Nonlinear Markov processes: Deterministic case
International Nuclear Information System (INIS)
Frank, T.D.
2008-01-01
Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution
Nonlinearly perturbed semi-Markov processes
Silvestrov, Dmitrii
2017-01-01
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...
Recombination Processes and Nonlinear Markov Chains.
Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail
2016-09-01
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.
Energy Technology Data Exchange (ETDEWEB)
Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)
2008-07-18
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
International Nuclear Information System (INIS)
Frank, T D
2008-01-01
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
Kirkwood, James R
2015-01-01
Review of ProbabilityShort HistoryReview of Basic Probability DefinitionsSome Common Probability DistributionsProperties of a Probability DistributionProperties of the Expected ValueExpected Value of a Random Variable with Common DistributionsGenerating FunctionsMoment Generating FunctionsExercisesDiscrete-Time, Finite-State Markov ChainsIntroductionNotationTransition MatricesDirected Graphs: Examples of Markov ChainsRandom Walk with Reflecting BoundariesGamblerâ€™s RuinEhrenfest ModelCentral Problem of Markov ChainsCondition to Ensure a Unique Equilibrium StateFinding the Equilibrium StateTransient and Recurrent StatesIndicator FunctionsPerron-Frobenius TheoremAbsorbing Markov ChainsMean First Passage TimeMean Recurrence Time and the Equilibrium StateFundamental Matrix for Regular Markov ChainsDividing a Markov Chain into Equivalence ClassesPeriodic Markov ChainsReducible Markov ChainsSummaryExercisesDiscrete-Time, Infinite-State Markov ChainsRenewal ProcessesDelayed Renewal ProcessesEquilibrium State f...
International Nuclear Information System (INIS)
Ermolaev, P; Volynsky, M
2014-01-01
Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.
Markov Chains and Markov Processes
Ogunbayo, Segun
2016-01-01
Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Grabski
2014-01-01
Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and
Markov process of muscle motors
International Nuclear Information System (INIS)
Kondratiev, Yu; Pechersky, E; Pirogov, S
2008-01-01
We study a Markov random process describing muscle molecular motor behaviour. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spends an exponential time depending on the state. The thin filament moves at a velocity proportional to the average of all displacements of all motors. We assume that the time which a motor stays in the bound state does not depend on its displacement. Then one can find an exact solution of a nonlinear equation appearing in the limit of an infinite number of motors
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Reviving Markov processes and applications
International Nuclear Information System (INIS)
Cai, H.
1988-01-01
In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications of the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability)
A relation between non-Markov and Markov processes
International Nuclear Information System (INIS)
Hara, H.
1980-01-01
With the aid of a transformation technique, it is shown that some memory effects in the non-Markov processes can be eliminated. In other words, some non-Markov processes are rewritten in a form obtained by the random walk process; the Markov process. To this end, two model processes which have some memory or correlation in the random walk process are introduced. An explanation of the memory in the processes is given. (orig.)
Markov Processes in Image Processing
Petrov, E. P.; Kharina, N. L.
2018-05-01
Digital images are used as an information carrier in different sciences and technologies. The aspiration to increase the number of bits in the image pixels for the purpose of obtaining more information is observed. In the paper, some methods of compression and contour detection on the basis of two-dimensional Markov chain are offered. Increasing the number of bits on the image pixels will allow one to allocate fine object details more precisely, but it significantly complicates image processing. The methods of image processing do not concede by the efficiency to well-known analogues, but surpass them in processing speed. An image is separated into binary images, and processing is carried out in parallel with each without an increase in speed, when increasing the number of bits on the image pixels. One more advantage of methods is the low consumption of energy resources. Only logical procedures are used and there are no computing operations. The methods can be useful in processing images of any class and assignment in processing systems with a limited time and energy resources.
Markov Decision Processes in Practice
Boucherie, Richardus J.; van Dijk, N.M.
2017-01-01
It is over 30 years ago since D.J. White started his series of surveys on practical applications of Markov decision processes (MDP), over 20 years after the phenomenal book by Martin Puterman on the theory of MDP, and over 10 years since Eugene A. Feinberg and Adam Shwartz published their Handbook
Frank, T. D.
2008-02-01
We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.
