size optimisation of reliable standalone wind–PV–battery, wind–PV–diesel and wind–PV–battery–diesel configurations is examined. For each configuration, first, using different values of safety factors, the optimal size of the system components which minimises the system cost is found deterministically. Then, for each case, using a Monte Carlo simulation, the effect of safety factors on the reliability and the cost are investigated. In performing reliability analysis, several reliability measures, namely, unmet load, blackout durations (total, maximum and average) and mean time between failures are considered. It is shown that the traditional methods of considering the effect of uncertainties in deterministic designs such as design for an autonomy period and employing safety factors have either little or unpredictable impact on the actual reliability of the designed wind–PV–battery configuration. In the case of wind–PV–diesel and wind–PV–battery–diesel configurations it is shown that, while using a high-enough margin of safety in sizing diesel generator leads to reliable systems, the optimum value for this margin of safety leading to a

A Class of Stochastic Hybrid Systems with State-Dependent Switching Noise

DEFF Research Database (Denmark)

Leth, John-Josef; Rasmussen, Jakob Gulddahl; Schiøler, Henrik

2012-01-01

In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed...

Heart rate variability as determinism with jump stochastic parameters.

Science.gov (United States)

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

2013-08-01

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

Optimal Control of Hybrid Systems in Air Traffic Applications

Science.gov (United States)

Kamgarpour, Maryam

Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient

Ranking shortest paths in Stochastic time-denpendent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...

K shortest paths in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan

2004-01-01

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...

A Stochastic Model for Malaria Transmission Dynamics

Directory of Open Access Journals (Sweden)

Rachel Waema Mbogo

2018-01-01

Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

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

Science.gov (United States)

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.

Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis

Directory of Open Access Journals (Sweden)

Zhanhui Lu

2014-01-01

Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.

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

Science.gov (United States)

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

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of

Electric field control of deterministic current-induced magnetization switching in a hybrid ferromagnetic/ferroelectric structure

Science.gov (United States)

Cai, Kaiming; Yang, Meiyin; Ju, Hailang; Wang, Sumei; Ji, Yang; Li, Baohe; Edmonds, Kevin William; Sheng, Yu; Zhang, Bao; Zhang, Nan; Liu, Shuai; Zheng, Houzhi; Wang, Kaiyou

2017-07-01

All-electrical and programmable manipulations of ferromagnetic bits are highly pursued for the aim of high integration and low energy consumption in modern information technology. Methods based on the spin-orbit torque switching in heavy metal/ferromagnet structures have been proposed with magnetic field, and are heading toward deterministic switching without external magnetic field. Here we demonstrate that an in-plane effective magnetic field can be induced by an electric field without breaking the symmetry of the structure of the thin film, and realize the deterministic magnetization switching in a hybrid ferromagnetic/ferroelectric structure with Pt/Co/Ni/Co/Pt layers on PMN-PT substrate. The effective magnetic field can be reversed by changing the direction of the applied electric field on the PMN-PT substrate, which fully replaces the controllability function of the external magnetic field. The electric field is found to generate an additional spin-orbit torque on the CoNiCo magnets, which is confirmed by macrospin calculations and micromagnetic simulations.

Achieving control and synchronization merely through a stochastically adaptive feedback coupling

Science.gov (United States)

Lin, Wei; Chen, Xin; Zhou, Shijie

2017-07-01

Techniques of deterministically adaptive feedback couplings have been successfully and extensively applied to realize control or/and synchronization in chaotic dynamical systems and even in complex dynamical networks. In this article, a technique of stochastically adaptive feedback coupling is novelly proposed to not only realize control in chaotic dynamical systems but also achieve synchronization in unidirectionally coupled systems. Compared with those deterministically adaptive couplings, the proposed stochastic technique interestingly shows some advantages from a physical viewpoint of time and energy consumptions. More significantly, the usefulness of the proposed stochastic technique is analytically validated by the theory of stochastic processes. It is anticipated that the proposed stochastic technique will be widely used in achieving system control and network synchronization.

Assessment of fusion facility dose rate map using mesh adaptivity enhancements of hybrid Monte Carlo/deterministic techniques

International Nuclear Information System (INIS)

Ibrahim, Ahmad M.; Wilson, Paul P.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Grove, Robert E.

2014-01-01

Highlights: •Calculate the prompt dose rate everywhere throughout the entire fusion energy facility. •Utilize FW-CADIS to accurately perform difficult neutronics calculations for fusion energy systems. •Develop three mesh adaptivity algorithms to enhance FW-CADIS efficiency in fusion-neutronics calculations. -- Abstract: Three mesh adaptivity algorithms were developed to facilitate and expedite the use of the CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques in accurate full-scale neutronics simulations of fusion energy systems with immense sizes and complicated geometries. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility and resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation. Additionally, because of the significant increase in the efficiency of FW-CADIS simulations, the three algorithms enabled this difficult calculation to be accurately solved on a regular computer cluster, eliminating the need for a world-class super computer

Stochastic Community Assembly: Does It Matter in Microbial Ecology?

Science.gov (United States)

Zhou, Jizhong; Ning, Daliang

2017-12-01

Understanding the mechanisms controlling community diversity, functions, succession, and biogeography is a central, but poorly understood, topic in ecology, particularly in microbial ecology. Although stochastic processes are believed to play nonnegligible roles in shaping community structure, their importance relative to deterministic processes is hotly debated. The importance of ecological stochasticity in shaping microbial community structure is far less appreciated. Some of the main reasons for such heavy debates are the difficulty in defining stochasticity and the diverse methods used for delineating stochasticity. Here, we provide a critical review and synthesis of data from the most recent studies on stochastic community assembly in microbial ecology. We then describe both stochastic and deterministic components embedded in various ecological processes, including selection, dispersal, diversification, and drift. We also describe different approaches for inferring stochasticity from observational diversity patterns and highlight experimental approaches for delineating ecological stochasticity in microbial communities. In addition, we highlight research challenges, gaps, and future directions for microbial community assembly research. Copyright © 2017 American Society for Microbiology.

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

Science.gov (United States)

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

2016-01-01

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

Research on nonlinear stochastic dynamical price model

International Nuclear Information System (INIS)

Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

2008-01-01

In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks

KAUST Repository

Moraes, Alvaro

2015-01-01

even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

Directory of Open Access Journals (Sweden)

Jian Zhang

2017-01-01

Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.

Aspects if stochastic models for short-term hydropower scheduling and bidding

Energy Technology Data Exchange (ETDEWEB)

Belsnes, Michael Martin [Sintef Energy, Trondheim (Norway); Follestad, Turid [Sintef Energy, Trondheim (Norway); Wolfgang, Ove [Sintef Energy, Trondheim (Norway); Fosso, Olav B. [Dep. of electric power engineering NTNU, Trondheim (Norway)

2012-07-01

This report discusses challenges met when turning from deterministic to stochastic decision support models for short-term hydropower scheduling and bidding. The report describes characteristics of the short-term scheduling and bidding problem, different market and bidding strategies, and how a stochastic optimization model can be formulated. A review of approaches for stochastic short-term modelling and stochastic modelling for the input variables inflow and market prices is given. The report discusses methods for approximating the predictive distribution of uncertain variables by scenario trees. Benefits of using a stochastic over a deterministic model are illustrated by a case study, where increased profit is obtained to a varying degree depending on the reservoir filling and price structure. Finally, an approach for assessing the effect of using a size restricted scenario tree to approximate the predictive distribution for stochastic input variables is described. The report is a summary of the findings of Work package 1 of the research project #Left Double Quotation Mark#Optimal short-term scheduling of wind and hydro resources#Right Double Quotation Mark#. The project aims at developing a prototype for an operational stochastic short-term scheduling model. Based on the investigations summarized in the report, it is concluded that using a deterministic equivalent formulation of the stochastic optimization problem is convenient and sufficient for obtaining a working prototype. (author)

Deterministic mean-variance-optimal consumption and investment

DEFF Research Database (Denmark)

Christiansen, Marcus; Steffensen, Mogens

2013-01-01

In dynamic optimal consumption–investment problems one typically aims to find an optimal control from the set of adapted processes. This is also the natural starting point in case of a mean-variance objective. In contrast, we solve the optimization problem with the special feature that the consum......In dynamic optimal consumption–investment problems one typically aims to find an optimal control from the set of adapted processes. This is also the natural starting point in case of a mean-variance objective. In contrast, we solve the optimization problem with the special feature...... that the consumption rate and the investment proportion are constrained to be deterministic processes. As a result we get rid of a series of unwanted features of the stochastic solution including diffusive consumption, satisfaction points and consistency problems. Deterministic strategies typically appear in unit......-linked life insurance contracts, where the life-cycle investment strategy is age dependent but wealth independent. We explain how optimal deterministic strategies can be found numerically and present an example from life insurance where we compare the optimal solution with suboptimal deterministic strategies...

A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion

Directory of Open Access Journals (Sweden)

O. H. Galal

2013-01-01

Full Text Available This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC. The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost.

Robust nonlinear autoregressive moving average model parameter estimation using stochastic recurrent artificial neural networks

DEFF Research Database (Denmark)

Chon, K H; Hoyer, D; Armoundas, A A

1999-01-01

In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic...... part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction...... error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate...

Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization

Science.gov (United States)

Sochi, Taha

2016-09-01

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method

International Nuclear Information System (INIS)

Inoue, Jun-ichi

2010-01-01

In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ∞)-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.

Are deterministic methods suitable for short term reserve planning?

International Nuclear Information System (INIS)

Voorspools, Kris R.; D'haeseleer, William D.

2005-01-01

Although deterministic methods for establishing minutes reserve (such as the N-1 reserve or the percentage reserve) ignore the stochastic nature of reliability issues, they are commonly used in energy modelling as well as in practical applications. In order to check the validity of such methods, two test procedures are developed. The first checks if the N-1 reserve is a logical fixed value for minutes reserve. The second test procedure investigates whether deterministic methods can realise a stable reliability that is independent of demand. In both evaluations, the loss-of-load expectation is used as the objective stochastic criterion. The first test shows no particular reason to choose the largest unit as minutes reserve. The expected jump in reliability, resulting in low reliability for reserve margins lower than the largest unit and high reliability above, is not observed. The second test shows that both the N-1 reserve and the percentage reserve methods do not provide a stable reliability level that is independent of power demand. For the N-1 reserve, the reliability increases with decreasing maximum demand. For the percentage reserve, the reliability decreases with decreasing demand. The answer to the question raised in the title, therefore, has to be that the probability based methods are to be preferred over the deterministic methods

Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.

Science.gov (United States)

Borgogno, Fabio; D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

2012-01-21

Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers. Copyright © 2011 Elsevier Ltd. All rights reserved.

Approximating Preemptive Stochastic Scheduling

OpenAIRE

Megow Nicole; Vredeveld Tjark

2009-01-01

We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments

Energy Technology Data Exchange (ETDEWEB)

Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard, E-mail: milena.wollmann@ufrgs.br, E-mail: vilhena@mat.ufrgs.br, E-mail: bardobodmann@ufrgs.br, E-mail: richard.vasques@fulbrightmail.org [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2015-07-01

The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)

The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments

International Nuclear Information System (INIS)

Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard

2015-01-01

The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

International Nuclear Information System (INIS)

Wan Li; Zhou Qinghua

2007-01-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

Science.gov (United States)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

Feasibility of a Monte Carlo-deterministic hybrid method for fast reactor analysis

Energy Technology Data Exchange (ETDEWEB)

Heo, W.; Kim, W.; Kim, Y. [Korea Advanced Institute of Science and Technology - KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of); Yun, S. [Korea Atomic Energy Research Institute - KAERI, 989-111 Daedeok-daero, Yuseong-gu, Daejeon, 305-353 (Korea, Republic of)

2013-07-01

A Monte Carlo and deterministic hybrid method is investigated for the analysis of fast reactors in this paper. Effective multi-group cross sections data are generated using a collision estimator in the MCNP5. A high order Legendre scattering cross section data generation module was added into the MCNP5 code. Both cross section data generated from MCNP5 and TRANSX/TWODANT using the homogeneous core model were compared, and were applied to DIF3D code for fast reactor core analysis of a 300 MWe SFR TRU burner core. For this analysis, 9 groups macroscopic-wise data was used. In this paper, a hybrid calculation MCNP5/DIF3D was used to analyze the core model. The cross section data was generated using MCNP5. The k{sub eff} and core power distribution were calculated using the 54 triangle FDM code DIF3D. A whole core calculation of the heterogeneous core model using the MCNP5 was selected as a reference. In terms of the k{sub eff}, 9-group MCNP5/DIF3D has a discrepancy of -154 pcm from the reference solution, 9-group TRANSX/TWODANT/DIF3D analysis gives -1070 pcm discrepancy. (authors)

Stochastic chaos in a Duffing oscillator and its control

International Nuclear Information System (INIS)

Wu Cunli; Lei Youming; Fang Tong

2006-01-01

Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

A Stochastic Hybrid Systems framework for analysis of Markov reward models

International Nuclear Information System (INIS)

Dhople, S.V.; DeVille, L.; Domínguez-García, A.D.

2014-01-01

In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: (i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and (ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application of the framework to performability analysis via analytical and numerical examples

Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage

Science.gov (United States)

Guo, Wenjuan; Cai, Yongli; Zhang, Qimin; Wang, Weiming

2018-02-01

This paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R0s can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease.

Multiobjective Output Feedback Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

S. Aberkane

2007-01-01

Full Text Available This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI process. The specifications and objectives under consideration include stochastic stability, ℋ2 and ℋ∞ (or more generally, stochastic integral quadratic constraints performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.

Stochastic Watershed Models for Risk Based Decision Making

Science.gov (United States)

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

Impact of mesh points number on the accuracy of deterministic calculations of control rods worth for Tehran research reactor

International Nuclear Information System (INIS)

Boustani, Ehsan; Amirkabir University of Technology, Tehran; Khakshournia, Samad

2016-01-01

In this paper two different computational approaches, a deterministic and a stochastic one, were used for calculation of the control rods worth of the Tehran research reactor. For the deterministic approach the MTRPC package composed of the WIMS code and diffusion code CITVAP was used, while for the stochastic one the Monte Carlo code MCNPX was applied. On comparing our results obtained by the Monte Carlo approach and those previously reported in the Safety Analysis Report (SAR) of Tehran research reactor produced by the deterministic approach large discrepancies were seen. To uncover the root cause of these discrepancies, some efforts were made and finally was discerned that the number of spatial mesh points in the deterministic approach was the critical cause of these discrepancies. Therefore, the mesh optimization was performed for different regions of the core such that the results of deterministic approach based on the optimized mesh points have a good agreement with those obtained by the Monte Carlo approach.

Impact of mesh points number on the accuracy of deterministic calculations of control rods worth for Tehran research reactor

Energy Technology Data Exchange (ETDEWEB)

Boustani, Ehsan [Nuclear Science and Technology Research Institute (NSTRI), Tehran (Iran, Islamic Republic of); Amirkabir University of Technology, Tehran (Iran, Islamic Republic of). Energy Engineering and Physics Dept.; Khakshournia, Samad [Amirkabir University of Technology, Tehran (Iran, Islamic Republic of). Energy Engineering and Physics Dept.

2016-12-15

In this paper two different computational approaches, a deterministic and a stochastic one, were used for calculation of the control rods worth of the Tehran research reactor. For the deterministic approach the MTRPC package composed of the WIMS code and diffusion code CITVAP was used, while for the stochastic one the Monte Carlo code MCNPX was applied. On comparing our results obtained by the Monte Carlo approach and those previously reported in the Safety Analysis Report (SAR) of Tehran research reactor produced by the deterministic approach large discrepancies were seen. To uncover the root cause of these discrepancies, some efforts were made and finally was discerned that the number of spatial mesh points in the deterministic approach was the critical cause of these discrepancies. Therefore, the mesh optimization was performed for different regions of the core such that the results of deterministic approach based on the optimized mesh points have a good agreement with those obtained by the Monte Carlo approach.

Hopf Bifurcation of Compound Stochastic van der Pol System

Directory of Open Access Journals (Sweden)

Shaojuan Ma

2016-01-01

Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.

Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm

International Nuclear Information System (INIS)

Takaishi, Tetsuya

2013-01-01

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

Directory of Open Access Journals (Sweden)

Jie Ran

2015-01-01

Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

Universal resources for approximate and stochastic measurement-based quantum computation

International Nuclear Information System (INIS)

Mora, Caterina E.; Piani, Marco; Miyake, Akimasa; Van den Nest, Maarten; Duer, Wolfgang; Briegel, Hans J.

2010-01-01

We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting, for example, from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained in M. Van den Nest et al. [New J. Phys. 9, 204 (2007)] for the exact, deterministic case can be lifted to the much more general approximate, stochastic case. This allows us to move from the idealized situation (exact, deterministic universality) considered in previous works to the practically relevant context of nonperfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We prove that approximate, stochastic universality is in general a weaker requirement than deterministic, exact universality and provide resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high

Trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus

International Nuclear Information System (INIS)

Du, Yongchang; Zhao, Yue; Wang, Qinpu; Zhang, Yuanbo; Xia, Huaicheng

2016-01-01

A trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus is presented in this paper, which includes the offline stochastic dynamic programming part and the online implementation part performed by equivalent consumption minimization strategy. In the offline part, historical driving cycles of the fixed route are divided into segments according to the position of bus stops, and then a segment-based stochastic driving condition model based on Markov chain is built. With the segment-based stochastic model obtained, the control set for real-time implemented equivalent consumption minimization strategy can be achieved by solving the offline stochastic dynamic programming problem. Results of stochastic dynamic programming are converted into a 3-dimensional lookup table of parameters for online implemented equivalent consumption minimization strategy. The proposed strategy is verified by both simulation and hardware-in-loop test of real-world driving cycle on an urban bus route. Simulation results show that the proposed method outperforms both the well-tuned equivalent consumption minimization strategy and the rule-based strategy in terms of fuel economy, and even proved to be close to the optimal result obtained by dynamic programming. Furthermore, the practical application potential of the proposed control method was proved by hardware-in-loop test. - Highlights: • A stochastic problem was formed based on a stochastic segment-based driving condition model. • Offline stochastic dynamic programming was employed to solve the stochastic problem. • The instant power split decision was made by the online equivalent consumption minimization strategy. • Good performance in fuel economy of the proposed method was verified by simulation results. • Practical application potential of the proposed method was verified by the hardware-in-loop test results.