Markov processes characterization and convergence
Ethier, Stewart N
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists."[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."-American Scientist"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."-Journal of Statistical PhysicsMarkov Proce...
Markov Decision Process Measurement Model.
LaMar, Michelle M
2018-03-01
Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.
Inhomogeneous Markov point processes by transformation
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Nielsen, Linda Stougaard
2000-01-01
We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....
Timed Comparisons of Semi-Markov Processes
DEFF Research Database (Denmark)
Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio
2018-01-01
-Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...
NonMarkov Ito Processes with 1- state memory
McCauley, Joseph L.
2010-08-01
A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.
Generated dynamics of Markov and quantum processes
Janßen, Martin
2016-01-01
This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put in...
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...
Bayesian analysis of Markov point processes
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper
2006-01-01
Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...... a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the "unknown" likelihood, perfect simulation algorithms for spatial point processes become useful....
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
Markov processes an introduction for physical scientists
Gillespie, Daniel T
1991-01-01
Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.Key Features* A self-contained, prgamatic exposition of the needed elements of random variable theory* Logically integrated derviations of the Chapman-Kolmogorov e
Continuity Properties of Distances for Markov Processes
DEFF Research Database (Denmark)
Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand
2014-01-01
In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable...
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Markov decision processes in artificial intelligence
Sigaud, Olivier
2013-01-01
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in Artificial Intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, Reinforcement Learning, Partially Observable MDPs, Markov games and the use of non-classical criteria). Then it presents more advanced research trends in the domain and gives some concrete examples using illustr
Renewal characterization of Markov modulated Poisson processes
Directory of Open Access Journals (Sweden)
Marcel F. Neuts
1989-01-01
Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.
Operational Markov Condition for Quantum Processes
Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan
2018-01-01
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.
Modeling nonhomogeneous Markov processes via time transformation.
Hubbard, R A; Inoue, L Y T; Fann, J R
2008-09-01
Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Dynamical fluctuations for semi-Markov processes
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel; Wynants, B.
2009-01-01
Roč. 42, č. 36 (2009), 365002/1-365002/21 ISSN 1751-8113 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520 Keywords : nonequilibrium fluctuations * semi-Markov processes Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.577, year: 2009 http://www.iop.org/EJ/abstract/1751-8121/42/36/365002
Neyman, Markov processes and survival analysis.
Yang, Grace
2013-07-01
J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.
A Markov Process Inspired Cellular Automata Model of Road Traffic
Wang, Fa; Li, Li; Hu, Jianming; Ji, Yan; Yao, Danya; Zhang, Yi; Jin, Xuexiang; Su, Yuelong; Wei, Zheng
2008-01-01
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize i...
Learning Markov Decision Processes for Model Checking
DEFF Research Database (Denmark)
Mao, Hua; Chen, Yingke; Jaeger, Manfred
2012-01-01
. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation......Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm...... on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system...
Derivation of Markov processes that violate detailed balance
Lee, Julian
2018-03-01
Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.
Pathwise duals of monotone and additive Markov processes
Czech Academy of Sciences Publication Activity Database
Sturm, A.; Swart, Jan M.
-, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf
Markov processes from K. Ito's perspective (AM-155)
Stroock, Daniel W
2003-01-01
Kiyosi Itô''s greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô''s program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov''s approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed incremen
Filtering of a Markov Jump Process with Counting Observations
International Nuclear Information System (INIS)
Ceci, C.; Gerardi, A.
2000-01-01
This paper concerns the filtering of an R d -valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions of the filtering equations are discussed
Continuous-time Markov decision processes theory and applications
Guo, Xianping
2009-01-01
This volume provides the first book entirely devoted to recent developments on the theory and applications of continuous-time Markov decision processes (MDPs). The MDPs presented here include most of the cases that arise in applications.
On mean reward variance in semi-Markov processes
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2005-01-01
Roč. 62, č. 3 (2005), s. 387-397 ISSN 1432-2994 R&D Projects: GA ČR(CZ) GA402/05/0115; GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov and semi-Markov processes with rewards * variance of cumulative reward * asymptotic behaviour Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.259, year: 2005
English, Thomas
2005-01-01
A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
Temme, P. K.
2010-01-01
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Bisimulation on Markov Processes over Arbitrary Measurable Spaces
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2014-01-01
We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a mea......We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates...
Embedding a State Space Model Into a Markov Decision Process
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Jørgensen, Erik; Højsgaard, Søren
2011-01-01
In agriculture Markov decision processes (MDPs) with finite state and action space are often used to model sequential decision making over time. For instance, states in the process represent possible levels of traits of the animal and transition probabilities are based on biological models...
Critical Age-Dependent Branching Markov Processes and their ...
Indian Academy of Sciences (India)
This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.
Lectures from Markov processes to Brownian motion
Chung, Kai Lai
1982-01-01
This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book ...
Hidden Markov processes theory and applications to biology
Vidyasagar, M
2014-01-01
This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are t
Berman-Konsowa principle for reversible Markov jump processes
Hollander, den W.Th.F.; Jansen, S.
2013-01-01
In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability
Testing the Adequacy of a Semi-Markov Process
2015-09-17
classical Brownian motion are two common examples of martingales. Submartingales and supermartingales are two extended classes of martingales. They... movements using Semi-Markov processes,” Tourism Management, Vol. 32, No. 4, 2011, pp. 844–851. [4] Titman, A. C. and Sharples, L. D., “Model
Elements of the theory of Markov processes and their applications
Bharucha-Reid, A T
2010-01-01
This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.
Envelopes of Sets of Measures, Tightness, and Markov Control Processes
International Nuclear Information System (INIS)
Gonzalez-Hernandez, J.; Hernandez-Lerma, O.
1999-01-01
We introduce upper and lower envelopes for sets of measures on an arbitrary topological space, which are then used to give a tightness criterion. These concepts are applied to show the existence of optimal policies for a class of Markov control processes
Cascade probabilistic function and the Markov's processes. Chapter 1
International Nuclear Information System (INIS)
2002-01-01
In the Chapter 1 the physical and mathematical descriptions of radiation processes are carried out. The relation of the cascade probabilistic functions (CPF) for electrons, protons, alpha-particles and ions with Markov's chain is shown. The algorithms for CPF calculation with accounting energy losses are given
On Characterisation of Markov Processes Via Martingale Problems
Indian Academy of Sciences (India)
This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.
Markov LIMID processes for representing and solving renewal problems
DEFF Research Database (Denmark)
Jørgensen, Erik; Kristensen, Anders Ringgaard; Nilsson, Dennis
2014-01-01
to model a Markov Limid Process, where each TemLimid represents a macro action. Algorithms are presented to find optimal plans for a sequence of such macro actions. Use of algorithms is illustrated based on an extended version of an example from pig production originally used to introduce the Limid concept...
Bearing Degradation Process Prediction Based on the Support Vector Machine and Markov Model
Directory of Open Access Journals (Sweden)
Shaojiang Dong
2014-01-01
Full Text Available Predicting the degradation process of bearings before they reach the failure threshold is extremely important in industry. This paper proposed a novel method based on the support vector machine (SVM and the Markov model to achieve this goal. Firstly, the features are extracted by time and time-frequency domain methods. However, the extracted original features are still with high dimensional and include superfluous information, and the nonlinear multifeatures fusion technique LTSA is used to merge the features and reduces the dimension. Then, based on the extracted features, the SVM model is used to predict the bearings degradation process, and the CAO method is used to determine the embedding dimension of the SVM model. After the bearing degradation process is predicted by SVM model, the Markov model is used to improve the prediction accuracy. The proposed method was validated by two bearing run-to-failure experiments, and the results proved the effectiveness of the methodology.
Active Learning of Markov Decision Processes for System Verification
DEFF Research Database (Denmark)
Chen, Yingke; Nielsen, Thomas Dyhre
2012-01-01
deterministic Markov decision processes from data by actively guiding the selection of input actions. The algorithm is empirically analyzed by learning system models of slot machines, and it is demonstrated that the proposed active learning procedure can significantly reduce the amount of data required...... demanding process, and this shortcoming has motivated the development of algorithms for automatically learning system models from observed system behaviors. Recently, algorithms have been proposed for learning Markov decision process representations of reactive systems based on alternating sequences...... of input/output observations. While alleviating the problem of manually constructing a system model, the collection/generation of observed system behaviors can also prove demanding. Consequently we seek to minimize the amount of data required. In this paper we propose an algorithm for learning...