Sensitivity analysis of the titan hybrid deterministic transport code for SPECT simulation

International Nuclear Information System (INIS)

Royston, Katherine K.; Haghighat, Alireza

2011-01-01

Single photon emission computed tomography (SPECT) has been traditionally simulated using Monte Carlo methods. The TITAN code is a hybrid deterministic transport code that has recently been applied to the simulation of a SPECT myocardial perfusion study. For modeling SPECT, the TITAN code uses a discrete ordinates method in the phantom region and a combined simplified ray-tracing algorithm with a fictitious angular quadrature technique to simulate the collimator and generate projection images. In this paper, we compare the results of an experiment with a physical phantom with predictions from the MCNP5 and TITAN codes. While the results of the two codes are in good agreement, they differ from the experimental data by ∼ 21%. In order to understand these large differences, we conduct a sensitivity study by examining the effect of different parameters including heart size, collimator position, collimator simulation parameter, and number of energy groups. (author)

Sizing for fuel cell/supercapacitor hybrid vehicles based on stochastic driving cycles

International Nuclear Information System (INIS)

Feroldi, Diego; Carignano, Mauro

2016-01-01

Highlights: • A sizing procedure based on the fulfilment of real driving conditions is proposed. • A methodology to generate long-term stochastic driving cycles is proposed. • A parametric optimization of the real-time EMS is conducted. • A trade-off design is adopted from a Pareto front. • A comparison with optimal consumption via Dynamic Programming is performed. - Abstract: In this article, a methodology for the sizing and analysis of fuel cell/supercapacitor hybrid vehicles is presented. The proposed sizing methodology is based on the fulfilment of power requirements, including sustained speed tests and stochastic driving cycles. The procedure to generate driving cycles is also presented in this paper. The sizing algorithm explicitly accounts for the Equivalent Consumption Minimization Strategy (ECMS). The performance is compared with optimal consumption, which is found using an off-line strategy via Dynamic Programming. The sizing methodology provides guidance for sizing the fuel cell and the supercapacitor number. The results also include analysis on oversizing the fuel cell and varying the parameters of the energy management strategy. The simulation results highlight the importance of integrating sizing and energy management into fuel cell hybrid vehicles.

Stochastic Landau equation with time-dependent drift

International Nuclear Information System (INIS)

Swift, J.B.; Hohenberg, P.C.; Ahlers, G.

1991-01-01

The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically

Optimal Stochastic Modeling and Control of Flexible Structures

Science.gov (United States)

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Hybrid SN/Monte Carlo research and results

International Nuclear Information System (INIS)

Baker, R.S.

1993-01-01

The neutral particle transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S N ) and stochastic (Monte Carlo) methods are applied. The Monte Carlo and S N regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid Monte Carlo/S N method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S N is well suited for by themselves. The hybrid method has been successfully applied to realistic shielding problems. The vectorized Monte Carlo algorithm in the hybrid method has been ported to the massively parallel architecture of the Connection Machine. Comparisons of performance on a vector machine (Cray Y-MP) and the Connection Machine (CM-2) show that significant speedups are obtainable for vectorized Monte Carlo algorithms on massively parallel machines, even when realistic problems requiring variance reduction are considered. However, the architecture of the Connection Machine does place some limitations on the regime in which the Monte Carlo algorithm may be expected to perform well

Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S Backscattering

KAUST Repository

Mai, Paul Martin; Imperatori, W.; Olsen, K. B.

2010-01-01

We present a new approach for computing broadband (0-10 Hz) synthetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green's functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation ηs, intrinsic attenuation ηi, and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our methodology to the 1994 Northridge earthquake and validating against near-field recordings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broadband simulations. This innovative hybrid ground-motion simulation approach, applicable to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S Backscattering

KAUST Repository

Mai, Paul Martin

2010-09-20

We present a new approach for computing broadband (0-10 Hz) synthetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green\\'s functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation ηs, intrinsic attenuation ηi, and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our methodology to the 1994 Northridge earthquake and validating against near-field recordings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broadband simulations. This innovative hybrid ground-motion simulation approach, applicable to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

Science.gov (United States)

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

2017-09-26

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

Stochastic Corn Yield Response Functions to Nitrogen for Corn after Corn, Corn after Cotton, and Corn after Soybeans

OpenAIRE

Boyer, Christopher N.; Larson, James A.; Roberts, Roland K.; McClure, Angela T.; Tyler, Donald D.; Zhou, Vivian

2013-01-01

Deterministic and stochastic yield response plateau functions were estimated to determine the expected profit-maximizing nitrogen rates, yields, and net returns for corn grown after corn, cotton, and soybeans. The stochastic response functions were more appropriate than their deterministic counterparts, and the linear response stochastic plateau described the data the best. The profit-maximizing nitrogen rates were similar for corn after corn, cotton, and soybeans, but relative to corn after ...

Ordinal optimization and its application to complex deterministic problems

Science.gov (United States)

Yang, Mike Shang-Yu

1998-10-01

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

ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process

Directory of Open Access Journals (Sweden)

E. K. Boukas

2004-01-01

Full Text Available This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.

Hybrid Differential Dynamic Programming with Stochastic Search

Science.gov (United States)

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.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

Science.gov (United States)

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

KAUST Repository

Tamellini, L.; Le Maî tre, O.; Nouy, A.

2014-01-01

In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.

Stochastic evolution of cosmological parameters in the early universe

Indian Academy of Sciences (India)

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early ...

The intrinsic stochasticity of near-integrable Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu

1989-09-01

Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).

Novel hybrid Monte Carlo/deterministic technique for shutdown dose rate analyses of fusion energy systems

International Nuclear Information System (INIS)

Ibrahim, Ahmad M.; Peplow, Douglas E.; Peterson, Joshua L.; Grove, Robert E.

2014-01-01

Highlights: •Develop the novel Multi-Step CADIS (MS-CADIS) hybrid Monte Carlo/deterministic method for multi-step shielding analyses. •Accurately calculate shutdown dose rates using full-scale Monte Carlo models of fusion energy systems. •Demonstrate the dramatic efficiency improvement of the MS-CADIS method for the rigorous two step calculations of the shutdown dose rate in fusion reactors. -- Abstract: The rigorous 2-step (R2S) computational system uses three-dimensional Monte Carlo transport simulations to calculate the shutdown dose rate (SDDR) in fusion reactors. Accurate full-scale R2S calculations are impractical in fusion reactors because they require calculating space- and energy-dependent neutron fluxes everywhere inside the reactor. The use of global Monte Carlo variance reduction techniques was suggested for accelerating the R2S neutron transport calculation. However, the prohibitive computational costs of these approaches, which increase with the problem size and amount of shielding materials, inhibit their ability to accurately predict the SDDR in fusion energy systems using full-scale modeling of an entire fusion plant. This paper describes a novel hybrid Monte Carlo/deterministic methodology that uses the Consistent Adjoint Driven Importance Sampling (CADIS) method but focuses on multi-step shielding calculations. The Multi-Step CADIS (MS-CADIS) methodology speeds up the R2S neutron Monte Carlo calculation using an importance function that represents the neutron importance to the final SDDR. Using a simplified example, preliminary results showed that the use of MS-CADIS enhanced the efficiency of the neutron Monte Carlo simulation of an SDDR calculation by a factor of 550 compared to standard global variance reduction techniques, and that the efficiency enhancement compared to analog Monte Carlo is higher than a factor of 10,000

On the use of reverse Brownian motion to accelerate hybrid simulations

Energy Technology Data Exchange (ETDEWEB)

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

2017-04-01

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

Improved operating strategies for uranium extraction: a stochastic simulation

International Nuclear Information System (INIS)

Broekman, B.R.

1986-01-01

Deterministic and stochastic simulations of a Western Transvaal uranium process are used in this research report to determine more profitable uranium plant operating strategies and to gauge the potential financial benefits of automatic process control. The deterministic simulation model was formulated using empirical and phenomenological process models. The model indicated that profitability increases significantly as the uranium leaching strategy becomes harsher. The stochastic simulation models use process variable distributions corresponding to manually and automatically controlled conditions to investigate the economic gains that may be obtained if a change is made from manual to automatic control of two important process variables. These lognormally distributed variables are the pachuca 1 sulphuric acid concentration and the ferric to ferrous ratio. The stochastic simulations show that automatic process control is justifiable in certain cases. Where the leaching strategy is relatively harsh, such as that in operation during January 1986, it is not possible to justify an automatic control system. Automatic control is, however, justifiable if a relatively mild leaching strategy is adopted. The stochastic and deterministic simulations represent two different approaches to uranium process modelling. This study has indicated the necessity for each approach to be applied in the correct context. It is contended that incorrect conclusions may have been drawn by other investigators in South Africa who failed to consider the two approaches separately

Langevin equation with the deterministic algebraically correlated noise

Energy Technology Data Exchange (ETDEWEB)

Ploszajczak, M. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); Srokowski, T. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)]|[Institute of Nuclear Physics, Cracow (Poland)

1995-12-31

Stochastic differential equations with the deterministic, algebraically correlated noise are solved for a few model problems. The chaotic force with both exponential and algebraic temporal correlations is generated by the adjoined extended Sinai billiard with periodic boundary conditions. The correspondence between the autocorrelation function for the chaotic force and both the survival probability and the asymptotic energy distribution of escaping particles is found. (author). 58 refs.

Langevin equation with the deterministic algebraically correlated noise

International Nuclear Information System (INIS)

Ploszajczak, M.; Srokowski, T.

1995-01-01

Stochastic differential equations with the deterministic, algebraically correlated noise are solved for a few model problems. The chaotic force with both exponential and algebraic temporal correlations is generated by the adjoined extended Sinai billiard with periodic boundary conditions. The correspondence between the autocorrelation function for the chaotic force and both the survival probability and the asymptotic energy distribution of escaping particles is found. (author)

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography.

Science.gov (United States)

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

The threshold of a stochastic delayed SIR epidemic model with vaccination

Science.gov (United States)

Liu, Qun; Jiang, Daqing

2016-11-01

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

Dynamic-stochastic modeling of snow cover formation on the European territory of Russia

OpenAIRE

A. N. Gelfan; V. M. Moreido

2014-01-01

A dynamic-stochastic model, which combines a deterministic model of snow cover formation with a stochastic weather generator, has been developed. The deterministic snow model describes temporal change of the snow depth, content of ice and liquid water, snow density, snowmelt, sublimation, re-freezing of melt water, and snow metamorphism. The model has been calibrated and validated against the long-term data of snow measurements over the territory of the European Russia. The model showed good ...

A stochastic framework for clearing of reactive power market

International Nuclear Information System (INIS)

Amjady, N.; Rabiee, A.; Shayanfar, H.A.

2010-01-01

This paper presents a new stochastic framework for clearing of day-ahead reactive power market. The uncertainty of generating units in the form of system contingencies are considered in the reactive power market-clearing procedure by the stochastic model in two steps. The Monte-Carlo Simulation (MCS) is first used to generate random scenarios. Then, in the second step, the stochastic market-clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. In each of these deterministic optimization problems, the objective function is total payment function (TPF) of generators which refers to the payment paid to the generators for their reactive power compensation. The effectiveness of the proposed model is examined based on the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS). (author)

Front propagation and clustering in the stochastic nonlocal Fisher equation

Science.gov (United States)

Ganan, Yehuda A.; Kessler, David A.

2018-04-01

In this work, we study the problem of front propagation and pattern formation in the stochastic nonlocal Fisher equation. We find a crossover between two regimes: a steadily propagating regime for not too large interaction range and a stochastic punctuated spreading regime for larger ranges. We show that the former regime is well described by the heuristic approximation of the system by a deterministic system where the linear growth term is cut off below some critical density. This deterministic system is seen not only to give the right front velocity, but also predicts the onset of clustering for interaction kernels which give rise to stable uniform states, such as the Gaussian kernel, for sufficiently large cutoff. Above the critical cutoff, distinct clusters emerge behind the front. These same features are present in the stochastic model for sufficiently small carrying capacity. In the latter, punctuated spreading, regime, the population is concentrated on clusters, as in the infinite range case, which divide and separate as a result of the stochastic noise. Due to the finite interaction range, if a fragment at the edge of the population separates sufficiently far, it stabilizes as a new cluster, and the processes begins anew. The deterministic cutoff model does not have this spreading for large interaction ranges, attesting to its purely stochastic origins. We show that this mode of spreading has an exponentially small mean spreading velocity, decaying with the range of the interaction kernel.

Stochastic congestion management in power markets using efficient scenario approaches

International Nuclear Information System (INIS)

Esmaili, Masoud; Amjady, Nima; Shayanfar, Heidar Ali

2010-01-01

Congestion management in electricity markets is traditionally performed using deterministic values of system parameters assuming a fixed network configuration. In this paper, a stochastic programming framework is proposed for congestion management considering the power system uncertainties comprising outage of generating units and transmission branches. The Forced Outage Rate of equipment is employed in the stochastic programming. Using the Monte Carlo simulation, possible scenarios of power system operating states are generated and a probability is assigned to each scenario. The performance of the ordinary as well as Lattice rank-1 and rank-2 Monte Carlo simulations is evaluated in the proposed congestion management framework. As a tradeoff between computation time and accuracy, scenario reduction based on the standard deviation of accepted scenarios is adopted. The stochastic congestion management solution is obtained by aggregating individual solutions of accepted scenarios. Congestion management using the proposed stochastic framework provides a more realistic solution compared with traditional deterministic solutions. Results of testing the proposed stochastic congestion management on the 24-bus reliability test system indicate the efficiency of the proposed framework.

Evaluation of Deterministic and Stochastic Components of Traffic Counts

Directory of Open Access Journals (Sweden)

Ivan Bošnjak

2012-10-01

Full Text Available Traffic counts or statistical evidence of the traffic processare often a characteristic of time-series data. In this paper fundamentalproblem of estimating deterministic and stochasticcomponents of a traffic process are considered, in the context of"generalised traffic modelling". Different methods for identificationand/or elimination of the trend and seasonal componentsare applied for concrete traffic counts. Further investigationsand applications of ARIMA models, Hilbert space formulationsand state-space representations are suggested.

Stochastic Optimal Dispatch of Virtual Power Plant considering Correlation of Distributed Generations

Directory of Open Access Journals (Sweden)

Jie Yu

2015-01-01

Full Text Available Virtual power plant (VPP is an aggregation of multiple distributed generations, energy storage, and controllable loads. Affected by natural conditions, the uncontrollable distributed generations within VPP, such as wind and photovoltaic generations, are extremely random and relative. Considering the randomness and its correlation of uncontrollable distributed generations, this paper constructs the chance constraints stochastic optimal dispatch of VPP including stochastic variables and its random correlation. The probability distributions of independent wind and photovoltaic generations are described by empirical distribution functions, and their joint probability density model is established by Frank-copula function. And then, sample average approximation (SAA is applied to convert the chance constrained stochastic optimization model into a deterministic optimization model. Simulation cases are calculated based on the AIMMS. Simulation results of this paper mathematic model are compared with the results of deterministic optimization model without stochastic variables and stochastic optimization considering stochastic variables but not random correlation. Furthermore, this paper analyzes how SAA sampling frequency and the confidence level influence the results of stochastic optimization. The numerical example results show the effectiveness of the stochastic optimal dispatch of VPP considering the randomness and its correlations of distributed generations.

Linear stochastic neutron transport theory

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

A stochastic model of enzyme kinetics

Science.gov (United States)

Stefanini, Marianne; Newman, Timothy; McKane, Alan

2003-10-01

Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.

Hybrid three-dimensional variation and particle filtering for nonlinear systems

International Nuclear Information System (INIS)

Leng Hong-Ze; Song Jun-Qiang

2013-01-01

This work addresses the problem of estimating the states of nonlinear dynamic systems with sparse observations. We present a hybrid three-dimensional variation (3DVar) and particle piltering (PF) method, which combines the advantages of 3DVar and particle-based filters. By minimizing the cost function, this approach will produce a better proposal distribution of the state. Afterwards the stochastic resampling step in standard PF can be avoided through a deterministic scheme. The simulation results show that the performance of the new method is superior to the traditional ensemble Kalman filtering (EnKF) and the standard PF, especially in highly nonlinear systems

Stochastic Analysis : A Series of Lectures

CERN Document Server

Dozzi, Marco; Flandoli, Franco; Russo, Francesco

2015-01-01

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...

STOCHASTIC GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION

Directory of Open Access Journals (Sweden)

Nataša Krejić

2014-12-01

Full Text Available This papers presents an overview of gradient based methods for minimization of noisy functions. It is assumed that the objective functions is either given with error terms of stochastic nature or given as the mathematical expectation. Such problems arise in the context of simulation based optimization. The focus of this presentation is on the gradient based Stochastic Approximation and Sample Average Approximation methods. The concept of stochastic gradient approximation of the true gradient can be successfully extended to deterministic problems. Methods of this kind are presented for the data fitting and machine learning problems.

Deterministically swapping frequency-bin entanglement from photon-photon to atom-photon hybrid systems

Science.gov (United States)

Ou, Bao-Quan; Liu, Chang; Sun, Yuan; Chen, Ping-Xing

2018-02-01

Inspired by the recent developments of the research on the atom-photon quantum interface and energy-time entanglement between single-photon pulses, we are motivated to study the deterministic protocol for the frequency-bin entanglement of the atom-photon hybrid system, which is analogous to the frequency-bin entanglement between single-photon pulses. We show that such entanglement arises naturally in considering the interaction between a frequency-bin entangled single-photon pulse pair and a single atom coupled to an optical cavity, via straightforward atom-photon phase gate operations. Its anticipated properties and preliminary examples of its potential application in quantum networking are also demonstrated. Moreover, we construct a specific quantum entanglement witness tool to detect such extended frequency-bin entanglement from a reasonably general set of separable states, and prove its capability theoretically. We focus on the energy-time considerations throughout the analysis.

MIRD Commentary: Proposed Name for a Dosimetry Unit Applicable to Deterministic Biological Effects-The Barendsen (Bd)

International Nuclear Information System (INIS)

Sgouros, George; Howell, R. W.; Bolch, Wesley E.; Fisher, Darrell R.

2009-01-01

The fundamental physical quantity for relating all biologic effects to radiation exposure is the absorbed dose, the energy imparted per unit mass of tissue. Absorbed dose is expressed in units of joules per kilogram (J/kg) and is given the special name gray (Gy). Exposure to ionizing radiation may cause both deterministic and stochastic biologic effects. To account for the relative effect per unit absorbed dose that has been observed for different types of radiation, the International Commission on Radiological Protection (ICRP) has established radiation weighting factors for stochastic effects. The product of absorbed dose in Gy and the radiation weighting factor is defined as the equivalent dose. Equivalent dose values are designated by a special named unit, the sievert (Sv). Unlike the situation for stochastic effects, no well-defined formalism and associated special named quantities have been widely adopted for deterministic effects. The therapeutic application of radionuclides and, specifically, -particle emitters in nuclear medicine has brought to the forefront the need for a well-defined dosimetry formalism applicable to deterministic effects that is accompanied by corresponding special named quantities. This commentary reviews recent proposals related to this issue and concludes with a recommendation to establish a new named quantity

New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation

International Nuclear Information System (INIS)

Ray, S. Saha; Singh, S.

2017-01-01

In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. (paper)

The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System

Directory of Open Access Journals (Sweden)

Shaolin Ji

2013-01-01

Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

Energy Technology Data Exchange (ETDEWEB)

Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)

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 imaging 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.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

International Nuclear Information System (INIS)

Johnson, Michael D.

2016-01-01

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 imaging 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.

A Nucleolus for Stochastic Cooperative Games

OpenAIRE

Suijs, J.P.M.

1996-01-01

This paper extends the definition of the nucleolus to stochastic cooperative games, that is, to cooperative games with random payoffs to the coalitions. It is shown that the nucleolus is nonempty and that it belongs to the core whenever the core is nonempty. Furthermore, it is shown for a particular class of stochastic cooperative games that the nucleolus can be determined by calculating the traditional nucleolus introduced by Schmeidler (1969) of a specific deterministic cooperative game.

Deterministic direct reprogramming of somatic cells to pluripotency.