Reggeon field theory and Markov processes
International Nuclear Information System (INIS)
Grassberger, P.; Sundermeyer, K.
1978-01-01
Reggeon field theory with a quartic coupling in addition to the standard cubic one is shown to be mathematically equivalent to a chemical process where a radical can undergo diffusion, absorption, recombination, and autocatalytic production. Physically, these 'radicals' are wee partons. (Auth.)
Identification of Optimal Policies in Markov Decision Processes
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
46 2010, č. 3 (2010), s. 558-570 ISSN 0023-5954. [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009] R&D Projects: GA ČR(CZ) GA402/08/0107; GA ČR GA402/07/1113 Institutional research plan: CEZ:AV0Z10750506 Keywords : finite state Markov decision processes * discounted and average costs * elimination of suboptimal policies Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/E/sladky-identification of optimal policies in markov decision processes.pdf
A Partially Observed Markov Decision Process for Dynamic Pricing
Yossi Aviv; Amit Pazgal
2005-01-01
In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework to study a dynamic pricing problem faced by sellers of fashion-like goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales ob...
Mean-Variance Optimization in Markov Decision Processes
Mannor, Shie; Tsitsiklis, John N.
2011-01-01
We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudo-polynomial exact and approximation algorithms.
On the entropy of a hidden Markov process.
Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech
2008-05-01
We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order.
Semi adiabatic theory of seasonal Markov processes
Energy Technology Data Exchange (ETDEWEB)
Talkner, P [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
The explicit form of the rate function for semi-Markov processes and its contractions
Sughiyama, Yuki; Kobayashi, Testuya J.
2018-03-01
We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.
International Nuclear Information System (INIS)
Hirschmann, H.
1983-06-01
The consequences of the basic assumptions of the semi-Markov process as defined from a homogeneous renewal process with a stationary Markov condition are reviewed. The notion of the semi-Markov process is generalized by its redefinition from a nonstationary Markov renewal process. For both the nongeneralized and the generalized case a representation of the first order conditional state probabilities is derived in terms of the transition probabilities of the Markov renewal process. Some useful calculation rules (regeneration rules) are derived for the conditional state probabilities of the semi-Markov process. Compared to the semi-Markov process in its usual definition the generalized process allows the analysis of a larger class of systems. For instance systems with arbitrarily distributed lifetimes of their components can be described. There is also a chance to describe systems which are modified during time by forces or manipulations from outside. (Auth.)
The cascade probabilistic functions and the Markov's processes. Chapter 1
International Nuclear Information System (INIS)
2003-01-01
In the Chapter 1 the physical and mathematical descriptions of radiation processes are carried out. The relation of the cascade probabilistic functions (CPF) with Markov's chain is shown. The CPF calculation for electrons with the energy losses taking into account are given. The calculation of the CPF on the computer was carried out. The estimation of energy losses contribution in the CPFs and radiation defects concentration are made. Besides calculation of the primarily knock-on atoms and radiation defects at electron irradiation with use of the CPF with taking into account energy losses are conducted
Variance reduction techniques in the simulation of Markov processes
International Nuclear Information System (INIS)
Lessi, O.
1987-01-01
We study a functional r of the stationary distribution of a homogeneous Markov chain. It is often difficult or impossible to perform the analytical calculation of r and so it is reasonable to estimate r by a simulation process. A consistent estimator r(n) of r is obtained with respect to a chain with a countable state space. Suitably modifying the estimator r(n) of r one obtains a new consistent estimator which has a smaller variance than r(n). The same is obtained in the case of finite state space
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
Thayakaran, R; Ramesh, N I
2013-01-01
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.
The application of Markov decision process in restaurant delivery robot
Wang, Yong; Hu, Zhen; Wang, Ying
2017-05-01
As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional path planning algorithm is not very ideal. To solve this problem, this paper proposes the Markov dynamic state immediate reward (MDR) path planning algorithm according to the traditional Markov decision process. First of all, it uses MDR to plan a global path, then navigates along this path. When the sensor detects there is no obstructions in front state, increase its immediate state reward value; when the sensor detects there is an obstacle in front, plan a global path that can avoid obstacle with the current position as the new starting point and reduce its state immediate reward value. This continues until the target is reached. When the robot learns for a period of time, it can avoid those places where obstacles are often present when planning the path. By analyzing the simulation experiment, the algorithm has achieved good results in the global path planning under the dynamic environment.
Stochastic model of milk homogenization process using Markov's chain
Directory of Open Access Journals (Sweden)
A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
Pavement maintenance optimization model using Markov Decision Processes
Mandiartha, P.; Duffield, C. F.; Razelan, I. S. b. M.; Ismail, A. b. H.
2017-09-01
This paper presents an optimization model for selection of pavement maintenance intervention using a theory of Markov Decision Processes (MDP). There are some particular characteristics of the MDP developed in this paper which distinguish it from other similar studies or optimization models intended for pavement maintenance policy development. These unique characteristics include a direct inclusion of constraints into the formulation of MDP, the use of an average cost method of MDP, and the policy development process based on the dual linear programming solution. The limited information or discussions that are available on these matters in terms of stochastic based optimization model in road network management motivates this study. This paper uses a data set acquired from road authorities of state of Victoria, Australia, to test the model and recommends steps in the computation of MDP based stochastic optimization model, leading to the development of optimum pavement maintenance policy.
The exit-time problem for a Markov jump process
Burch, N.; D'Elia, M.; Lehoucq, R. B.
2014-12-01
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
Rate estimation in partially observed Markov jump processes with measurement errors
Amrein, Michael; Kuensch, Hans R.
2010-01-01
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion approximations. Markov chain Monte Carlo and particle filter type algorithms are introduced, which allow sampling from the posterior distribution of t...
Perturbation approach to scaled type Markov renewal processes with infinite mean
Pajor-Gyulai, Zsolt; Szász, Domokos
2010-01-01
Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary interest here is the asymptotic distribution of the Markovian parameter at time t \\to \\infty. The limit, of course, depends on the stationary distribution of the Markov chain. The results, however, are essentially different depending on whether the expectation...
Control Design for Untimed Petri Nets Using Markov Decision Processes
Directory of Open Access Journals (Sweden)
Cherki Daoui
2017-01-01
Full Text Available Design of control sequences for discrete event systems (DESs has been presented modelled by untimed Petri nets (PNs. PNs are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations and parallelisms. The domains of application include, but are not restricted to, manufacturing systems, computer science and transportation networks. We are motivated by the observation that such systems need to plan their production or services. The paper is more particularly concerned with control issues in uncertain environments when unexpected events occur or when control errors disturb the behaviour of the system. To deal with such uncertainties, a new approach based on discrete time Markov decision processes (MDPs has been proposed that associates the modelling power of PNs with the planning power of MDPs. Finally, the simulation results illustrate the benefit of our method from the computational point of view. (original abstract
Accelerated decomposition techniques for large discounted Markov decision processes
Larach, Abdelhadi; Chafik, S.; Daoui, C.
2017-12-01
Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.
Simulation-based algorithms for Markov decision processes
Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I
2013-01-01
Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...
Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?
Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.
2018-01-01
Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.
Bayesian inference for Markov jump processes with informative observations.
Golightly, Andrew; Wilkinson, Darren J
2015-04-01
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.
Markov Jump Processes Approximating a Non-Symmetric Generalized Diffusion
International Nuclear Information System (INIS)
Limić, Nedžad
2011-01-01
Consider a non-symmetric generalized diffusion X(⋅) in ℝ d determined by the differential operator A(x) = -Σ ij ∂ i a ij (x)∂ j + Σ i b i (x)∂ i . In this paper the diffusion process is approximated by Markov jump processes X n (⋅), in homogeneous and isotropic grids G n ⊂ℝ d , which converge in distribution in the Skorokhod space D([0,∞),ℝ d ) to the diffusion X(⋅). The generators of X n (⋅) are constructed explicitly. Due to the homogeneity and isotropy of grids, the proposed method for d≥3 can be applied to processes for which the diffusion tensor {a ij (x)} 11 dd fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric generalized diffusion. Simulations are carried out in terms of jump processes X n (⋅). For piece-wise constant functions a ij on ℝ d and piece-wise continuous functions a ij on ℝ 2 the construction and principal algorithm are described enabling an easy implementation into a computer code.