Science.gov (United States)

Rais, Yoach; Zviran, Asaf; Geula, Shay; Gafni, Ohad; Chomsky, Elad; Viukov, Sergey; Mansour, Abed AlFatah; Caspi, Inbal; Krupalnik, Vladislav; Zerbib, Mirie; Maza, Itay; Mor, Nofar; Baran, Dror; Weinberger, Leehee; Jaitin, Diego A; Lara-Astiaso, David; Blecher-Gonen, Ronnie; Shipony, Zohar; Mukamel, Zohar; Hagai, Tzachi; Gilad, Shlomit; Amann-Zalcenstein, Daniela; Tanay, Amos; Amit, Ido; Novershtern, Noa; Hanna, Jacob H

2013-10-03

Somatic cells can be inefficiently and stochastically reprogrammed into induced pluripotent stem (iPS) cells by exogenous expression of Oct4 (also called Pou5f1), Sox2, Klf4 and Myc (hereafter referred to as OSKM). The nature of the predominant rate-limiting barrier(s) preventing the majority of cells to successfully and synchronously reprogram remains to be defined. Here we show that depleting Mbd3, a core member of the Mbd3/NuRD (nucleosome remodelling and deacetylation) repressor complex, together with OSKM transduction and reprogramming in naive pluripotency promoting conditions, result in deterministic and synchronized iPS cell reprogramming (near 100% efficiency within seven days from mouse and human cells). Our findings uncover a dichotomous molecular function for the reprogramming factors, serving to reactivate endogenous pluripotency networks while simultaneously directly recruiting the Mbd3/NuRD repressor complex that potently restrains the reactivation of OSKM downstream target genes. Subsequently, the latter interactions, which are largely depleted during early pre-implantation development in vivo, lead to a stochastic and protracted reprogramming trajectory towards pluripotency in vitro. The deterministic reprogramming approach devised here offers a novel platform for the dissection of molecular dynamics leading to establishing pluripotency at unprecedented flexibility and resolution.

Analytic solution of the two-dimensional Fokker-Planck equation governing stochastic ion heating by a lower hybrid wave

International Nuclear Information System (INIS)

Malescio, G.

1981-04-01

The two-dimensional Fokker-Planck equation describing the ion motion in a coherent lower hybrid wave above the stochasticity threshold is analytically solved. An expression is given for the steady state power dissipation

A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields

International Nuclear Information System (INIS)

Fluck, Manuel; Crawford, Curran

2016-01-01

Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization. (paper)

Characterizing economic trends by Bayesian stochastic model specifi cation search

OpenAIRE

Grassi, Stefano; Proietti, Tommaso

2010-01-01

We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate...

The stochastic energy-Casimir method

Science.gov (United States)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

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

Science.gov (United States)

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

2003-01-01

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

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

Science.gov (United States)

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

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

Drift-Implicit Multi-Level Monte Carlo Tau-Leap Methods for Stochastic Reaction Networks

KAUST Repository

Ben Hammouda, Chiheb

2015-01-01

-space and deterministic ones. These stochastic models constitute the theory of stochastic reaction networks (SRNs). Furthermore, in some cases, the dynamics of fast and slow time scales can be well separated and this is characterized by what is called sti

Stochastic failure modelling of unidirectional composite ply failure

International Nuclear Information System (INIS)

Whiteside, M.B.; Pinho, S.T.; Robinson, P.

2012-01-01

Stochastic failure envelopes are generated through parallelised Monte Carlo Simulation of a physically based failure criteria for unidirectional carbon fibre/epoxy matrix composite plies. Two examples are presented to demonstrate the consequence on failure prediction of both statistical interaction of failure modes and uncertainty in global misalignment. Global variance-based Sobol sensitivity indices are computed to decompose the observed variance within the stochastic failure envelopes into contributions from physical input parameters. The paper highlights a selection of the potential advantages stochastic methodologies offer over the traditional deterministic approach.

Combined Deterministic and Stochastic Approach to Determine Spatial Distribution of Drought Frequency and Duration in the Great Hungarian Plain

Science.gov (United States)

Szabó, J. A.; Kuti, L.; Bakacsi, Zs.; Pásztor, L.; Tahy, Á.

2009-04-01

data for the multi-year simulation of SVAT processes. In order to test the elaborated methods, a sub-area of the full domain has been designated as a pilot area for this study. Considering our aims, major achievements with respect to the objectives have been accomplished for the pilot area within the scope of this work includes: - Harmonized 3D grid model to describe hydraulic properties of the unsaturated zone has been created (Pásztor, L. et al 2002 and 2005, Kuti, L. 2007); - The spatially distributed physically based distributed parameter SVAT model DIWA (DIstributed WAtershed) (Szabó, J.A., 2007) has been adapted; - The stochastic characteristics and parameters of the weather generator has been derived from measured data series; - Coupling the stochastic weather generator with the deterministic DIWA SVAT-type model also has been done. In this paper, the results of the coupled (deterministic - stochastic) model simulation based analysis of regional drought frequency and duration for a sub-area of the full domain of the Great Hungarian Plain will be reported. First the harmonized 3D grid model of the hydraulic properties of the unsaturated zone will be presented. Then a brief characterisation of the DIWA model will be given. The Markov chain based stochastic weather generator also will be presented. Finally, the results of multi-year drought frequency and duration analysis at the pilot area and conclusions will be discussed. Keywords: Drought frequency and duration analysis; multivariate analyses; recurrence analyses; extreme events; stochastic weather generator; spatially distributed SVAT model; 3D grid model of hydraulic properties of the unsaturated zone. References: Kuti, L. (2007): Agrogeological investigation of soil fertility limiting factors int he soil-parent roc-groundwater system in Hungary. In: Environment & Progress, Cluj-Napoca, nr. 10. pp. 131-145. Pásztor, L. - Szabó, J. - Bakacsi, Zs. (2002): GIS processing of large scale soil maps in Hungary

Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes

DEFF Research Database (Denmark)

Starke, Jens; Reichert, Christian; Eiswirth, Markus

2007-01-01

of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement...

Chance Constrained Input Relaxation to Congestion in Stochastic DEA. An Application to Iranian Hospitals.

Science.gov (United States)

Kheirollahi, Hooshang; Matin, Behzad Karami; Mahboubi, Mohammad; Alavijeh, Mehdi Mirzaei

2015-01-01

This article developed an approached model of congestion, based on relaxed combination of inputs, in stochastic data envelopment analysis (SDEA) with chance constrained programming approaches. Classic data envelopment analysis models with deterministic data have been used by many authors to identify congestion and estimate its levels; however, data envelopment analysis with stochastic data were rarely used to identify congestion. This article used chance constrained programming approaches to replace stochastic models with "deterministic equivalents". This substitution leads us to non-linear problems that should be solved. Finally, the proposed method based on relaxed combination of inputs was used to identify congestion input in six Iranian hospital with one input and two outputs in the period of 2009 to 2012.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics

Directory of Open Access Journals (Sweden)

Nicolas Wieder

2011-01-01

pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

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

International Nuclear Information System (INIS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2017-01-01

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. (topical review)

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

KAUST Repository

Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.

2010-01-01

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

Science.gov (United States)

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.

Simulation of anaerobic digestion processes using stochastic algorithm.

Science.gov (United States)

Palanichamy, Jegathambal; Palani, Sundarambal

2014-01-01

The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. The proposed model was verified by comparing the results of Gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'τ' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

Science.gov (United States)

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

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations

Directory of Open Access Journals (Sweden)

Toufik Guendouzi

2014-08-01

Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.

Computer Aided Continuous Time Stochastic Process Modelling

DEFF Research Database (Denmark)

Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay

2001-01-01

A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...

Parameter-free resolution of the superposition of stochastic signals

Energy Technology Data Exchange (ETDEWEB)

Scholz, Teresa, E-mail: tascholz@fc.ul.pt [Center for Theoretical and Computational Physics, University of Lisbon (Portugal); Raischel, Frank [Center for Geophysics, IDL, University of Lisbon (Portugal); Closer Consulting, Av. Eng. Duarte Pacheco Torre 1 15" 0, 1070-101 Lisboa (Portugal); Lopes, Vitor V. [DEIO-CIO, University of Lisbon (Portugal); UTEC–Universidad de Ingeniería y Tecnología, Lima (Peru); Lehle, Bernd; Wächter, Matthias; Peinke, Joachim [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Lind, Pedro G. [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Institute of Physics, University of Osnabrück, Osnabrück (Germany)

2017-01-30

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent stochastic processes, one of which is an Ornstein–Uhlenbeck process and the other a general (non-linear) Langevin process. The method is able to distinguish between the stochastic processes, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.

Modeling and simulation of a controlled steam generator in the context of dynamic reliability using a Stochastic Hybrid Automaton

International Nuclear Information System (INIS)

Babykina, Génia; Brînzei, Nicolae; Aubry, Jean-François; Deleuze, Gilles

2016-01-01

The paper proposes a modeling framework to support Monte Carlo simulations of the behavior of a complex industrial system. The aim is to analyze the system dependability in the presence of random events, described by any type of probability distributions. Continuous dynamic evolutions of physical parameters are taken into account by a system of differential equations. Dynamic reliability is chosen as theoretical framework. Based on finite state automata theory, the formal model is built by parallel composition of elementary sub-models using a bottom-up approach. Considerations of a stochastic nature lead to a model called the Stochastic Hybrid Automaton. The Scilab/Scicos open source environment is used for implementation. The case study is carried out on an example of a steam generator of a nuclear power plant. The behavior of the system is studied by exploring its trajectories. Possible system trajectories are analyzed both empirically, using the results of Monte Carlo simulations, and analytically, using the formal system model. The obtained results are show to be relevant. The Stochastic Hybrid Automaton appears to be a suitable tool to address the dynamic reliability problem and to model real systems of high complexity; the bottom-up design provides precision and coherency of the system model. - Highlights: • A part of a nuclear power plant is modeled in the context of dynamic reliability. • Stochastic Hybrid Automaton is used as an input model for Monte Carlo simulations. • The model is formally built using a bottom-up approach. • The behavior of the system is analyzed empirically and analytically. • A formally built SHA shows to be a suitable tool to approach dynamic reliability.

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

Science.gov (United States)

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

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

Lin Chao

2016-01-01

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

Transport stochastic multi-dimensional media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.

1996-01-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

Transport stochastic multi-dimensional media

Energy Technology Data Exchange (ETDEWEB)

Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

1996-12-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

Reactivity effect breakdown calculations with deterministic and stochastic perturbations analysis – JEFF-3.1.1 to JEFF3.2T1 (BRC-2009 actinides application

Directory of Open Access Journals (Sweden)

Morillon B.

2013-03-01

Full Text Available JEFF-3.1.1 is the reference nuclear data library in CEA for the design calculations of the next nuclear power plants. The validation of the new neutronics code systems is based on this library and changes in nuclear data should be looked at closely. Some new actinides evaluation files at high energies have been proposed by CEA/Bruyères-le-Chatel in 2009 and have been integrated in JEFF3.2T1 test release. For the new release JEFF-3.2, CEA will build new evaluation files for the actinides, which should be a combination of the new evaluated data coming from BRC-2009 in the high energy range and improvements or new evaluations in the resolved and unresolved resonance range from CEA-Cadarache. To prepare the building of these new files, benchmarking the BRC-2009 library in comparison with the JEFF-3.1.1 library was very important. The crucial points to evaluate were the improvements in the continuum range and the discrepancies in the resonance range. The present work presents for a selected set of benchmarks the discrepancies in the effective multiplication factor obtained while using the JEFF-3.1.1 or JEFF-3.2T1 library with the deterministic code package ERANOS/PARIS and the stochastic code TRIPOLI-4. They have both been used to calculate cross section perturbations or other nuclear data perturbations when possible. This has permittted to identify the origin of the discrepancies in reactivity calculations. In addition, this work also shows the importance of cross section processing validation. Actually, some fast neutron spectrum calculations have led to opposite tendancies between the deterministic code package and the stochastic code. Some particular nuclear data (MT=5 in ENDF terminology seem to be incompatible with the current MERGE or GECCO processing codes.

A stochastic programming approach to manufacturing flow control

OpenAIRE

Haurie, Alain; Moresino, Francesco

2012-01-01

This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sample...

A stochastic analysis for a phytoplankton-zooplankton model

International Nuclear Information System (INIS)

Ge, G; Wang, H-L; Xu, J

2008-01-01

A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation

Stochastic production planning for a biofuel supply chain under demand and price uncertainties

International Nuclear Information System (INIS)

Awudu, Iddrisu; Zhang, Jun

2013-01-01

Highlights: ► The proposed stochastic model outperforms the deterministic model. ► The price of biofuel is modeled as Geometric Brownian Motion (GBM). ► The proposed model can be applied in any biofuel supply chain. -- Abstract: In this paper, we propose a stochastic production planning model for a biofuel supply chain under demand and price uncertainties. The supply chain consists of biomass suppliers, biofuel refinery plants and distribution centers. A stochastic linear programming model is proposed within a single-period planning framework to maximize the expected profit. Decisions such as the amount of raw materials purchased, the amount of raw materials consumed and the amount of products produced are considered. Demands of end products are uncertain with known probability distributions. The prices of end products follow Geometric Brownian Motion (GBM). Benders decomposition (BD) with Monte Carlo simulation technique is applied to solve the proposed model. To demonstrate the effectiveness of the proposed stochastic model and the decomposition algorithm, a representative supply chain for an ethanol plant in North Dakota is considered. To investigate the results of the proposed model, a simulation framework is developed to compare the performances of deterministic model and proposed stochastic model. The results from the simulation indicate the proposed model obtain higher expected profit than the deterministic model under different uncertainty settings. Sensitivity analyses are performed to gain management insight on how profit changes due to the uncertainties affect the model developed.

Model selection for integrated pest management with stochasticity.

Science.gov (United States)

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

2018-04-07

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

Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm

International Nuclear Information System (INIS)

Takaishi, Tetsuya

2014-01-01

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model

Dynamics of non-holonomic systems with stochastic transport

Science.gov (United States)

Holm, D. D.; Putkaradze, V.

2018-01-01

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

Stochastic 2-D Navier-Stokes Equation

International Nuclear Information System (INIS)

Menaldi, J.L.; Sritharan, S.S.

2002-01-01

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution

Neuro-Inspired Computing with Stochastic Electronics

KAUST Repository

Naous, Rawan

2016-01-06

The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.

Scattering theory of stochastic electromagnetic light waves.

Science.gov (United States)

Wang, Tao; Zhao, Daomu

2010-07-15

We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

Science.gov (United States)

Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system

International Nuclear Information System (INIS)

Jiang, Yibo; Xu, Jian; Sun, Yuanzhang; Wei, Congying; Wang, Jing; Ke, Deping; Li, Xiong; Yang, Jun; Peng, Xiaotao; Tang, Bowen

2017-01-01

Highlights: • Improving the utilization of wind power by the demand response of residential hybrid energy system. • An optimal scheduling of home energy management system integrating micro-CHP. • The scattered response capability of consumers is aggregated by demand bidding curve. • A stochastic day-ahead economic dispatch model considering demand response and wind power. - Abstract: As the installed capacity of wind power is growing, the stochastic variability of wind power leads to the mismatch of demand and generated power. Employing the regulating capability of demand to improve the utilization of wind power has become a new research direction. Meanwhile, the micro combined heat and power (micro-CHP) allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. However, the impact of the demand response with hybrid energy system contained micro-CHP on the large-scale wind power utilization has not been analyzed quantitatively. This paper proposes an operation optimization model of the residential hybrid energy system based on price response, integrating micro-CHP and smart appliances intelligently. Moreover, a novel load aggregation method is adopted to centralize scattered response capability of residential load. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is constructed. Furthermore, simulation is conducted respectively on the modified 6-bus system and IEEE 118-bus system. The results show that with the method proposed, the wind power curtailment of the system decreases by 78% in 6-bus system. In the meantime, the energy costs of residential consumers and the operating costs of the power system reduced by 10.7% and 11.7% in 118-bus system, respectively.

Solution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite Expansion

KAUST Repository

Al-Juhani, Amnah

2014-01-06

The solution of the stochastic differential equations (SDEs) using Wiener-Hermite expansion (WHE) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In WHE approach, there is no randomness directly involved in the computations. One does not have to rely on pseudo random number generators, and there is no need to solve the SDEs repeatedly for many realizations. Instead, the deterministic system is solved only once. For previous research efforts see [2, 4].

Modeling and Prediction Using Stochastic Differential Equations

DEFF Research Database (Denmark)

Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

2016-01-01

Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...

Iterative acceleration methods for Monte Carlo and deterministic criticality calculations

Energy Technology Data Exchange (ETDEWEB)

Urbatsch, T.J.

1995-11-01

If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.

Iterative acceleration methods for Monte Carlo and deterministic criticality calculations

International Nuclear Information System (INIS)

Urbatsch, T.J.

1995-11-01

If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors

An efficient algorithm for the stochastic simulation of the hybridization of DNA to microarrays

Directory of Open Access Journals (Sweden)

Laurenzi Ian J

2009-12-01

Full Text Available Abstract Background Although oligonucleotide microarray technology is ubiquitous in genomic research, reproducibility and standardization of expression measurements still concern many researchers. Cross-hybridization between microarray probes and non-target ssDNA has been implicated as a primary factor in sensitivity and selectivity loss. Since hybridization is a chemical process, it may be modeled at a population-level using a combination of material balance equations and thermodynamics. However, the hybridization reaction network may be exceptionally large for commercial arrays, which often possess at least one reporter per transcript. Quantification of the kinetics and equilibrium of exceptionally large chemical systems of this type is numerically infeasible with customary approaches. Results In this paper, we present a robust and computationally efficient algorithm for the simulation of hybridization processes underlying microarray assays. Our method may be utilized to identify the extent to which nucleic acid targets (e.g. cDNA will cross-hybridize with probes, and by extension, characterize probe robustnessusing the information specified by MAGE-TAB. Using this algorithm, we characterize cross-hybridization in a modified commercial microarray assay. Conclusions By integrating stochastic simulation with thermodynamic prediction tools for DNA hybridization, one may robustly and rapidly characterize of the selectivity of a proposed microarray design at the probe and "system" levels. Our code is available at http://www.laurenzi.net.

Rate response of neurons subject to fast or frozen noise: from stochastic and homogeneous to deterministic and heterogeneous populations.

Science.gov (United States)

Alijani, Azadeh Khajeh; Richardson, Magnus J E

2011-07-01

The response of a neuronal population to afferent drive can be expected to be sensitive to both the distribution and dynamics of membrane voltages within the population. Voltage fluctuations can be driven by synaptic noise, neuromodulators, or cellular inhomogeneities: processes ranging from millisecond autocorrelation times to effectively static or "frozen" noise. Here we extend previous studies of filtered fluctuations to the experimentally verified exponential integrate-and-fire model. How fast or frozen fluctuations affect the steady-state rate and firing-rate response are both examined using perturbative solutions and limits of a 1 + 2 dimensional Fokker-Planck equation. The central finding is that, under conditions of a more-or-less constant population voltage variance, the firing-rate response is only weakly dependent on the fluctuation filter constant: The voltage distribution is the principal determinant of the population response. This result is unexpected given the nature of the systems underlying the extreme limits of fast and frozen fluctuations; the first limit represents a homogeneous population of neurons firing stochastically, whereas the second limit is equivalent to a heterogeneous population of neurons firing deterministically.

Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

Hooke–Jeeves Method-used Local Search in a Hybrid Global Optimization Algorithm

Directory of Open Access Journals (Sweden)

V. D. Sulimov

2014-01-01

Full Text Available Modern methods for optimization investigation of complex systems are based on development and updating the mathematical models of systems because of solving the appropriate inverse problems. Input data desirable for solution are obtained from the analysis of experimentally defined consecutive characteristics for a system or a process. Causal characteristics are the sought ones to which equation coefficients of mathematical models of object, limit conditions, etc. belong. The optimization approach is one of the main ones to solve the inverse problems. In the main case it is necessary to find a global extremum of not everywhere differentiable criterion function. Global optimization methods are widely used in problems of identification and computation diagnosis system as well as in optimal control, computing to-mography, image restoration, teaching the neuron networks, other intelligence technologies. Increasingly complicated systems of optimization observed during last decades lead to more complicated mathematical models, thereby making solution of appropriate extreme problems significantly more difficult. A great deal of practical applications may have the problem con-ditions, which can restrict modeling. As a consequence, in inverse problems the criterion functions can be not everywhere differentiable and noisy. Available noise means that calculat-ing the derivatives is difficult and unreliable. It results in using the optimization methods without calculating the derivatives.An efficiency of deterministic algorithms of global optimization is significantly restrict-ed by their dependence on the extreme problem dimension. When the number of variables is large they use the stochastic global optimization algorithms. As stochastic algorithms yield too expensive solutions, so this drawback restricts their applications. Developing hybrid algo-rithms that combine a stochastic algorithm for scanning the variable space with deterministic local search

Extending Stochastic Network Calculus to Loss Analysis

Directory of Open Access Journals (Sweden)

Chao Luo

2013-01-01

Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.

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

Science.gov (United States)

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

2005-12-01

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

Dynamic analysis of a stochastic rumor propagation model

Science.gov (United States)

Jia, Fangju; Lv, Guangying

2018-01-01

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

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

Science.gov (United States)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

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

Tsunamigenic scenarios for southern Peru and northern Chile seismic gap: Deterministic and probabilistic hybrid approach for hazard assessment

Science.gov (United States)

González-Carrasco, J. F.; Gonzalez, G.; Aránguiz, R.; Yanez, G. A.; Melgar, D.; Salazar, P.; Shrivastava, M. N.; Das, R.; Catalan, P. A.; Cienfuegos, R.

2017-12-01

Plausible worst-case tsunamigenic scenarios definition plays a relevant role in tsunami hazard assessment focused in emergency preparedness and evacuation planning for coastal communities. During the last decade, the occurrence of major and moderate tsunamigenic earthquakes along worldwide subduction zones has given clues about critical parameters involved in near-field tsunami inundation processes, i.e. slip spatial distribution, shelf resonance of edge waves and local geomorphology effects. To analyze the effects of these seismic and hydrodynamic variables over the epistemic uncertainty of coastal inundation, we implement a combined methodology using deterministic and probabilistic approaches to construct 420 tsunamigenic scenarios in a mature seismic gap of southern Peru and northern Chile, extended from 17ºS to 24ºS. The deterministic scenarios are calculated using a regional distribution of trench-parallel gravity anomaly (TPGA) and trench-parallel topography anomaly (TPTA), three-dimensional Slab 1.0 worldwide subduction zones geometry model and published interseismic coupling (ISC) distributions. As result, we find four higher slip deficit zones interpreted as major seismic asperities of the gap, used in a hierarchical tree scheme to generate ten tsunamigenic scenarios with seismic magnitudes fluctuates between Mw 8.4 to Mw 8.9. Additionally, we construct ten homogeneous slip scenarios as inundation baseline. For the probabilistic approach, we implement a Karhunen - Loève expansion to generate 400 stochastic tsunamigenic scenarios over the maximum extension of the gap, with the same magnitude range of the deterministic sources. All the scenarios are simulated through a non-hydrostatic tsunami model Neowave 2D, using a classical nesting scheme, for five coastal major cities in northern Chile (Arica, Iquique, Tocopilla, Mejillones and Antofagasta) obtaining high resolution data of inundation depth, runup, coastal currents and sea level elevation. The

Stochastic dynamics modeling solute transport in porous media modeling solute transport in porous media

CERN Document Server

Kulasiri, Don

2002-01-01

Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...

Water Quality Trading when Nonpoint Pollution Loads are Stochastic

OpenAIRE

Ghosh, Gaurav; Shortle, James

2009-01-01

We compare two tradable permit markets in their ability to meet a stated environmental target at least cost when some polluters have stochastic and non-measurable emissions. The environmental target is of the safety-first type, which requires probabilistic emissions control. One market is built around the trading ratio, which defines the substitution rate between stochastic and deterministic pollution, and is modeled on existing markets for water quality trading. The other market is built aro...

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.

2013-01-01

The input to the stochastic orienteering problem consists of a budget $B$ and metric $(V,d)$ where each vertex $v$ has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

On the Adaptivity Gap of Stochastic Orienteering

NARCIS (Netherlands)

N. Bansal (Nikhil); V. Nagarajan

2013-01-01

htmlabstractThe input to the stochastic orienteering problem consists of a budget B and metric (V,d) where each vertex v has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

The Asymptotic Behaviour of a Stochastic 3D LANS-α Model

International Nuclear Information System (INIS)

Caraballo, Tomas; Marquez-Duran, Antonio M.; Real, Jose

2006-01-01

The long-time behaviour of a stochastic 3D LANS-α model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of the model. Finally, we analyse the effects produced by stochastic perturbations in the deterministic version of the system (persistence of exponential stability as well as possible stabilisation effects produced by the noise). The general results are applied to our stochastic LANS-α system throughout the paper

Deterministic hazard quotients (HQs): Heading down the wrong road

International Nuclear Information System (INIS)

Wilde, L.; Hunter, C.; Simpson, J.

1995-01-01

The use of deterministic hazard quotients (HQs) in ecological risk assessment is common as a screening method in remediation of brownfield sites dominated by total petroleum hydrocarbon (TPH) contamination. An HQ ≥ 1 indicates further risk evaluation is needed, but an HQ ≤ 1 generally excludes a site from further evaluation. Is the predicted hazard known with such certainty that differences of 10% (0.1) do not affect the ability to exclude or include a site from further evaluation? Current screening methods do not quantify uncertainty associated with HQs. To account for uncertainty in the HQ, exposure point concentrations (EPCs) or ecological benchmark values (EBVs) are conservatively biased. To increase understanding of the uncertainty associated with HQs, EPCs (measured and modeled) and toxicity EBVs were evaluated using a conservative deterministic HQ method. The evaluation was then repeated using a probabilistic (stochastic) method. The probabilistic method used data distributions for EPCs and EBVs to generate HQs with measurements of associated uncertainty. Sensitivity analyses were used to identify the most important factors significantly influencing risk determination. Understanding uncertainty associated with HQ methods gives risk managers a more powerful tool than deterministic approaches

Predicting Footbridge Response using Stochastic Load Models

DEFF Research Database (Denmark)

Pedersen, Lars; Frier, Christian

2013-01-01

Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

Science.gov (United States)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Analysis of dynamic regimes in stochastically forced Kaldor model

International Nuclear Information System (INIS)

Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev

2015-01-01

We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan

2015-10-26

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.

2015-01-01

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Influence of wind energy forecast in deterministic and probabilistic sizing of reserves

Energy Technology Data Exchange (ETDEWEB)

Gil, A.; Torre, M. de la; Dominguez, T.; Rivas, R. [Red Electrica de Espana (REE), Madrid (Spain). Dept. Centro de Control Electrico

2010-07-01

One of the challenges in large-scale wind energy integration in electrical systems is coping with wind forecast uncertainties at the time of sizing generation reserves. These reserves must be sized large enough so that they don't compromise security of supply or the balance of the system, but economic efficiency must be also kept in mind. This paper describes two methods of sizing spinning reserves taking into account wind forecast uncertainties, deterministic using a probabilistic wind forecast and probabilistic using stochastic variables. The deterministic method calculates the spinning reserve needed by adding components each of them in order to overcome one single uncertainty: demand errors, the biggest thermal generation loss and wind forecast errors. The probabilistic method assumes that demand forecast errors, short-term thermal group unavailability and wind forecast errors are independent stochastic variables and calculates the probability density function of the three variables combined. These methods are being used in the case of the Spanish peninsular system, in which wind energy accounted for 14% of the total electrical energy produced in the year 2009 and is one of the systems in the world with the highest wind penetration levels. (orig.)

Optimal timing of joint replacement using mathematical programming and stochastic programming models.

Science.gov (United States)

Keren, Baruch; Pliskin, Joseph S

2011-12-01

The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.

Stochastic quantum mechanics and quantum spacetime

International Nuclear Information System (INIS)

Prugovecki, E.

1984-01-01

This monograph's principal intent is to provide a systematic and self-contained introduction to an alternative unification of relativity with quantum theory based on stochastic phase spaces and stochastic geometries, and presented at a level accessible to graduate students in theoretical and mathematical physics as well as to professional physicists and mathematicians. The proposed framework for unification embraces classical as well as quantum theories by implementing an epistemic idea first put forth by M. Born, namely that all physical theories should be formulated in terms of stochastic rather than deterministic values for measurable quantities. The framework gives rise to a whole range of yet unresearched problems, whose solutions are bound to shed some light on the relationship between relativity and quantum theories of the most fundamental physical and mathematical levels. (Auth.)

Spatial stochasticity and non-continuum effects in gas flows

Energy Technology Data Exchange (ETDEWEB)

Dadzie, S. Kokou, E-mail: k.dadzie@glyndwr.ac.uk [Mechanical and Aeronautical Engineering, Glyndwr University, Mold Road, Wrexham LL11 2AW (United Kingdom); Reese, Jason M., E-mail: jason.reese@strath.ac.uk [Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ (United Kingdom)

2012-02-06

We investigate the relationship between spatial stochasticity and non-continuum effects in gas flows. A kinetic model for a dilute gas is developed using strictly a stochastic molecular model reasoning, without primarily referring to either the Liouville or the Boltzmann equations for dilute gases. The kinetic equation, a stochastic version of the well-known deterministic Boltzmann equation for dilute gas, is then associated with a set of macroscopic equations for the case of a monatomic gas. Tests based on a heat conduction configuration and sound wave dispersion show that spatial stochasticity can explain some non-continuum effects seen in gases. -- Highlights: ► We investigate effects of molecular spatial stochasticity in non-continuum regime. ► Present a simplify spatial stochastic kinetic equation. ► Present a spatial stochastic macroscopic flow equations. ► Show effects of the new model on sound wave dispersion prediction. ► Show effects of the new approach in density profiles in a heat conduction.

Hybrid Methods for Muon Accelerator Simulations with Ionization Cooling

Energy Technology Data Exchange (ETDEWEB)

Kunz, Josiah [Anderson U.; Snopok, Pavel [Fermilab; Berz, Martin [Michigan State U.; Makino, Kyoko [Michigan State U.

2018-03-28

Muon ionization cooling involves passing particles through solid or liquid absorbers. Careful simulations are required to design muon cooling channels. New features have been developed for inclusion in the transfer map code COSY Infinity to follow the distribution of charged particles through matter. To study the passage of muons through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map--Monte-Carlo approach in which transfer map methods describe the deterministic behavior of the particles, and Monte-Carlo methods are used to provide corrections accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics are represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed are expected to simplify the optimization of cooling channels which is usually computationally demanding. Progress on the development of the required algorithms and their application to modeling muon ionization cooling channels is reported.

Stochastic models: theory and simulation.

Energy Technology Data Exchange (ETDEWEB)

Field, Richard V., Jr.

2008-03-01

Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

Planning under uncertainty solving large-scale stochastic linear programs

Energy Technology Data Exchange (ETDEWEB)

Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft

1992-12-01

For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.

Stochastic Optimal Control of Parallel Hybrid Electric Vehicles

Directory of Open Access Journals (Sweden)

Feiyan Qin

2017-02-01

Full Text Available Energy management strategies (EMSs in hybrid electric vehicles (HEVs are highly related to the fuel economy and emission performances. However, EMS constitutes a challenging problem due to the complex structure of a HEV and the unknown or partially known driving cycles. To meet this problem, this paper adopts a stochastic dynamic programming (SDP method for the EMS of a specially designed vehicle, a pre-transmission single-shaft torque-coupling parallel HEV. In this parallel HEV, the auto clutch output is connected to the transmission input through an electric motor, which benefits an efficient motor assist operation. In this EMS, demanded torque of driver is modeled as a one-state Markov process to represent the uncertainty of future driving situations. The obtained EMS has been evaluated with ADVISOR2002 over two standard government drive cycles and a self-defined one, and compared with a dynamic programming (DP one and a rule-based one. Simulation results have shown the real-time performance of the proposed approach, and potential vehicle performance improvement relative to the rule-based one.

Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process.

Science.gov (United States)

Beil, Michael; Lück, Sebastian; Fleischer, Frank; Portet, Stéphanie; Arendt, Wolfgang; Schmidt, Volker

2009-02-21

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

Stochastic Effects; Application in Nuclear Physics

International Nuclear Information System (INIS)

Mazonka, O.

2000-04-01

Stochastic effects in nuclear physics refer to the study of the dynamics of nuclear systems evolving under stochastic equations of motion. In this dissertation we restrict our attention to classical scattering models. We begin with introduction of the model of nuclear dynamics and deterministic equations of evolution. We apply a Langevin approach - an additional property of the model, which reflect the statistical nature of low energy nuclear behaviour. We than concentrate our attention on the problem of calculating tails of distribution functions, which actually is the problem of calculating probabilities of rare outcomes. Two general strategies are proposed. Result and discussion follow. Finally in the appendix we consider stochastic effects in nonequilibrium systems. A few exactly solvable models are presented. For one model we show explicitly that stochastic behaviour in a microscopic description can lead to ordered collective effects on the macroscopic scale. Two others are solved to confirm the predictions of the fluctuation theorem. (author)

Optimal Control Inventory Stochastic With Production Deteriorating

Science.gov (United States)

Affandi, Pardi

2018-01-01

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

Susceptibility of optimal train schedules to stochastic disturbances of process times

DEFF Research Database (Denmark)

Larsen, Rune; Pranzo, Marco; D’Ariano, Andrea

2013-01-01

study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact...... and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced...

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mourad Kerboua

2014-12-01

Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks

KAUST Repository

Moraes, Alvaro

2015-01-07

Stochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.

Simulation and Statistical Inference of Stochastic Reaction Networks with Applications to Epidemic Models

KAUST Repository

Moraes, Alvaro

2015-01-01

Epidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.; Lee, J.; Vygen, J.

2014-01-01

The input to the stochastic orienteering problem [14] consists of a budget B and metric (V,d) where each vertex v¿¿¿V has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a

On the adaptivity gap of stochastic orienteering

NARCIS (Netherlands)

Bansal, N.; Nagarajan, V.

2015-01-01

The input to the stochastic orienteering problem (Gupta et al. in SODA, pp 1522–1538,  2012) consists of a budget B and metric (V, d) where each vertex(Formula presented.) has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are

Forward and Inverse Modeling of Self-potential. A Tomography of Groundwater Flow and Comparison Between Deterministic and Stochastic Inversion Methods

Science.gov (United States)

Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.

2016-12-01

Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.

Stochastic Modeling of Traffic Air Pollution

DEFF Research Database (Denmark)

Thoft-Christensen, Palle

2014-01-01

In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...

Front propagation and effect of memory in stochastic desertification models with an absorbing state

Science.gov (United States)

Herman, Dor; Shnerb, Nadav M.

2017-08-01

Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.

Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis

Directory of Open Access Journals (Sweden)

Moslem Moradi

2015-06-01

Full Text Available Here in, an application of a new seismic inversion algorithm in one of Iran’s oilfields is described. Stochastic (geostatistical seismic inversion, as a complementary method to deterministic inversion, is perceived as contribution combination of geostatistics and seismic inversion algorithm. This method integrates information from different data sources with different scales, as prior information in Bayesian statistics. Data integration leads to a probability density function (named as a posteriori probability that can yield a model of subsurface. The Markov Chain Monte Carlo (MCMC method is used to sample the posterior probability distribution, and the subsurface model characteristics can be extracted by analyzing a set of the samples. In this study, the theory of stochastic seismic inversion in a Bayesian framework was described and applied to infer P-impedance and porosity models. The comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more detailed information of subsurface character. Since multiple realizations are extracted by this method, an estimation of pore volume and uncertainty in the estimation were analyzed.

A stochastic formulation of the Bass model of new-product diffusion

Directory of Open Access Journals (Sweden)

Niu Shun-Chen

2002-01-01

Full Text Available For a large variety of new products, the Bass Model (BM describes the empirical cumulative-adoptions curve extremely well. The BM postulates that the trajectory of cumulative adoptions of a new product follows a deterministic function whose instantaneous growth rate depends on two parameters, one of which captures an individual's intrinsic tendency to purchase, independent of the number of previous adopters, and the other captures a positive force of influence on an individual by previous adopters. In this paper, we formulate a stochastic version of the BM, which we call the Stochastic Bass Model (SBM, where the trajectory of cumulative number of adoptions is governed by a pure birth process. We show that with an appropriately-chosen set of birth rates, the fractions of individuals who have adopted the product by time t in a family of SBMs indexed by the size of the target population converge in probability to the deterministic fraction in a corresponding BM, when the population size approaches infinity. The formulation therefore supports and expands the BM by allowing stochastic trajectories.

Joint market clearing in a stochastic framework considering power system security

International Nuclear Information System (INIS)

Aghaei, J.; Shayanfar, H.A.; Amjady, N.

2009-01-01

This paper presents a new stochastic framework for provision of reserve requirements (spinning and non-spinning reserves) as well as energy in day-ahead simultaneous auctions by pool-based aggregated market scheme. The uncertainty of generating units in the form of system contingencies are considered in the market clearing procedure by the stochastic model. The solution methodology consists of two stages, which firstly, employs Monte-Carlo Simulation (MCS) for random scenario generation. Then, the stochastic market clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. The objective function of each of these deterministic optimization problems consists of offered cost function (including both energy and reserves offer costs), Lost Opportunity Cost (LOC) and Expected Interruption Cost (EIC). Each optimization problem is solved considering AC power flow and security constraints of the power system. The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS) and simulation studies are carried out to examine the effectiveness of the proposed method.

Stochastic processes dominate during boreal bryophyte community assembly.

Science.gov (United States)

Fenton, Nicole J; Bergeron, Yves

2013-09-01

Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of

Studies to the stochastic theory of coupled reactorkinetic-thermohydraulic systems Pt. 2

International Nuclear Information System (INIS)

Mesko, L.

1983-06-01

The description is given of the noise phenomena taking place in a multivariable coupled system by a comprehensive model based on the theory of stochastic fluctuations. A comparison is made with models using transfer function formalism for systems characterized by deterministic open and closed loop signal transmission properties. The advantages of the stochastic model are illustrated by simple reactor dynamical examples having diagnostical importance. (author)

Stochastic dynamic modeling of regular and slow earthquakes

Science.gov (United States)

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

2017-12-01

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

Shock-induced explosive chemistry in a deterministic sample configuration.