On the record process of time-reversible spectrally-negative Markov additive processes
J. Ivanovs; M.R.H. Mandjes (Michel)
2009-01-01
htmlabstractWe study the record process of a spectrally-negative Markov additive process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs
Discounted semi-Markov decision processes : linear programming and policy iteration
Wessels, J.; van Nunen, J.A.E.E.
1975-01-01
For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal
Discounted semi-Markov decision processes : linear programming and policy iteration
Wessels, J.; van Nunen, J.A.E.E.
1974-01-01
For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Students' Progress throughout Examination Process as a Markov Chain
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
International Nuclear Information System (INIS)
Kupchishin, A.A.; Kupchishin, A.I.; Shmygaleva, T.A.
2002-01-01
Within framework of the cascade-probabilistic (CP) method the radiation and physical processes are studied, theirs relation with Markov's processes are found. The conclusion that CP-function for electrons, protons, alpha-particles and ions are describing by unhomogeneous Markov's chain is drawn. The algorithms are developed, the CP-functions calculations for charged particles, concentration of radiation defects in solids at ion irradiation are carried out as well. Tables for CPF different parameters and radiation defects concentration at charged particle interaction with solids are given. The book consists of the introduction and two chapters: (1) Cascade probabilistic function and the Markov's processes; (2) Radiation defects formation in solids as a part of the Markov's processes. The book is intended for specialists on the radiation defects mathematical stimulation, solid state physics, elementary particles physics and applied mathematics
A Method for Speeding Up Value Iteration in Partially Observable Markov Decision Processes
Zhang, Nevin Lianwen; Lee, Stephen S.; Zhang, Weihong
2013-01-01
We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov decision processes (MDPs). The technique can be easily incorporated into any existing POMDP value iteration algorithms. Experiments have been conducted on several test problems with one POMDP value iteration algorithm called incremental pruning. We find that th...
On Markov processes in the hadron-nuclear and nuclear-nuclear collisions at superhigh energies
International Nuclear Information System (INIS)
Lebedeva, A.A.; Rus'kin, V.I.
2001-01-01
In the article the possibility of the Markov processes use as simulation method for mean characteristics of hadron-nuclear and nucleus-nuclear collisions at superhigh energies is discussed. The simple (hadron-nuclear collisions) and non-simple (nucleus-nuclear collisions) non-uniform Markov process of output constant spectrum and absorption in a nucleon's nucleus-target with rapidity y are considered. The expression allowing to simulate the different collision modes were obtained
Simulation based sequential Monte Carlo methods for discretely observed Markov processes
Neal, Peter
2014-01-01
Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective sequential Monte Carlo (SMC) algorithm for obtaining samples from the posterior distribution of the parameters. In particular, we introduce two key innovations, coupled simulations, which allow us to study multiple parameter values on the basis of a single sim...
Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks
Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming
2018-04-01
Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.
Properly quantized history-dependent Parrondo games, Markov processes, and multiplexing circuits
Energy Technology Data Exchange (ETDEWEB)
Bleiler, Steven A. [Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR 97207 (United States); Khan, Faisal Shah, E-mail: faisal.khan@kustar.ac.a [Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi (United Arab Emirates)
2011-05-09
Highlights: History-dependent Parrondo games are viewed as Markov processes. Quantum mechanical analogues of these Markov processes are constructed. These quantum analogues restrict to the original process on measurement. Relationship between these analogues and a quantum circuits is exhibited. - Abstract: In the context of quantum information theory, 'quantization' of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done 'properly', a faithful copy of the original construction is required to exist within the new quantum one, just as is required when a function is extended to a larger domain. Here procedures for extending history-dependent Parrondo games, Markov processes and multiplexing circuits to their quantum versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed.