Energy Technology Data Exchange (ETDEWEB)

Stuecker, John Nicholas; Castaneda, Jaime N.; Cesarano, Joseph, III (,; ); Trott, Wayne Merle; Baer, Melvin R.; Tappan, Alexander Smith

2005-10-01

Explosive initiation and energy release have been studied in two sample geometries designed to minimize stochastic behavior in shock-loading experiments. These sample concepts include a design with explosive material occupying the hole locations of a close-packed bed of inert spheres and a design that utilizes infiltration of a liquid explosive into a well-defined inert matrix. Wave profiles transmitted by these samples in gas-gun impact experiments have been characterized by both velocity interferometry diagnostics and three-dimensional numerical simulations. Highly organized wave structures associated with the characteristic length scales of the deterministic samples have been observed. Initiation and reaction growth in an inert matrix filled with sensitized nitromethane (a homogeneous explosive material) result in wave profiles similar to those observed with heterogeneous explosives. Comparison of experimental and numerical results indicates that energetic material studies in deterministic sample geometries can provide an important new tool for validation of models of energy release in numerical simulations of explosive initiation and performance.

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

Science.gov (United States)

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

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

Population density equations for stochastic processes with memory kernels

Science.gov (United States)

Lai, Yi Ming; de Kamps, Marc

2017-06-01

We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

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

Science.gov (United States)

Liu, Qun; Chen, Qingmei; Jiang, Daqing

2016-05-01

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

Deterministic and stochastic analysis of alternative climate targets under differentiated cooperation regimes

International Nuclear Information System (INIS)

Loulou, Richard; Labriet, Maryse; Kanudia, Amit

2009-01-01

in the reference scenario. This is particularly observable in the power generation sector and in some end-use sectors. Finally, the article discusses the pros and cons of the stochastic programming treatment of forcing targets, and compares it with the separate simulations of the various deterministic cases.

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Dynamic-Programming Approaches to Single- and Multi-Stage Stochastic Knapsack Problems for Portfolio Optimization

National Research Council Canada - National Science Library

Khoo, Wai

1999-01-01

.... These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type...

Backward Stochastic H2/H∞ Control: Infinite Horizon Case

Directory of Open Access Journals (Sweden)

Zhen Wu

2014-01-01

Full Text Available The mixed H2/H∞ control problem is studied for systems governed by infinite horizon backward stochastic differential equations (BSDEs with exogenous disturbance signal. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The equivalent feedback solution is also discussed. Contrary to deterministic or stochastic forward case, the feedback solution is no longer feedback of the current state; rather, it is feedback of the entire history of the state.

Reserves and cash flows under stochastic retirement

DEFF Research Database (Denmark)

Gad, Kamille Sofie Tågholt; Nielsen, Jeppe Woetmann

2016-01-01

Uncertain time of retirement and uncertain structure of retirement benefits are risk factors for life insurance companies. Nevertheless, classical life insurance models assume these are deterministic. In this paper, we include the risk from stochastic time of retirement and stochastic benefit...... structure in a classical finite-state Markov model for a life insurance contract. We include discontinuities in the distribution of the retirement time. First, we derive formulas for appropriate scaling of the benefits according to the time of retirement and discuss the link between the scaling...... and the guarantees provided. Stochastic retirement creates a need to rethink the construction of disability products for high ages and ways to handle this are discussed. We show how to calculate market reserves and how to use modified transition probabilities to calculate expected cash flows without significantly...

Stochastic optimized life cycle models for risk mitigation in power system applications

International Nuclear Information System (INIS)

Sageder, A.

1998-01-01

This ork shows the relevance of stochastic optimization in complex power system applications. It was proven that usual deterministic mean value models not only predict inaccurate results but are also most often on the risky side. The change in the market effects all kind of evaluation processes (e.g. fuel type and technology but especially financial engineering evaluations) in the endeavor of a strict risk mitigation comparison. But not only IPPs also traditional Utilities dash for risk/return optimized investment opportunities. In this study I developed a 2-phase model which can support a decision-maker in finding optimal solutions on investment and profitability. It has to be stated, that in this study no objective function will be optimized in an algorithmically way. On the one hand focus is laid on finding optimal solutions out of different choices (highest return at lowest possible risk); on the other hand the endeavor was to provide a decision makers with a better assessment of the likelihood of outcomes on investment considerations. The first (deterministic) phase computes in a Total Cost of Ownership (TCO) approach (Life cycle Calculation; DCF method). Most of the causal relations (day of operation, escalation of personal expanses, inflation, depreciation period, etc.) are defined within this phase. The second (stochastic) phase is a total new way in optimizing risk/return relations. With the some decision theory mathematics an expected value of stochastic solutions can be calculated. Furthermore probability function have to be defined out of historical data. The model not only supports profitability analysis (including regress and sensitivity analysis) but also supports a decision-maker in a decision process. Emphasis was laid on risk-return analysis, which can give the decision-maker first hand informations of the type of risk return problem (risk concave, averse or linear). Five important parameters were chosen which have the characteristics of typical

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim

2012-01-01

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.

2012-05-22

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

GillespieSSA: Implementing the Gillespie Stochastic Simulation Algorithm in R

Directory of Open Access Journals (Sweden)

Mario Pineda-Krch

2008-02-01

Full Text Available The deterministic dynamics of populations in continuous time are traditionally described using coupled, first-order ordinary differential equations. While this approach is accurate for large systems, it is often inadequate for small systems where key species may be present in small numbers or where key reactions occur at a low rate. The Gillespie stochastic simulation algorithm (SSA is a procedure for generating time-evolution trajectories of finite populations in continuous time and has become the standard algorithm for these types of stochastic models. This article presents a simple-to-use and flexible framework for implementing the SSA using the high-level statistical computing language R and the package GillespieSSA. Using three ecological models as examples (logistic growth, Rosenzweig-MacArthur predator-prey model, and Kermack-McKendrick SIRS metapopulation model, this paper shows how a deterministic model can be formulated as a finite-population stochastic model within the framework of SSA theory and how it can be implemented in R. Simulations of the stochastic models are performed using four different SSA Monte Carlo methods: one exact method (Gillespie's direct method; and three approximate methods (explicit, binomial, and optimized tau-leap methods. Comparison of simulation results confirms that while the time-evolution trajectories obtained from the different SSA methods are indistinguishable, the approximate methods are up to four orders of magnitude faster than the exact methods.

Can we observe open loop transfer functions in a stochastic feedback system ?

International Nuclear Information System (INIS)

Kishida, Kuniharu; Suda, Nobuhide.

1991-01-01

There are two kinds of problems concerning open loop and closed loop transfer functions in a feedback system. One is a problem even in the deterministic case, and the other is in the stochastic case. In the deterministic case it is guaranteed under a necessary and sufficient condition that total sum of degrees of sub-transfer functions coincides to the degree of the total system. In the stochastic case a systematic understanding of a physical state model, a theoretical innovation model and a data-oriented innovation model is indispensable for determination of open loop transfer functions from time series data. Undesirable factors appear in determination of open loop transfer functions, since a transfer function matrix from input noises to output variables has a redundancy factor of diagonal matrix. (author)

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

Science.gov (United States)

Sakai, Kenshi; Upadhyaya, Shrinivasa K; Andrade-Sanchez, Pedro; Sviridova, Nina V

2017-03-01

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

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

Science.gov (United States)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

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

On stochastic differential equations with random delay

International Nuclear Information System (INIS)

Krapivsky, P L; Luck, J M; Mallick, K

2011-01-01

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an nth-order equation with random delay, the corresponding deterministic equation has order n + 1. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as exp((3/2) t 2/3 ) in reduced units. We then investigate the effect of introducing a discrete time step ε. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as ε goes to zero is studied in detail on the example of a first-order linear differential equation

Dynamic stochastic optimization

CERN Document Server

Ermoliev, Yuri; Pflug, Georg

2004-01-01

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective an...

The cardiorespiratory interaction: a nonlinear stochastic model and its synchronization properties

Science.gov (United States)

Bahraminasab, A.; Kenwright, D.; Stefanovska, A.; McClintock, P. V. E.

2007-06-01

We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.

Importance of vesicle release stochasticity in neuro-spike communication.

Science.gov (United States)

Ramezani, Hamideh; Akan, Ozgur B

2017-07-01

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

Stochastic Levy Divergence and Maxwell's Equations

Directory of Open Access Journals (Sweden)

B. O. Volkov

2015-01-01

Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This

Stochastic Turing Patterns: Analysis of Compartment-Based Approaches

KAUST Repository

Cao, Yang; Erban, Radek

2014-01-01

© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.

Stochastic Turing Patterns: Analysis of Compartment-Based Approaches

KAUST Repository

Cao, Yang

2014-11-25

© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.

Characterisation of Exponential Convergence to Nonequilibrium Limits for Stochastic Volterra Equations

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John A. D. Appleby

2008-01-01

Full Text Available This paper considers necessary and sufficient conditions for the solution of a stochastically and deterministically perturbed Volterra equation to converge exponentially to a nonequilibrium and nontrivial limit. Convergence in an almost sure and pth mean sense is obtained.

Polynomial asymptotic stability of damped stochastic differential equations

Directory of Open Access Journals (Sweden)

John Appleby

2004-08-01

Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.

Hybrid Stochastic Forecasting Model for Management of Large Open Water Reservoir with Storage Function

Science.gov (United States)

Kozel, Tomas; Stary, Milos

2017-12-01

The main advantage of stochastic forecasting is fan of possible value whose deterministic method of forecasting could not give us. Future development of random process is described better by stochastic then deterministic forecasting. Discharge in measurement profile could be categorized as random process. Content of article is construction and application of forecasting model for managed large open water reservoir with supply function. Model is based on neural networks (NS) and zone models, which forecasting values of average monthly flow from inputs values of average monthly flow, learned neural network and random numbers. Part of data was sorted to one moving zone. The zone is created around last measurement average monthly flow. Matrix of correlation was assembled only from data belonging to zone. The model was compiled for forecast of 1 to 12 month with using backward month flows (NS inputs) from 2 to 11 months for model construction. Data was got ridded of asymmetry with help of Box-Cox rule (Box, Cox, 1964), value r was found by optimization. In next step were data transform to standard normal distribution. The data were with monthly step and forecast is not recurring. 90 years long real flow series was used for compile of the model. First 75 years were used for calibration of model (matrix input-output relationship), last 15 years were used only for validation. Outputs of model were compared with real flow series. For comparison between real flow series (100% successfully of forecast) and forecasts, was used application to management of artificially made reservoir. Course of water reservoir management using Genetic algorithm (GE) + real flow series was compared with Fuzzy model (Fuzzy) + forecast made by Moving zone model. During evaluation process was founding the best size of zone. Results show that the highest number of input did not give the best results and ideal size of zone is in interval from 25 to 35, when course of management was almost same for

Stochastic Simulation of Integrated Circuits with Nonlinear Black-Box Components via Augmented Deterministic Equivalents

Directory of Open Access Journals (Sweden)

MANFREDI, P.

2014-11-01

Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.

Frequency domain fatigue damage estimation methods suitable for deterministic load spectra

Energy Technology Data Exchange (ETDEWEB)

Henderson, A.R.; Patel, M.H. [University Coll., Dept. of Mechanical Engineering, London (United Kingdom)

2000-07-01

The evaluation of fatigue damage due to load spectra, directly in the frequency domain, is a complex phenomena but with the benefit of significant computation time savings. Various formulae have been suggested but have usually relating to a specific application only. The Dirlik method is the exception and is applicable to general cases of continuous stochastic spectra. This paper describes three approaches for evaluating discrete deterministic load spectra generated by the floating wind turbine model developed the UCL/RAL research project. (Author)

Application of fast orthogonal search to linear and nonlinear stochastic systems

DEFF Research Database (Denmark)

Chon, K H; Korenberg, M J; Holstein-Rathlou, N H

1997-01-01

Standard deterministic autoregressive moving average (ARMA) models consider prediction errors to be unexplainable noise sources. The accuracy of the estimated ARMA model parameters depends on producing minimum prediction errors. In this study, an accurate algorithm is developed for estimating...... linear and nonlinear stochastic ARMA model parameters by using a method known as fast orthogonal search, with an extended model containing prediction errors as part of the model estimation process. The extended algorithm uses fast orthogonal search in a two-step procedure in which deterministic terms...

Fisher-Wright model with deterministic seed bank and selection.

Science.gov (United States)

Koopmann, Bendix; Müller, Johannes; Tellier, Aurélien; Živković, Daniel

2017-04-01

Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached. Copyright © 2016 Elsevier Inc. All rights reserved.

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

International Nuclear Information System (INIS)

Biondo, Elliott D.; Wilson, Paul P. H.

2017-01-01

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation of an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 _± 5 • _1_0_"_4 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.

Evaluation of the Plant-Craig stochastic convection scheme in an ensemble forecasting system

Science.gov (United States)

Keane, R. J.; Plant, R. S.; Tennant, W. J.

2015-12-01

The Plant-Craig stochastic convection parameterization (version 2.0) is implemented in the Met Office Regional Ensemble Prediction System (MOGREPS-R) and is assessed in comparison with the standard convection scheme with a simple stochastic element only, from random parameter variation. A set of 34 ensemble forecasts, each with 24 members, is considered, over the month of July 2009. Deterministic and probabilistic measures of the precipitation forecasts are assessed. The Plant-Craig parameterization is found to improve probabilistic forecast measures, particularly the results for lower precipitation thresholds. The impact on deterministic forecasts at the grid scale is neutral, although the Plant-Craig scheme does deliver improvements when forecasts are made over larger areas. The improvements found are greater in conditions of relatively weak synoptic forcing, for which convective precipitation is likely to be less predictable.

The effect of spatial heterogeneity on the extinction transition in stochastic population dynamics

International Nuclear Information System (INIS)

Kessler, David A; Shnerb, Nadav M

2009-01-01

Stochastic logistic-type growth on a static heterogeneous substrate is studied both above and below the drift-induced delocalization transition. Using agent-based simulations, the delocalization of the highest eigenfunction of the deterministic operator is connected with the large N limit of the stochastic theory. It is seen that the localization length of the deterministic theory controls the divergence of the spatial correlation length with N at the transition. It is argued that, in the presence of a strong wind, the extinction transition belongs to the directed percolation universality class, as any finite colony made of discrete agents is washed away from a heterogeneity with compact support. Some of the difficulties in the analysis of the extinction transition in the presence of a weak wind, where there is a localized active state, are discussed.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

Science.gov (United States)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Integration of renewable generation uncertainties into stochastic unit commitment considering reserve and risk: A comparative study

International Nuclear Information System (INIS)

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2016-01-01

The uncertainties of renewable energy have brought great challenges to power system commitment, dispatches and reserve requirement. This paper presents a comparative study on integration of renewable generation uncertainties into SCUC (stochastic security-constrained unit commitment) considering reserve and risk. Renewable forecast uncertainties are captured by a list of PIs (prediction intervals). A new scenario generation method is proposed to generate scenarios from these PIs. Different system uncertainties are considered as scenarios in the stochastic SCUC problem formulation. Two comparative simulations with single (E1: wind only) and multiple sources of uncertainty (E2: load, wind, solar and generation outages) are investigated. Five deterministic and four stochastic case studies are performed. Different generation costs, reserve strategies and associated risks are compared under various scenarios. Demonstrated results indicate the overall costs of E2 is lower than E1 due to penetration of solar power and the associated risk in deterministic cases of E2 is higher than E1. It implies the superimposed effect of uncertainties during uncertainty integration. The results also demonstrate that power systems run a higher level of risk during peak load hours, and that stochastic models are more robust than deterministic ones. - Highlights: • An extensive comparative study for renewable integration is presented. • A novel scenario generation method is proposed. • Wind and solar uncertainties are represented by a list of prediction intervals. • Unit commitment and dispatch costs are discussed considering reserve and risk.

Stochastic Analysis of Differential GPS Surveys for Earth Dam ...

African Journals Online (AJOL)

In GPS measurement, we try to model not just the deterministic part of the measurement but also try to account for their stochastic behavior using the measurement variance-covariance matrix. The variance-covariance matrices are computed as part of a least squares adjustment. In this study, the results of GPS survey by ...

Developing a stochastic conflict resolution model for urban runoff quality management: Application of info-gap and bargaining theories

Science.gov (United States)

Ghodsi, Seyed Hamed; Kerachian, Reza; Estalaki, Siamak Malakpour; Nikoo, Mohammad Reza; Zahmatkesh, Zahra

2016-02-01

In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.

Two-stage stochastic programming model for the regional-scale electricity planning under demand uncertainty

International Nuclear Information System (INIS)

Huang, Yun-Hsun; Wu, Jung-Hua; Hsu, Yu-Ju

2016-01-01

Traditional electricity supply planning models regard the electricity demand as a deterministic parameter and require the total power output to satisfy the aggregate electricity demand. But in today's world, the electric system planners are facing tremendously complex environments full of uncertainties, where electricity demand is a key source of uncertainty. In addition, electricity demand patterns are considerably different for different regions. This paper developed a multi-region optimization model based on two-stage stochastic programming framework to incorporate the demand uncertainty. Furthermore, the decision tree method and Monte Carlo simulation approach are integrated into the model to simplify electricity demands in the form of nodes and determine the values and probabilities. The proposed model was successfully applied to a real case study (i.e. Taiwan's electricity sector) to show its applicability. Detail simulation results were presented and compared with those generated by a deterministic model. Finally, the long-term electricity development roadmap at a regional level could be provided on the basis of our simulation results. - Highlights: • A multi-region, two-stage stochastic programming model has been developed. • The decision tree and Monte Carlo simulation are integrated into the framework. • Taiwan's electricity sector is used to illustrate the applicability of the model. • The results under deterministic and stochastic cases are shown for comparison. • Optimal portfolios of regional generation technologies can be identified.

Systematic Evaluation of Stochastic Methods in Power System Scheduling and Dispatch with Renewable Energy

Energy Technology Data Exchange (ETDEWEB)

Wang, Yishen [Univ. of Washington, Seattle, WA (United States); Argonne National Lab. (ANL), Argonne, IL (United States); Zhou, Zhi [Argonne National Lab. (ANL), Argonne, IL (United States); Liu, Cong [Argonne National Lab. (ANL), Argonne, IL (United States); Electric Reliability Council of Texas (ERCOT), Austin, TX (United States); Botterud, Audun [Argonne National Lab. (ANL), Argonne, IL (United States)

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 a 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.

Deterministic Diffusion in Delayed Coupled Maps

International Nuclear Information System (INIS)

Sozanski, M.

2005-01-01

Coupled Map Lattices (CML) are discrete time and discrete space dynamical systems used for modeling phenomena arising in nonlinear systems with many degrees of freedom. In this work, the dynamical and statistical properties of a modified version of the CML with global coupling are considered. The main modification of the model is the extension of the coupling over a set of local map states corresponding to different time iterations. The model with both stochastic and chaotic one-dimensional local maps is studied. Deterministic diffusion in the CML under variation of a control parameter is analyzed for unimodal maps. As a main result, simple relations between statistical and dynamical measures are found for the model and the cases where substituting nonlinear lattices with simpler processes is possible are presented. (author)

Stochastic Gabor reflectivity and acoustic impedance inversion

Science.gov (United States)

Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

2018-02-01

, obtaining bias could help the method to estimate reliable AI. To justify the effect of random noise on deterministic and stochastic inversion results, a stationary noisy trace with signal-to-noise ratio equal to 2 was used. The results highlight the inability of deterministic inversion in dealing with a noisy data set even using a high number of regularization parameters. Also, despite the low level of signal, stochastic Gabor inversion not only can estimate correctly the wavelet’s properties but also, because of bias from well logs, the inversion result is very close to the real AI. Comparing deterministic and introduced inversion results on a real data set shows that low resolution results, especially in the deeper parts of seismic sections using deterministic inversion, creates significant reliability problems for seismic prospects, but this pitfall is solved completely using stochastic Gabor inversion. The estimated AI using Gabor inversion in the time domain is much better and faster than general Gabor inversion in the frequency domain. This is due to the extra number of windows required to analyze the time-frequency information and also the amount of temporal increment between windows. In contrast, stochastic Gabor inversion can estimate trustable physical properties close to the real characteristics. Applying to a real data set could give an ability to detect the direction of volcanic intrusion and the ability of lithology distribution delineation along the fan. Comparing the inversion results highlights the efficiency of stochastic Gabor inversion to delineate lateral lithology changes because of the improved frequency content and zero phasing of the final inversion volume.