Road maintenance optimization through a discrete-time semi-Markov decision process
International Nuclear Information System (INIS)
Zhang Xueqing; Gao Hui
2012-01-01
Optimization models are necessary for efficient and cost-effective maintenance of a road network. In this regard, road deterioration is commonly modeled as a discrete-time Markov process such that an optimal maintenance policy can be obtained based on the Markov decision process, or as a renewal process such that an optimal maintenance policy can be obtained based on the renewal theory. However, the discrete-time Markov process cannot capture the real time at which the state transits while the renewal process considers only one state and one maintenance action. In this paper, road deterioration is modeled as a semi-Markov process in which the state transition has the Markov property and the holding time in each state is assumed to follow a discrete Weibull distribution. Based on this semi-Markov process, linear programming models are formulated for both infinite and finite planning horizons in order to derive optimal maintenance policies to minimize the life-cycle cost of a road network. A hypothetical road network is used to illustrate the application of the proposed optimization models. The results indicate that these linear programming models are practical for the maintenance of a road network having a large number of road segments and that they are convenient to incorporate various constraints on the decision process, for example, performance requirements and available budgets. Although the optimal maintenance policies obtained for the road network are randomized stationary policies, the extent of this randomness in decision making is limited. The maintenance actions are deterministic for most states and the randomness in selecting actions occurs only for a few states.
Markov decision processes: a tool for sequential decision making under uncertainty.
Alagoz, Oguzhan; Hsu, Heather; Schaefer, Andrew J; Roberts, Mark S
2010-01-01
We provide a tutorial on the construction and evaluation of Markov decision processes (MDPs), which are powerful analytical tools used for sequential decision making under uncertainty that have been widely used in many industrial and manufacturing applications but are underutilized in medical decision making (MDM). We demonstrate the use of an MDP to solve a sequential clinical treatment problem under uncertainty. Markov decision processes generalize standard Markov models in that a decision process is embedded in the model and multiple decisions are made over time. Furthermore, they have significant advantages over standard decision analysis. We compare MDPs to standard Markov-based simulation models by solving the problem of the optimal timing of living-donor liver transplantation using both methods. Both models result in the same optimal transplantation policy and the same total life expectancies for the same patient and living donor. The computation time for solving the MDP model is significantly smaller than that for solving the Markov model. We briefly describe the growing literature of MDPs applied to medical decisions.
The application of Markov decision process with penalty function in restaurant delivery robot
Wang, Yong; Hu, Zhen; Wang, Ying
2017-05-01
As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional Markov decision process path planning algorithm is not save, the robot is very close to the table and chairs. To solve this problem, this paper proposes the Markov Decision Process with a penalty term called MDPPT path planning algorithm according to the traditional Markov decision process (MDP). For MDP, if the restaurant delivery robot bumps into an obstacle, the reward it receives is part of the current status reward. For the MDPPT, the reward it receives not only the part of the current status but also a negative constant term. Simulation results show that the MDPPT algorithm can plan a more secure path.
Nonlinear filtering for LIDAR signal processing
Directory of Open Access Journals (Sweden)
D. G. Lainiotis
1996-01-01
Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.
Abhinav, S.; Manohar, C. S.
2018-03-01
The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.
Continuous strong Markov processes in dimension one a stochastic calculus approach
Assing, Sigurd
1998-01-01
The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.
An integrated Markov decision process and nested logit consumer response model of air ticket pricing
Lu, J.; Feng, T.; Timmermans, H.P.J.; Yang, Z.
2017-01-01
The paper attempts to propose an optimal air ticket pricing model during the booking horizon by taking into account passengers' purchasing behavior of air tickets. A Markov decision process incorporating a nested logit consumer response model is established to modeling the dynamic pricing process.
Efficient tests for equivalence of hidden Markov processes and quantum random walks
U. Faigle; A. Schönhuth (Alexander)
2011-01-01
htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations
Multiorder nonlinear diffraction in frequency doubling processes
DEFF Research Database (Denmark)
Saltiel, Solomon M.; Neshev, Dragomir N.; Krolikowski, Wieslaw
2009-01-01
We analyze experimentally light scattering from 2 nonlinear gratings and observe two types of second-harmonic frequency-scattering processes. The first process is identified as Raman–Nath type nonlinear diffraction that is explained by applying only transverse phase-matching conditions. The angular...... position of this type of diffraction is defined by the ratio of the second-harmonic wavelength and the grating period. In contrast, the second type of nonlinear scattering process is explained by the longitudinal phase matching only, being insensitive to the nonlinear grating...