Exponential power spectra, deterministic chaos and Lorentzian pulses in plasma edge dynamics

International Nuclear Information System (INIS)

Maggs, J E; Morales, G J

2012-01-01

Exponential spectra have been observed in the edges of tokamaks, stellarators, helical devices and linear machines. The observation of exponential power spectra is significant because such a spectral character has been closely associated with the phenomenon of deterministic chaos by the nonlinear dynamics community. The proximate cause of exponential power spectra in both magnetized plasma edges and nonlinear dynamics models is the occurrence of Lorentzian pulses in the time signals of fluctuations. Lorentzian pulses are produced by chaotic behavior in the separatrix regions of plasma E × B flow fields or the limit cycle regions of nonlinear models. Chaotic advection, driven by the potential fields of drift waves in plasmas, results in transport. The observation of exponential power spectra and Lorentzian pulses suggests that fluctuations and transport at the edge of magnetized plasmas arise from deterministic, rather than stochastic, dynamics. (paper)

Stochastic partial differential equations an introduction

CERN Document Server

Liu, Wei

2015-01-01

This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...

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

Directory of Open Access Journals (Sweden)

Yanfeng Liang

2016-01-01

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

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

Science.gov (United States)

Liang, Yanfeng; Greenhalgh, David; Mao, Xuerong

2016-01-01

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

Stochasticity induced by coherent wavepackets

International Nuclear Information System (INIS)

Fuchs, V.; Krapchev, V.; Ram, A.; Bers, A.

1983-02-01

We consider the momentum transfer and diffusion of electrons periodically interacting with a coherent longitudinal wavepacket. Such a problem arises, for example, in lower-hybrid current drive. We establish the stochastic threshold, the stochastic region δv/sub stoch/ in velocity space, the associated momentum transfer j, and the diffusion coefficient D. We concentrate principally on the weak-field regime, tau/sub autocorrelation/ < tau/sub bounce/

On a Stochastic SEIS Model with Treatment Rate of Latent Population

Directory of Open Access Journals (Sweden)

Shujing Gao

2014-01-01

Full Text Available The asymptotic dynamics of a stochastic SEIS epidemic model with treatment rate of latent population is investigated. First, we show that the system provides a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: if R0, which is called the basic reproduction number of the corresponding deterministic model, is not more than unity, the solution of the model is oscillating around the disease-free equilibrium of the corresponding deterministic system, whereas if R0 is larger than unity, we show how the solution spirals around the endemic equilibrium of deterministic system under certain parametric restrictions. Finally, numerical simulations are carried out to support our theoretical findings.

Strongly Deterministic Population Dynamics in Closed Microbial Communities

Directory of Open Access Journals (Sweden)

Zak Frentz

2015-10-01

Full Text Available Biological systems are influenced by random processes at all scales, including molecular, demographic, and behavioral fluctuations, as well as by their interactions with a fluctuating environment. We previously established microbial closed ecosystems (CES as model systems for studying the role of random events and the emergent statistical laws governing population dynamics. Here, we present long-term measurements of population dynamics using replicate digital holographic microscopes that maintain CES under precisely controlled external conditions while automatically measuring abundances of three microbial species via single-cell imaging. With this system, we measure spatiotemporal population dynamics in more than 60 replicate CES over periods of months. In contrast to previous studies, we observe strongly deterministic population dynamics in replicate systems. Furthermore, we show that previously discovered statistical structure in abundance fluctuations across replicate CES is driven by variation in external conditions, such as illumination. In particular, we confirm the existence of stable ecomodes governing the correlations in population abundances of three species. The observation of strongly deterministic dynamics, together with stable structure of correlations in response to external perturbations, points towards a possibility of simple macroscopic laws governing microbial systems despite numerous stochastic events present on microscopic levels.

Stochastic ice stream dynamics.

Science.gov (United States)

Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca

2016-08-09

Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.

Noise-sustained fluctuations in stochastic dynamics with a delay.

Science.gov (United States)

D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

2012-04-01

Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

Science.gov (United States)

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.

Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

Directory of Open Access Journals (Sweden)

S. K. Barik

2012-01-01

Full Text Available Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

Science.gov (United States)

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.

Top-down fabrication of plasmonic nanostructures for deterministic coupling to single quantum emitters

NARCIS (Netherlands)

Pfaff, W.; Vos, A.; Hanson, R.

2013-01-01

Metal nanostructures can be used to harvest and guide the emission of single photon emitters on-chip via surface plasmon polaritons. In order to develop and characterize photonic devices based on emitter-plasmon hybrid structures, a deterministic and scalable fabrication method for such structures

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

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T. E. Govindan

2011-01-01

Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

Comparison of TITAN hybrid deterministic transport code and MCNP5 for simulation of SPECT

International Nuclear Information System (INIS)

Royston, K.; Haghighat, A.; Yi, C.

2010-01-01

Traditionally, Single Photon Emission Computed Tomography (SPECT) simulations use Monte Carlo methods. The hybrid deterministic transport code TITAN has recently been applied to the simulation of a SPECT myocardial perfusion study. The TITAN SPECT simulation uses the discrete ordinates formulation in the phantom region and a simplified ray-tracing formulation outside of the phantom. A SPECT model has been created in the Monte Carlo Neutral particle (MCNP)5 Monte Carlo code for comparison. In MCNP5 the collimator is directly modeled, but TITAN instead simulates the effect of collimator blur using a circular ordinate splitting technique. Projection images created using the TITAN code are compared to results using MCNP5 for three collimator acceptance angles. Normalized projection images for 2.97 deg, 1.42 deg and 0.98 deg collimator acceptance angles had maximum relative differences of 21.3%, 11.9% and 8.3%, respectively. Visually the images are in good agreement. Profiles through the projection images were plotted to find that the TITAN results followed the shape of the MCNP5 results with some differences in magnitude. A timing comparison on 16 processors found that the TITAN code completed the calculation 382 to 2787 times faster than MCNP5. Both codes exhibit good parallel performance. (author)

A deterministic alternative to the full configuration interaction quantum Monte Carlo method

Energy Technology Data Exchange (ETDEWEB)

Tubman, Norm M.; Lee, Joonho; Takeshita, Tyler Y.; Head-Gordon, Martin; Whaley, K. Birgitta [University of California, Berkeley, Berkeley, California 94720 (United States)

2016-07-28

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for a wide range of systems, including the difficult Cr{sub 2} molecule. We demonstrate for systems like Cr{sub 2} that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. In addition our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C{sub 2}.

The critical domain size of stochastic population models.

Science.gov (United States)

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

2017-02-01

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

Stochastic analysis of uncertain thermal characteristic of foundation soils surrounding the crude oil pipeline in permafrost regions

International Nuclear Information System (INIS)

Wang, Tao; Zhou, Guoqing; Wang, Jianzhou; Zhao, Xiaodong

2016-01-01

Highlights: • The influence of stochastic properties and conditions on permafrost foundation was investigated. • A stochastic analysis for the uncertain thermal characteristic of crude oil pipe is presented. • The mean temperature and standard deviation of foundation soils are obtained and analyzed. • Average standard deviation and maximum standard deviation of foundation soils increase with time. - Abstract: For foundation soils surrounding the crude oil pipeline in permafrost regions, the soil properties and the upper boundary conditions are stochastic because of complex geological processes and changeable atmospheric environment. The conventional finite element analysis of thermal characteristics for crude oil pipeline is always deterministic, rather than taking stochastic parameters and conditions into account. This study investigated the stochastic influence of an underground crude oil pipeline on the thermal stability of the permafrost foundation on the basis of a stochastic analysis model and the stochastic finite element method. A stochastic finite element program is compiled by Matrix Laboratory (MATLAB) software, and the random temperature fields of foundation soils surrounding a crude oil pipeline in a permafrost region are obtained and analyzed by Neumann stochastic finite element method (NSFEM). The results provide a new way to predict the thermal effects of the crude oil pipeline in permafrost regions, and it shows that the standard deviations in temperature increase with time when considering the stochastic effect of soil properties and boundary conditions, which imply that the results of conventional deterministic analysis may be far from the true value, even if in different seasons. It can improve our understanding of the random temperature field of foundation soils surrounding the crude oil pipeline and provide a theoretical basis for actual engineering design in permafrost regions.

Modeling and Simulation of Multi-scale Environmental Systems with Generalized Hybrid Petri Nets

Directory of Open Access Journals (Sweden)

Mostafa eHerajy

2015-07-01

Full Text Available Predicting and studying the dynamics and properties of environmental systems necessitates the construction and simulation of mathematical models entailing different levels of complexities. Such type of computational experiments often require the combination of discrete and continuous variables as well as processes operating at different time scales. Furthermore, the iterative steps of constructing and analyzing environmental models might involve researchers with different background. Hybrid Petri nets may contribute in overcoming such challenges as they facilitate the implementation of systems integrating discrete and continuous dynamics. Additionally, the visual depiction of model components will inevitably help to bridge the gap between scientists with distinct expertise working on the same problem. Thus, modeling environmental systems with hybrid Petri nets enables the construction of complex processes while keeping the models comprehensible for researchers working on the same project with significantly divergent education path. In this paper we propose the utilization of a special class of hybrid Petri nets, Generalized Hybrid Petri Nets (GHPN, to model and simulate environmental systems exposing processes interacting at different time-scales. GHPN integrate stochastic and deterministic semantics as well as other types of special basic events. Moreover, a case study is presented to illustrate the use of GHPN in constructing and simulating multi-timescale environmental scenarios.

Limits for Stochastic Reaction Networks

DEFF Research Database (Denmark)

Cappelletti, Daniele

Reaction systems have been introduced in the 70s to model biochemical systems. Nowadays their range of applications has increased and they are fruitfully used in dierent elds. The concept is simple: some chemical species react, the set of chemical reactions form a graph and a rate function...... is associated with each reaction. Such functions describe the speed of the dierent reactions, or their propensities. Two modelling regimes are then available: the evolution of the dierent species concentrations can be deterministically modelled through a system of ODE, while the counts of the dierent species...... at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...

A stochastic SIRS epidemic model with infectious force under intervention strategies

Science.gov (United States)

Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming

2015-12-01

In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S 1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate

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Chaoqun Xu

2013-01-01

Full Text Available We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

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Mingzhu Song

2016-01-01

Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

Stochastic optimization of a multi-feedstock lignocellulosic-based bioethanol supply chain under multiple uncertainties

International Nuclear Information System (INIS)

Osmani, Atif; Zhang, Jun

2013-01-01

An integrated multi-feedstock (i.e. switchgrass and crop residue) lignocellulosic-based bioethanol supply chain is studied under jointly occurring uncertainties in switchgrass yield, crop residue purchase price, bioethanol demand and sales price. A two-stage stochastic mathematical model is proposed to maximize expected profit by optimizing the strategic and tactical decisions. A case study based on ND (North Dakota) state in the U.S. demonstrates that in a stochastic environment it is cost effective to meet 100% of ND's annual gasoline demand from bioethanol by using switchgrass as a primary and crop residue as a secondary biomass feedstock. Although results show that the financial performance is degraded as variability of the uncertain parameters increases, the proposed stochastic model increasingly outperforms the deterministic model under uncertainties. The locations of biorefineries (i.e. first-stage integer variables) are insensitive to the uncertainties. Sensitivity analysis shows that “mean” value of stochastic parameters has a significant impact on the expected profit and optimal values of first-stage continuous variables. Increase in level of mean ethanol demand and mean sale price results in higher bioethanol production. When mean switchgrass yield is at low level and mean crop residue price is at high level, all the available marginal land is used for switchgrass cultivation. - Highlights: • Two-stage stochastic MILP model for maximizing profit of a multi-feedstock lignocellulosic-based bioethanol supply chain. • Multiple uncertainties in switchgrass yield, crop residue purchase price, bioethanol demand, and bioethanol sale price. • Proposed stochastic model outperforms the traditional deterministic model under uncertainties. • Stochastic parameters significantly affect marginal land allocation for switchgrass cultivation and bioethanol production. • Location of biorefineries is found to be insensitive to the stochastic environment

Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

Directory of Open Access Journals (Sweden)

Mohammad Bayat

2013-01-01

Full Text Available The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

Asymptotic behavior of non-autonomous stochastic parabolic equations with nonlinear Laplacian principal part

Directory of Open Access Journals (Sweden)

Bixiang Wang

2013-08-01

Full Text Available We prove the existence and uniqueness of random attractors for the p-Laplace equation driven simultaneously by non-autonomous deterministic and stochastic forcing. The nonlinearity of the equation is allowed to have a polynomial growth rate of any order which may be greater than p. We further establish the upper semicontinuity of random attractors as the intensity of noise approaches zero. In addition, we show the pathwise periodicity of random attractors when all non-autonomous deterministic forcing terms are time periodic.

Analysis of RLC Elements under Stochastic Conditions Using the First and the Second Moments

Directory of Open Access Journals (Sweden)

WALCZAK, J.

2015-11-01

Full Text Available This paper describes a method of determining the first two moments of the response for basic components of electrical circuits, i.e. resistors, inductors and capacitors. The paper goal was to obtain closed form formulae for the moments describing voltage or current stochastic processes. It has been assumed that the element parameters R (resistance, L (inductance and C (capacitance could be random variables, deterministic functions or stochastic processes and excitations are second order stochastic processes. Moreover, two cases of dependence between the random parameters and the excitation stochastic processes have been considered. The obtained results enable determination of exact solutions for the first two moments without application of numerical algorithms.

Modeling stochasticity and robustness in gene regulatory networks.

Science.gov (United States)

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

2009-06-15

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

A general analytical solution for the stochastic Milne problem using Karhunen–Loeve (K–L) expansion

International Nuclear Information System (INIS)

Hussein, A.; Selim, M.M.

2013-01-01

This paper considers the solution of the stochastic integro-differential equation of Milne problem with random operator. The Pomraning–Eddington method is implemented to get a closed form solution deterministically. Relying on the spectral properties of the covariance function, the Karhunen–Loeve (K–L) expansion is used to represent the input stochastic process in the deterministic solution. This leads to an explicit expression for the solution process as a multivariate functional of a set of uncorrelated random variables. By using different distributions for these variables, the work is realized through computing the mean and the variance of the solution. The numerical results are found in agreement with those obtained in the literature. -- Highlights: •The solution of the stochastic Milne problem is considered. •We dealt with the random cross-section itself not with the optical transformation of it. •Pomraning–Eddington method together with the (K–L) expansion were implemented. •The solution process is obtained as a functional of a set of uncorrelated random variables. •Good results are obtained for different distributions of these variables

Continuum modeling of ion-beam eroded surfaces under normal incidence: Impact of stochastic fluctuations

International Nuclear Information System (INIS)

Dreimann, Karsten; Linz, Stefan J.

2010-01-01

Graphical abstract: Deterministic surface pattern (left) and its stochastic counterpart (right) arising in a stochastic damped Kuramoto-Sivashinsky equation that serves as a model equation for ion-beam eroded surfaces and is systematically investigated. - Abstract: Using a recently proposed field equation for the surface evolution of ion-beam eroded semiconductor target materials under normal incidence, we systematically explore the impact of additive stochastic fluctuations that are permanently present during the erosion process. Specifically, we investigate the dependence of the surface roughness, the underlying pattern forming properties and the bifurcation behavior on the strength of the fluctuations.

Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics

KAUST Repository

Bressloff, Paul C.

2010-01-01

We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand

Solving stochastic inflation for arbitrary potentials

International Nuclear Information System (INIS)

Martin, Jerome; Musso, Marcello

2006-01-01

A perturbative method for solving the Langevin equation of inflationary cosmology in the presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models, namely, large field, small field, hybrid, and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case

A stochastic-field description of finite-size spiking neural networks.

Science.gov (United States)

Dumont, Grégory; Payeur, Alexandre; Longtin, André

2017-08-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity-the density of active neurons per unit time-is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.

Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics

KAUST Repository

Bressloff, Paul C.

2010-11-03

We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers- Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles). © 2010 The American Physical Society.

Simulation of dose deposition in stereotactic synchrotron radiation therapy: a fast approach combining Monte Carlo and deterministic algorithms

Energy Technology Data Exchange (ETDEWEB)

Smekens, F; Freud, N; Letang, J M; Babot, D [CNDRI (Nondestructive Testing using Ionizing Radiations) Laboratory, INSA-Lyon, 69621 Villeurbanne Cedex (France); Adam, J-F; Elleaume, H; Esteve, F [INSERM U-836, Equipe 6 ' Rayonnement Synchrotron et Recherche Medicale' , Institut des Neurosciences de Grenoble (France); Ferrero, C; Bravin, A [European Synchrotron Radiation Facility, Grenoble (France)], E-mail: francois.smekens@insa-lyon.fr

2009-08-07

A hybrid approach, combining deterministic and Monte Carlo (MC) calculations, is proposed to compute the distribution of dose deposited during stereotactic synchrotron radiation therapy treatment. The proposed approach divides the computation into two parts: (i) the dose deposited by primary radiation (coming directly from the incident x-ray beam) is calculated in a deterministic way using ray casting techniques and energy-absorption coefficient tables and (ii) the dose deposited by secondary radiation (Rayleigh and Compton scattering, fluorescence) is computed using a hybrid algorithm combining MC and deterministic calculations. In the MC part, a small number of particle histories are simulated. Every time a scattering or fluorescence event takes place, a splitting mechanism is applied, so that multiple secondary photons are generated with a reduced weight. The secondary events are further processed in a deterministic way, using ray casting techniques. The whole simulation, carried out within the framework of the Monte Carlo code Geant4, is shown to converge towards the same results as the full MC simulation. The speed of convergence is found to depend notably on the splitting multiplicity, which can easily be optimized. To assess the performance of the proposed algorithm, we compare it to state-of-the-art MC simulations, accelerated by the track length estimator technique (TLE), considering a clinically realistic test case. It is found that the hybrid approach is significantly faster than the MC/TLE method. The gain in speed in a test case was about 25 for a constant precision. Therefore, this method appears to be suitable for treatment planning applications.

Incorporating Wind Power Forecast Uncertainties Into Stochastic Unit Commitment Using Neural Network-Based Prediction Intervals.

Science.gov (United States)

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2015-09-01

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

Deterministic ripple-spreading model for complex networks.

Science.gov (United States)

Hu, Xiao-Bing; Wang, Ming; Leeson, Mark S; Hines, Evor L; Di Paolo, Ezequiel

2011-04-01

This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.

Stochastic population oscillations in spatial predator-prey models

International Nuclear Information System (INIS)

Taeuber, Uwe C

2011-01-01

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.

Streamflow disaggregation: a nonlinear deterministic approach

Directory of Open Access Journals (Sweden)

B. Sivakumar

2004-01-01

Full Text Available This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1 reconstruction of the scalar (streamflow series in a multi-dimensional phase-space for representing the transformation dynamics; and (2 use of a local approximation (nearest neighbor method for disaggregation. The approach is employed for streamflow disaggregation in the Mississippi River basin, USA. Data of successively doubled resolutions between daily and 16 days (i.e. daily, 2-day, 4-day, 8-day, and 16-day are studied, and disaggregations are attempted only between successive resolutions (i.e. 2-day to daily, 4-day to 2-day, 8-day to 4-day, and 16-day to 8-day. Comparisons between the disaggregated values and the actual values reveal excellent agreements for all the cases studied, indicating the suitability of the approach for streamflow disaggregation. A further insight into the results reveals that the best results are, in general, achieved for low embedding dimensions (2 or 3 and small number of neighbors (less than 50, suggesting possible presence of nonlinear determinism in the underlying transformation process. A decrease in accuracy with increasing disaggregation scale is also observed, a possible implication of the existence of a scaling regime in streamflow.

Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo

2013-05-23

This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.

Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

KAUST Repository

Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský , Tomá š

2009-01-01

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example

A hybrid modelling approach to simulating foot-and-mouth disease outbreaks in Australian livestock

Directory of Open Access Journals (Sweden)

Richard A Bradhurst

2015-03-01

Full Text Available Foot-and-mouth disease (FMD is a highly contagious and economically important viral disease of cloven-hoofed animals. Australia's freedom from FMD underpins a valuable trade in live animals and animal products. An outbreak of FMD would result in the loss of export markets and cause severe disruption to domestic markets. The prevention of, and contingency planning for, FMD are of key importance to government, industry, producers and the community. The spread and control of FMD is complex and dynamic due to a highly contagious multi-host pathogen operating in a heterogeneous environment across multiple jurisdictions. Epidemiological modelling is increasingly being recognized as a valuable tool for investigating the spread of disease under different conditions and the effectiveness of control strategies. Models of infectious disease can be broadly classified as: population-based models that are formulated from the top-down and employ population-level relationships to describe individual-level behaviour, individual-based models that are formulated from the bottom-up and aggregate individual-level behaviour to reveal population-level relationships, or hybrid models which combine the two approaches into a single model.The Australian Animal Disease Spread (AADIS hybrid model employs a deterministic equation-based model (EBM to model within-herd spread of FMD, and a stochastic, spatially-explicit agent-based model (ABM to model between-herd spread and control. The EBM provides concise and computationally efficient predictions of herd prevalence and clinical signs over time. The ABM captures the complex, stochastic and heterogeneous environment in which an FMD epidemic operates. The AADIS event-driven hybrid EBM/ABM architecture is a flexible, efficient and extensible framework for modelling the spread and control of disease in livestock on a national scale. We present an overview of the AADIS hybrid approach and a description of the model

Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps

International Nuclear Information System (INIS)

Zhao, Yu; Yuan, Sanling

2016-01-01

Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.

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

Science.gov (United States)

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.

A hybrid meta-heuristic algorithm for the vehicle routing problem with stochastic travel times considering the driver's satisfaction

Science.gov (United States)

Tavakkoli-Moghaddam, Reza; Alinaghian, Mehdi; Salamat-Bakhsh, Alireza; Norouzi, Narges

2012-05-01

A vehicle routing problem is a significant problem that has attracted great attention from researchers in recent years. The main objectives of the vehicle routing problem are to minimize the traveled distance, total traveling time, number of vehicles and cost function of transportation. Reducing these variables leads to decreasing the total cost and increasing the driver's satisfaction level. On the other hand, this satisfaction, which will decrease by increasing the service time, is considered as an important logistic problem for a company. The stochastic time dominated by a probability variable leads to variation of the service time, while it is ignored in classical routing problems. This paper investigates the problem of the increasing service time by using the stochastic time for each tour such that the total traveling time of the vehicles is limited to a specific limit based on a defined probability. Since exact solutions of the vehicle routing problem that belong to the category of NP-hard problems are not practical in a large scale, a hybrid algorithm based on simulated annealing with genetic operators was proposed to obtain an efficient solution with reasonable computational cost and time. Finally, for some small cases, the related results of the proposed algorithm were compared with results obtained by the Lingo 8 software. The obtained results indicate the efficiency of the proposed hybrid simulated annealing algorithm.

A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems

Directory of Open Access Journals (Sweden)

Angel A. Juan

2015-12-01

Full Text Available Many combinatorial optimization problems (COPs encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but they frequently assume that the problem inputs, the underlying objective function, and the set of optimization constraints are deterministic. However, uncertainty is all around us, which often makes deterministic models oversimplified versions of real-life systems. After completing an extensive review of related work, this paper describes a general methodology that allows for extending metaheuristics through simulation to solve stochastic COPs. ‘Simheuristics’ allow modelers for dealing with real-life uncertainty in a natural way by integrating simulation (in any of its variants into a metaheuristic-driven framework. These optimization-driven algorithms rely on the fact that efficient metaheuristics already exist for the deterministic version of the corresponding COP. Simheuristics also facilitate the introduction of risk and/or reliability analysis criteria during the assessment of alternative high-quality solutions to stochastic COPs. Several examples of applications in different fields illustrate the potential of the proposed methodology.

A stochastic collocation method for the second order wave equation with a discontinuous random speed

KAUST Repository

Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

2012-01-01

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical

Stochastic bifurcation in a model of love with colored noise

Science.gov (United States)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

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

Estimation of local concentration from measurements of stochastic adsorption dynamics using carbon nanotube-based sensors

International Nuclear Information System (INIS)

Jang, Hong; Lee, Jay H.; Braatz, Richard D.

2016-01-01

This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.

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

Science.gov (United States)

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

2018-05-01

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

Noise transmission and delay-induced stochastic oscillations in biochemical network motifs

International Nuclear Information System (INIS)

Liu Sheng-Jun; Wang Qi; Liu Bo; Yan Shi-Wei; Sakata Fumihiko

2011-01-01

With the aid of stochastic delayed-feedback differential equations, we derive an analytic expression for the power spectra of reacting molecules included in a generic biological network motif that is incorporated with a feedback mechanism and time delays in gene regulation. We systematically analyse the effects of time delays, the feedback mechanism, and biological stochasticity on the power spectra. It has been clarified that the time delays together with the feedback mechanism can induce stochastic oscillations at the molecular level and invalidate the noise addition rule for a modular description of the noise propagator. Delay-induced stochastic resonance can be expected, which is related to the stability loss of the reaction systems and Hopf bifurcation occurring for solutions of the corresponding deterministic reaction equations. Through the analysis of the power spectrum, a new approach is proposed to estimate the oscillation period. (interdisciplinary physics and related areas of science and technology)

Location deterministic biosensing from quantum-dot-nanowire assemblies

International Nuclear Information System (INIS)

Liu, Chao; Kim, Kwanoh; Fan, D. L.

2014-01-01

Semiconductor quantum dots (QDs) with high fluorescent brightness, stability, and tunable sizes, have received considerable interest for imaging, sensing, and delivery of biomolecules. In this research, we demonstrate location deterministic biochemical detection from arrays of QD-nanowire hybrid assemblies. QDs with diameters less than 10 nm are manipulated and precisely positioned on the tips of the assembled Gold (Au) nanowires. The manipulation mechanisms are quantitatively understood as the synergetic effects of dielectrophoretic (DEP) and alternating current electroosmosis (ACEO) due to AC electric fields. The QD-nanowire hybrid sensors operate uniquely by concentrating bioanalytes to QDs on the tips of nanowires before detection, offering much enhanced efficiency and sensitivity, in addition to the position-predictable rationality. This research could result in advances in QD-based biomedical detection and inspires an innovative approach for fabricating various QD-based nanodevices.

A Deterministic Safety Assessment of a Pyro-processed Waste Repository

International Nuclear Information System (INIS)

Lee, Youn Myoung; Jeong, Jong Tae; Choi, Jong Won

2012-01-01

A GoldSim template program for a safety assessment of a hybrid-typed repository system, called 'A-KRS', in which two kinds of pyro-processed radioactive wastes, low-level metal wastes and ceramic high-level wastes that arise from the pyro-processing of PWR nuclear spent fuels are disposed of, has been developed. This program is ready both for a deterministic and probabilistic total system performance assessment which is able to evaluate nuclide release from the repository and farther transport into the geosphere and biosphere under various normal, disruptive natural and manmade events, and scenarios. The A-KRS has been deterministically assessed with 5 various normal and abnormal scenarios associated with nuclide release and transport in and around the repository. Dose exposure rates to the farming exposure group have been evaluated in accordance with all the scenarios and then compared among other.

Trapping in stochastic mechanics and applications to covers of clouds and radiation belts

International Nuclear Information System (INIS)

Albeverio, S.; Blanchard, P.; Combe, P.; Rodriguez, R.; Sirugue, M.; Sirugue-Collin, M.

1984-11-01

It is possible to assign a stochastic acceleration to conservative stochastic diffusion processes. As a basic assumption, this stochastic acceleration is set equal to the deterministic smooth component of the external force acting on the particle, whereas the influences of the remainder is modelled by a diffusion coefficient. In this paper, we shall try to see whether it can account for the observation in two cases: the cover of clouds of planets and the radiation belts in the planetary magnetic field. We describe the basic properties of Newtonian Diffusion Stochastic Processes and indicate their connection with Schroedinger-like equations. Furthermore we give a heuristic interpretation of the nodal surfaces as impenetrable barriers for Newtonian Stochastic Diffusion Processes. The possible applications to the observed average cloud covering in the planetary atmosphere are presented we discuss the radiation belts (Van Allen Belts) along the previous ideas

Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems

Directory of Open Access Journals (Sweden)

Hossein Shokouhi-Nejad

2014-01-01

Full Text Available This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.

Multi-choice stochastic transportation problem involving general form of distributions.

Science.gov (United States)

Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood

2014-01-01

Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.

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

Energy Technology Data Exchange (ETDEWEB)

Shao, Sihong, E-mail: sihong@math.pku.edu.cn [LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)

2015-11-01

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

A hybrid evolutionary algorithm for multi-objective anatomy-based dose optimization in high-dose-rate brachytherapy

International Nuclear Information System (INIS)

Lahanas, M; Baltas, D; Zamboglou, N

2003-01-01

Multiple objectives must be considered in anatomy-based dose optimization for high-dose-rate brachytherapy and a large number of parameters must be optimized to satisfy often competing objectives. For objectives expressed solely in terms of dose variances, deterministic gradient-based algorithms can be applied and a weighted sum approach is able to produce a representative set of non-dominated solutions. As the number of objectives increases, or non-convex objectives are used, local minima can be present and deterministic or stochastic algorithms such as simulated annealing either cannot be used or are not efficient. In this case we employ a modified hybrid version of the multi-objective optimization algorithm NSGA-II. This, in combination with the deterministic optimization algorithm, produces a representative sample of the Pareto set. This algorithm can be used with any kind of objectives, including non-convex, and does not require artificial importance factors. A representation of the trade-off surface can be obtained with more than 1000 non-dominated solutions in 2-5 min. An analysis of the solutions provides information on the possibilities available using these objectives. Simple decision making tools allow the selection of a solution that provides a best fit for the clinical goals. We show an example with a prostate implant and compare results obtained by variance and dose-volume histogram (DVH) based objectives

HYDRASTAR - a code for stochastic simulation of groundwater flow

International Nuclear Information System (INIS)

Norman, S.

1992-05-01

The computer code HYDRASTAR was developed as a tool for groundwater flow and transport simulations in the SKB 91 safety analysis project. Its conceptual ideas can be traced back to a report by Shlomo Neuman in 1988, see the reference section. The main idea of the code is the treatment of the rock as a stochastic continuum which separates it from the deterministic methods previously employed by SKB and also from the discrete fracture models. The current report is a comprehensive description of HYDRASTAR including such topics as regularization or upscaling of a hydraulic conductivity field, unconditional and conditional simulation of stochastic processes, numerical solvers for the hydrology and streamline equations and finally some proposals for future developments

Models of gas-grain chemistry in interstellar cloud cores with a stochastic approach to surface chemistry

Science.gov (United States)

Stantcheva, T.; Herbst, E.

2004-08-01

We present a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In the model, the gas-phase chemistry is treated via rate equations while the diffusive granular chemistry is treated stochastically. The two phases are coupled through accretion and evaporation. A small network of surface reactions accounts for the surface production of the stable molecules water, formaldehyde, methanol, carbon dioxide, ammonia, and methane. The calculations are run for a time of 107 years at three different temperatures: 10 K, 15 K, and 20 K. The results are compared with those produced in a totally deterministic gas-grain model that utilizes the rate equation method for both the gas-phase and surface chemistry. The results of the different models are in agreement for the abundances of the gaseous species except for later times when the surface chemistry begins to affect the gas. The agreement for the surface species, however, is somewhat mixed. The average abundances of highly reactive surface species can be orders of magnitude larger in the stochastic-deterministic model than in the purely deterministic one. For non-reactive species, the results of the models can disagree strongly at early times, but agree to well within an order of magnitude at later times for most molecules. Strong exceptions occur for CO and H2CO at 10 K, and for CO2 at 20 K. The agreement seems to be best at a temperature of 15 K. As opposed to the use of the normal rate equation method of surface chemistry, the modified rate method is in significantly better agreement with the stochastic-deterministic approach. Comparison with observations of molecular ices in dense clouds shows mixed agreement.

Deterministic and stochastic transport theories for the analysis of complex nuclear systems

International Nuclear Information System (INIS)

Giffard, F.X.

2000-01-01

In the field of reactor and fuel cycle physics, particle transport plays an important role. Neutronic design, operation and evaluation calculations of nuclear systems make use of large and powerful computer codes. However, current limitations in terms of computer resources make it necessary to introduce simplifications and approximations in order to keep calculation time and cost within reasonable limits. Two different types of methods are available in these codes. The first one is the deterministic method, which is applicable in most practical cases but requires approximations. The other method is the Monte Carlo method, which does not make these approximations but which generally requires exceedingly long running times. The main motivation of this work is to investigate the possibility of a combined use of the two methods in such a way as to retain their advantages while avoiding their drawbacks. Our work has mainly focused on the speed-up of 3-D continuous energy Monte Carlo calculations (TRIPOLI-4 code) by means of an optimized biasing scheme derived from importance maps obtained from the deterministic code ERANOS. The application of this method to two different practical shielding-type problems has demonstrated its efficiency: speed-up factors of 100 have been reached. In addition, the method offers the advantage of being easily implemented as it is not very sensitive to the choice of the importance mesh grid. It has also been demonstrated that significant speed-ups can be achieved by this method in the case of coupled neutron-gamma transport problems, provided that the interdependence of the neutron and photon importance maps is taken into account. Complementary studies are necessary to tackle a problem brought out by this work, namely undesirable jumps in the Monte Carlo variance estimates. (author)

Developments based on stochastic and determinist methods for studying complex nuclear systems

International Nuclear Information System (INIS)

Giffard, F.X.

2000-01-01

In the field of reactor and fuel cycle physics, particle transport plays and important role. Neutronic design, operation and evaluation calculations of nuclear system make use of large and powerful computer codes. However, current limitations in terms of computer resources make it necessary to introduce simplifications and approximations in order to keep calculation time and cost within reasonable limits. Two different types of methods are available in these codes. The first one is the deterministic method, which is applicable in most practical cases but requires approximations. The other method is the Monte Carlo method, which does not make these approximations but which generally requires exceedingly long running times. The main motivation of this work is to investigate the possibility of a combined use of the two methods in such a way as to retain their advantages while avoiding their drawbacks. Our work has mainly focused on the speed-up of 3-D continuous energy Monte Carlo calculations (TRIPOLI-4 code) by means of an optimized biasing scheme derived from importance maps obtained from the deterministic code ERANOS. The application of this method to two different practical shielding-type problems has demonstrated its efficiency: speed-up factors of 100 have been reached. In addition, the method offers the advantage of being easily implemented as it is not very to the choice of the importance mesh grid. It has also been demonstrated that significant speed-ups can be achieved by this method in the case of coupled neutron-gamma transport problems, provided that the interdependence of the neutron and photon importance maps is taken into account. Complementary studies are necessary to tackle a problem brought out by this work, namely undesirable jumps in the Monte Carlo variance estimates. (author)

Stochastic resonance in models of neuronal ensembles

International Nuclear Information System (INIS)

Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.

1997-01-01

Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society

Global behavior analysis for stochastic system of 1,3-PD continuous fermentation

Science.gov (United States)

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

2017-12-01

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

Stochastic modeling of the energy supply system with uncertain fuel price – A case of emerging technologies for distributed power generation

International Nuclear Information System (INIS)

Mirkhani, Sh.; Saboohi, Y.

2012-01-01

Highlights: ► An existing bottom-up deterministic energy system model (ESM) has limited capability in handling the uncertainties. ► Uncertainty has been modeled based on GBM. Probabilistic scenarios are generated based on Cox–Ross method. ► A multistage stochastic model has been developed where scenarios are integrated in the energy system model. ► A distributed generation system has been introduced as a case study where fuel price is considered as an uncertain parameter. - Abstract: A deterministic energy supply model with bottom-up structure has limited capability in handling the uncertainties. To enhance the applicability of such a model in an uncertain environment two main issues have been investigated in the present paper. First, a binomial lattice is generated based on the stochastic nature of the source of uncertainty. Second, an energy system model (ESM) has been reformulated as a multistage stochastic problem. The result of the application of the modified energy model encompasses all uncertain outcomes together and enables optimal timing of capacity expansion. The performance of the model has been demonstrated with the help of a case study. The case study has been formulated on the assumption that a gas fired engine competes with renewable energy technologies in an uncertain environment where the price of natural gas is volatile. The result of stochastic model has then been compared with those of a deterministic model by studying the expected value of perfect information (EVPI) and the value of stochastic solution (VSS). Finally the results of the sensitivity analysis have been discussed where the characteristics of uncertainty of the price of fuel are varied.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-03-28

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Some considerations on stochastic neutron populations (u)

International Nuclear Information System (INIS)

Souto, Francisco J.; Prinja, Anil K.

2010-01-01

The neutron population in a multiplying body containing a weak random source may depart considerably from its average or expected value. The resulting behavior of the system is then unpredictable and a fully stochastic description of the neutron population becomes necessary. Stochastic considerations are especially important when dealing with pulsed reactors or in the case of criticality excursions in the presence of a weak source. Using the theory of discrete-state continuous-time Markov processes, and subject to some physical approximations, Bell (I) obtained approximate solutions for the neutron number probability distributions (pdf), with and without an intrinsic rapdom neutron source, that were valid at late times and/ large neutron populations. In recent work (4), we obtained exact solutions for Bell's model problem, and in this paper we use these exact probability distributions to: (I) assess the accuracy of Bell's asymptotic solutions and show how the latter follow from the exact solutions, (2) rigorously examine the probability of obtaining a divergent chain reaction, and (3) demonstrate the existence of an abrupt transition from a stochastic to a deterministic phase with increasing source strength.

Optimal Stochastic Advertising Strategies for the U.S. Beef Industry

OpenAIRE

Kun C. Lee; Stanley Schraufnagel; Earl O. Heady

1982-01-01

An important decision variable in the promotional strategy for the beef sector is the optimal level of advertising expenditures over time. Optimal stochastic and deterministic advertising expenditures are derived for the U.S. beef industry for the period `1966 through 1980. They are compared with historical levels and gains realized by optimal advertising strategies are measured. Finally, the optimal advertising expenditures in the future are forecasted.

Stochastic Collocation Applications in Computational Electromagnetics

Directory of Open Access Journals (Sweden)

Dragan Poljak

2018-01-01

Full Text Available The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR, human exposure to electromagnetic fields, and buried lines and grounding systems.

Simulation-optimization framework for multi-site multi-season hybrid stochastic streamflow modeling

Science.gov (United States)

Srivastav, Roshan; Srinivasan, K.; Sudheer, K. P.

2016-11-01

A simulation-optimization (S-O) framework is developed for the hybrid stochastic modeling of multi-site multi-season streamflows. The multi-objective optimization model formulated is the driver and the multi-site, multi-season hybrid matched block bootstrap model (MHMABB) is the simulation engine within this framework. The multi-site multi-season simulation model is the extension of the existing single-site multi-season simulation model. A robust and efficient evolutionary search based technique, namely, non-dominated sorting based genetic algorithm (NSGA - II) is employed as the solution technique for the multi-objective optimization within the S-O framework. The objective functions employed are related to the preservation of the multi-site critical deficit run sum and the constraints introduced are concerned with the hybrid model parameter space, and the preservation of certain statistics (such as inter-annual dependence and/or skewness of aggregated annual flows). The efficacy of the proposed S-O framework is brought out through a case example from the Colorado River basin. The proposed multi-site multi-season model AMHMABB (whose parameters are obtained from the proposed S-O framework) preserves the temporal as well as the spatial statistics of the historical flows. Also, the other multi-site deficit run characteristics namely, the number of runs, the maximum run length, the mean run sum and the mean run length are well preserved by the AMHMABB model. Overall, the proposed AMHMABB model is able to show better streamflow modeling performance when compared with the simulation based SMHMABB model, plausibly due to the significant role played by: (i) the objective functions related to the preservation of multi-site critical deficit run sum; (ii) the huge hybrid model parameter space available for the evolutionary search and (iii) the constraint on the preservation of the inter-annual dependence. Split-sample validation results indicate that the AMHMABB model is

Maximal stochastic transport in the Lorenz equations

Energy Technology Data Exchange (ETDEWEB)

Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

2016-01-08

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

Climate change threatens polar bear populations: a stochastic demographic analysis.

Science.gov (United States)

Hunter, Christine M; Caswell, Hal; Runge, Michael C; Regehr, Eric V; Amstrup, Steve C; Stirling, Ian

2010-10-01

The polar bear (Ursus maritimus) depends on sea ice for feeding, breeding, and movement. Significant reductions in Arctic sea ice are forecast to continue because of climate warming. We evaluated the impacts of climate change on polar bears in the southern Beaufort Sea by means of a demographic analysis, combining deterministic, stochastic, environment-dependent matrix population models with forecasts of future sea ice conditions from IPCC general circulation models (GCMs). The matrix population models classified individuals by age and breeding status; mothers and dependent cubs were treated as units. Parameter estimates were obtained from a capture-recapture study conducted from 2001 to 2006. Candidate statistical models allowed vital rates to vary with time and as functions of a sea ice covariate. Model averaging was used to produce the vital rate estimates, and a parametric bootstrap procedure was used to quantify model selection and parameter estimation uncertainty. Deterministic models projected population growth in years with more extensive ice coverage (2001-2003) and population decline in years with less ice coverage (2004-2005). LTRE (life table response experiment) analysis showed that the reduction in lambda in years with low sea ice was due primarily to reduced adult female survival, and secondarily to reduced breeding. A stochastic model with two environmental states, good and poor sea ice conditions, projected a declining stochastic growth rate, log lambdas, as the frequency of poor ice years increased. The observed frequency of poor ice years since 1979 would imply log lambdas approximately - 0.01, which agrees with available (albeit crude) observations of population size. The stochastic model was linked to a set of 10 GCMs compiled by the IPCC; the models were chosen for their ability to reproduce historical observations of sea ice and were forced with "business as usual" (A1B) greenhouse gas emissions. The resulting stochastic population

An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis

KAUST Repository

Yücel, Abdulkadir C.

2010-07-01

The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a system\\'s excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.). To bound the probability of system malfunction, fast and accurate techniques to quantify the uncertainty in system observables (e.g., voltages across mission-critical circuit elements) are called for. Recently proposed stochastic frameworks [1-2] combine deterministic electromagnetic (EM) simulators with stochastic collocation (SC) methods that approximate system observables using generalized polynomial chaos expansion (gPC) [3] (viz. orthogonal polynomials spanning the entire random domain) to estimate their statistical moments and probability density functions (pdfs). When constructing gPC expansions, the EM simulator is used solely to evaluate system observables at collocation points prescribed by the SC-gPC scheme. The frameworks in [1-2] therefore are non-intrusive and straightforward to implement. That said, they become inefficient and inaccurate for system observables that vary rapidly or are discontinuous in the random variables (as their representations may require very high-order polynomials). © 2010 IEEE.

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

Science.gov (United States)

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.

PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING

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A. A. Lobaty

2017-01-01

Full Text Available At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology.  The identification problem is dependent on a priori information about identification object, besides that  the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.. The paper considers a problem for determination of system parameters  (identification object which is assigned by the stochastic mathematical model including random functions of time. It has been shown  that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of  parameters in a mathematical model of  the stochastic system by non-gradient random searching. A specific  feature  of the algorithm is its applicability  practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm  ensures searching of  an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method  while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.

A hybrid deterministic-probabilistic approach to model the mechanical response of helically arranged hierarchical strands

Science.gov (United States)

Fraldi, M.; Perrella, G.; Ciervo, M.; Bosia, F.; Pugno, N. M.

2017-09-01

Very recently, a Weibull-based probabilistic strategy has been successfully applied to bundles of wires to determine their overall stress-strain behaviour, also capturing previously unpredicted nonlinear and post-elastic features of hierarchical strands. This approach is based on the so-called "Equal Load Sharing (ELS)" hypothesis by virtue of which, when a wire breaks, the load acting on the strand is homogeneously redistributed among the surviving wires. Despite the overall effectiveness of the method, some discrepancies between theoretical predictions and in silico Finite Element-based simulations or experimental findings might arise when more complex structures are analysed, e.g. helically arranged bundles. To overcome these limitations, an enhanced hybrid approach is proposed in which the probability of rupture is combined with a deterministic mechanical model of a strand constituted by helically-arranged and hierarchically-organized wires. The analytical model is validated comparing its predictions with both Finite Element simulations and experimental tests. The results show that generalized stress-strain responses - incorporating tension/torsion coupling - are naturally found and, once one or more elements break, the competition between geometry and mechanics of the strand microstructure, i.e. the different cross sections and helical angles of the wires in the different hierarchical levels of the strand, determines the no longer homogeneous stress redistribution among the surviving wires whose fate is hence governed by a "Hierarchical Load Sharing" criterion.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Electricity price modeling with stochastic time change

International Nuclear Information System (INIS)

Borovkova, Svetlana; Schmeck, Maren Diane

2017-01-01

In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.

SU-C-BRC-03: Development of a Novel Strategy for On-Demand Monte Carlo and Deterministic Dose Calculation Treatment Planning and Optimization for External Beam Photon and Particle Therapy

Energy Technology Data Exchange (ETDEWEB)

Yang, Y M; Bush, K; Han, B; Xing, L [Department of Radiation Oncology, Stanford University School of Medicine, Stanford, CA (United States)

2016-06-15

Purpose: Accurate and fast dose calculation is a prerequisite of precision radiation therapy in modern photon and particle therapy. While Monte Carlo (MC) dose calculation provides high dosimetric accuracy, the drastically increased computational time hinders its routine use. Deterministic dose calculation methods are fast, but problematic in the presence of tissue density inhomogeneity. We leverage the useful features of deterministic methods and MC to develop a hybrid dose calculation platform with autonomous utilization of MC and deterministic calculation depending on the local geometry, for optimal accuracy and speed. Methods: Our platform utilizes a Geant4 based “localized Monte Carlo” (LMC) method that isolates MC dose calculations only to volumes that have potential for dosimetric inaccuracy. In our approach, additional structures are created encompassing heterogeneous volumes. Deterministic methods calculate dose and energy fluence up to the volume surfaces, where the energy fluence distribution is sampled into discrete histories and transported using MC. Histories exiting the volume are converted back into energy fluence, and transported deterministically. By matching boundary conditions at both interfaces, deterministic dose calculation account for dose perturbations “downstream” of localized heterogeneities. Hybrid dose calculation was performed for water and anthropomorphic phantoms. Results: We achieved <1% agreement between deterministic and MC calculations in the water benchmark for photon and proton beams, and dose differences of 2%–15% could be observed in heterogeneous phantoms. The saving in computational time (a factor ∼4–7 compared to a full Monte Carlo dose calculation) was found to be approximately proportional to the volume of the heterogeneous region. Conclusion: Our hybrid dose calculation approach takes advantage of the computational efficiency of deterministic method and accuracy of MC, providing a practical tool for high

SU-C-BRC-03: Development of a Novel Strategy for On-Demand Monte Carlo and Deterministic Dose Calculation Treatment Planning and Optimization for External Beam Photon and Particle Therapy

International Nuclear Information System (INIS)

Yang, Y M; Bush, K; Han, B; Xing, L

2016-01-01

Purpose: Accurate and fast dose calculation is a prerequisite of precision radiation therapy in modern photon and particle therapy. While Monte Carlo (MC) dose calculation provides high dosimetric accuracy, the drastically increased computational time hinders its routine use. Deterministic dose calculation methods are fast, but problematic in the presence of tissue density inhomogeneity. We leverage the useful features of deterministic methods and MC to develop a hybrid dose calculation platform with autonomous utilization of MC and deterministic calculation depending on the local geometry, for optimal accuracy and speed. Methods: Our platform utilizes a Geant4 based “localized Monte Carlo” (LMC) method that isolates MC dose calculations only to volumes that have potential for dosimetric inaccuracy. In our approach, additional structures are created encompassing heterogeneous volumes. Deterministic methods calculate dose and energy fluence up to the volume surfaces, where the energy fluence distribution is sampled into discrete histories and transported using MC. Histories exiting the volume are converted back into energy fluence, and transported deterministically. By matching boundary conditions at both interfaces, deterministic dose calculation account for dose perturbations “downstream” of localized heterogeneities. Hybrid dose calculation was performed for water and anthropomorphic phantoms. Results: We achieved <1% agreement between deterministic and MC calculations in the water benchmark for photon and proton beams, and dose differences of 2%–15% could be observed in heterogeneous phantoms. The saving in computational time (a factor ∼4–7 compared to a full Monte Carlo dose calculation) was found to be approximately proportional to the volume of the heterogeneous region. Conclusion: Our hybrid dose calculation approach takes advantage of the computational efficiency of deterministic method and accuracy of MC, providing a practical tool for high

Time-ordered product expansions for computational stochastic system biology

International Nuclear Information System (INIS)

Mjolsness, Eric

2013-01-01

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. (paper)

Groundwater Management at Varamin Plain: The Consideration of Stochastic and Environmental Effects

International Nuclear Information System (INIS)

Najafi Alamdarlo, H.; Ahmadian, M.; Khalilian, S.

2016-01-01

Groundwater is one of the common resources in Varamin Plain, but due to over extraction it has been exposed to ruin. This phenomenon will lead to economic and environmental problems. On the other hand, the world is expected to face with more stochastic events of water supply. Furthermore, incorporating stochastic consideration of water supply becomes more acute in designing water facilities. Therefore, the strategies should be applied to improve managing resources and increase the efficiency of irrigation system. Hence, in this study the effect of efficiency improvement of irrigation system on the exploitation of groundwater and cropping pattern is examined in deterministic and stochastic condition using Nash bargaining theory. The results showed that farmers in B scenario are more willing to cooperate and as a result of their cooperation, they lose only 3 percentages of their present value of the objective function. Therefore, the efficiency improvement of irrigation system can result in improving the cooperation between farmers and increasing the amount of reserves.Groundwater is one of the common resources in Varamin Plain, but due to over extraction it has been exposed to ruin. This phenomenon will lead to economic and environmental problems. On the other hand, the world is expected to face with more stochastic events of water supply. Furthermore, incorporating stochastic consideration of water supply becomes more acute in designing water facilities. Therefore, the strategies should be applied to improve managing resources and increase the efficiency of irrigation system. Hence, in this study the effect of efficiency improvement of irrigation system on the exploitation of groundwater and cropping pattern is examined in deterministic and stochastic condition using Nash bargaining theory. The results showed that farmers in B scenario are more willing to cooperate and as a result of their cooperation, they lose only 3 percentages of their present value of the

Applicability of deterministic methods in seismic site effects modeling

International Nuclear Information System (INIS)

Cioflan, C.O.; Radulian, M.; Apostol, B.F.; Ciucu, C.

2005-01-01

The up-to-date information related to local geological structure in the Bucharest urban area has been integrated in complex analyses of the seismic ground motion simulation using deterministic procedures. The data recorded for the Vrancea intermediate-depth large earthquakes are supplemented with synthetic computations all over the city area. The hybrid method with a double-couple seismic source approximation and a relatively simple regional and local structure models allows a satisfactory reproduction of the strong motion records in the frequency domain (0.05-1)Hz. The new geological information and a deterministic analytical method which combine the modal summation technique, applied to model the seismic wave propagation between the seismic source and the studied sites, with the mode coupling approach used to model the seismic wave propagation through the local sedimentary structure of the target site, allows to extend the modelling to higher frequencies of earthquake engineering interest. The results of these studies (synthetic time histories of the ground motion parameters, absolute and relative response spectra etc) for the last 3 Vrancea strong events (August 31,1986 M w =7.1; May 30,1990 M w = 6.9 and October 27, 2004 M w = 6.0) can complete the strong motion database used for the microzonation purposes. Implications and integration of the deterministic results into the urban planning and disaster management strategies are also discussed. (authors)

Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs

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Youness El Ansari

2017-01-01

Full Text Available We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero. The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results.

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

Energy Technology Data Exchange (ETDEWEB)

Kulp, C. W., E-mail: Kulp@lycoming.edu [Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701 (United States); Zunino, L., E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata—CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina)

2014-09-01

In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.

Age distribution dynamics with stochastic jumps in mortality.

Science.gov (United States)

Calabrese, Salvatore; Porporato, Amilcare; Laio, Francesco; D'Odorico, Paolo; Ridolfi, Luca

2017-11-01

While deterministic age distribution models have been extensively studied and applied in various disciplines, little work has been devoted to understanding the role of stochasticity in birth and mortality terms. In this paper, we analyse a stochastic M'Kendrick-von Foerster equation in which jumps in mortality represent intense losses of population due to external events. We present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments. We also derive the dynamics of the mean age of the population and its harmonic mean. The framework is then used to calculate the age distribution of salt in the soil root zone, where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events.

Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems

Science.gov (United States)

Tubman, Norm; Whaley, Birgitta

The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

Science.gov (United States)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Predicting population extinction or disease outbreaks with stochastic models

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Linda J. S. Allen

2017-01-01

Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.

Accelerated Genetic Algorithm Solutions Of Some Parametric Families Of Stochastic Differential Equations

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Eman Ali Hussain

2015-01-01

Full Text Available Absract In this project A new method for solving Stochastic Differential Equations SDEs deriving by Wiener process numerically will be construct and implement using Accelerated Genetic Algorithm AGA. An SDE is a differential equation in which one or more of the terms and hence the solutions itself is a stochastic process. Solving stochastic differential equations requires going away from the recognizable deterministic setting of ordinary and partial differential equations into a world where the evolution of a quantity has an inherent random component and where the expected behavior of this quantity can be described in terms of probability distributions. We applied our method on the Ito formula which is equivalent to the SDE to find approximation solution of the SDEs. Numerical experiments illustrate the behavior of the proposed method.

Attempts at a numerical realisation of stochastic differential equations containing Preisach operator

International Nuclear Information System (INIS)

McCarthy, S; Rachinskii, D

2011-01-01

We describe two Euler type numerical schemes obtained by discretisation of a stochastic differential equation which contains the Preisach memory operator. Equations of this type are of interest in areas such as macroeconomics and terrestrial hydrology where deterministic models containing the Preisach operator have been developed but do not fully encapsulate stochastic aspects of the area. A simple price dynamics model is presented as one motivating example for our studies. Some numerical evidence is given that the two numerical schemes converge to the same limit as the time step decreases. We show that the Preisach term introduces a damping effect which increases on the parts of the trajectory demonstrating a stronger upwards or downwards trend. The results are preliminary to a broader programme of research of stochastic differential equations with the Preisach hysteresis operator.

Scheduling stochastic two-machine flow shop problems to minimize expected makespan

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Mehdi Heydari

2013-07-01

Full Text Available During the past few years, despite tremendous contribution on deterministic flow shop problem, there are only limited number of works dedicated on stochastic cases. This paper examines stochastic scheduling problems in two-machine flow shop environment for expected makespan minimization where processing times of jobs are normally distributed. Since jobs have stochastic processing times, to minimize the expected makespan, the expected sum of the second machine’s free times is minimized. In other words, by minimization waiting times for the second machine, it is possible to reach the minimum of the objective function. A mathematical method is proposed which utilizes the properties of the normal distributions. Furthermore, this method can be used as a heuristic method for other distributions, as long as the means and variances are available. The performance of the proposed method is explored using some numerical examples.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.

2014-01-06

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

KAUST Repository

El-Beltagy, Mohamed A.; Al-Mulla, Noah

2014-01-01

Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

Molecules with an induced dipole moment in a stochastic electric field.

Science.gov (United States)

Band, Y B; Ben-Shimol, Y

2013-10-01

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

A stochastic-bayesian model for the fracture probability of PWR pressure vessels

Energy Technology Data Exchange (ETDEWEB)

Francisco, Alexandre S.; Duran, Jorge Alberto R., E-mail: afrancisco@metal.eeimvr.uff.br, E-mail: duran@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Dept. de Engenharia Mecanica

2013-07-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)

A stochastic-bayesian model for the fracture probability of PWR pressure vessels

International Nuclear Information System (INIS)

Francisco, Alexandre S.; Duran, Jorge Alberto R.

2013-01-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

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

Extinction in neutrally stable stochastic Lotka-Volterra models

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Dobrinevski, Alexander; Frey, Erwin

2012-05-01

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

Development of a generalized stochastic model for the analysis of monoenergetic space-time nuclear factor Kinetics

International Nuclear Information System (INIS)

Pham, Nhu Viet Ha

2011-02-01

To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the Its stochastic differential equations was newly developed for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the Its stochastic differential equations in order to derive the SSKM. The proposed model

The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates

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Yilun Shang

2013-01-01

Full Text Available We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows.

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

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Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

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

Noise suppress or express exponential growth for hybrid Hopfield neural networks

International Nuclear Information System (INIS)

Zhu Song; Shen Yi; Chen Guici

2010-01-01

In this Letter, we will show that noise can make the given hybrid Hopfield neural networks whose solution may grows exponentially become the new stochastic hybrid Hopfield neural networks whose solution will grows at most polynomially. On the other hand, we will also show that noise can make the given hybrid Hopfield neural networks whose solution grows at most polynomially become the new stochastic hybrid Hopfield neural networks whose solution will grows at exponentially. In other words, we will reveal that the noise can suppress or express exponential growth for hybrid Hopfield neural networks.

Phenotypic switching of populations of cells in a stochastic environment

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

2018-02-01

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