Theory and Applications of Weakly Interacting Markov Processes
2018-02-03
between a node and its neighbor is inversely 3 proportional to the total number of neighbors of that node. Such stochastic systems arise in many different...jumps and models with simultaneous jumps that arise in applications. (1.ii.d) Uniform in Time Interacting Particle Approximations for Nonlinear...problems. (1.iv.a) Diffusion Approximations for Controlled Weakly Interacting Large Finite State Systems with Simultaneous Jumps [25]. We consider a rate
Nonlinear transformations of random processes
Deutsch, Ralph
2017-01-01
This concise treatment of nonlinear noise techniques encountered in system applications is suitable for advanced undergraduates and graduate students. It is also a valuable reference for systems analysts and communication engineers. 1962 edition.
Markov Processes: Exploring the Use of Dynamic Visualizations to Enhance Student Understanding
Pfannkuch, Maxine; Budgett, Stephanie
2016-01-01
Finding ways to enhance introductory students' understanding of probability ideas and theory is a goal of many first-year probability courses. In this article, we explore the potential of a prototype tool for Markov processes using dynamic visualizations to develop in students a deeper understanding of the equilibrium and hitting times…
Data-based inference of generators for Markov jump processes using convex optimization
D.T. Crommelin (Daan); E. Vanden-Eijnden (Eric)
2009-01-01
textabstractA variational approach to the estimation of generators for Markov jump processes from discretely sampled data is discussed and generalized. In this approach, one first calculates the spectrum of the discrete maximum likelihood estimator for the transition matrix consistent with
Strategy Complexity of Finite-Horizon Markov Decision Processes and Simple Stochastic Games
DEFF Research Database (Denmark)
Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu
2012-01-01
Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to maximize the probability to reach a target state in a given...
Joseph Buongiorno; Mo Zhou; Craig Johnston
2017-01-01
Markov decision process models were extended to reflect some consequences of the risk attitude of forestry decision makers. One approach consisted of maximizing the expected value of a criterion subject to an upper bound on the variance or, symmetrically, minimizing the variance subject to a lower bound on the expected value.Â The other method used the certainty...
Spectral analysis of multi-dimensional self-similar Markov processes
International Nuclear Information System (INIS)
Modarresi, N; Rezakhah, S
2010-01-01
In this paper we consider a discrete scale invariant (DSI) process {X(t), t in R + } with scale l > 1. We consider a fixed number of observations in every scale, say T, and acquire our samples at discrete points α k , k in W, where α is obtained by the equality l = α T and W = {0, 1, ...}. We thus provide a discrete time scale invariant (DT-SI) process X(.) with the parameter space {α k , k in W}. We find the spectral representation of the covariance function of such a DT-SI process. By providing the harmonic-like representation of multi-dimensional self-similar processes, spectral density functions of them are presented. We assume that the process {X(t), t in R + } is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of the DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally, we find the spectral density matrix of such a DT-SIM process and show that its associated T-dimensional self-similar Markov process is fully specified by {R H j (1), R j H (0), j = 0, 1, ..., T - 1}, where R H j (τ) is the covariance function of jth and (j + τ)th observations of the process.
Reliability analysis of nuclear component cooling water system using semi-Markov process model
International Nuclear Information System (INIS)
Veeramany, Arun; Pandey, Mahesh D.
2011-01-01
Research highlights: → Semi-Markov process (SMP) model is used to evaluate system failure probability of the nuclear component cooling water (NCCW) system. → SMP is used because it can solve reliability block diagram with a mixture of redundant repairable and non-repairable components. → The primary objective is to demonstrate that SMP can consider Weibull failure time distribution for components while a Markov model cannot → Result: the variability in component failure time is directly proportional to the NCCW system failure probability. → The result can be utilized as an initiating event probability in probabilistic safety assessment projects. - Abstract: A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.
Broadband Nonlinear Signal Processing in Silicon Nanowires
DEFF Research Database (Denmark)
Yvind, Kresten; Pu, Minhao; Hvam, Jørn Märcher
The fast non-linearity of silicon allows Tbit/s optical signal processing. By choosing suitable dimensions of silicon nanowires their dispersion can be tailored to ensure a high nonlinearity at power levels low enough to avoid significant two-photon abso We have fabricated low insertion...
Input saturation in nonlinear multivariable processes resolved by nonlinear decoupling
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1995-04-01
Full Text Available A new method is presented for the resolution of the problem of input saturation in nonlinear multivariable process control by means of elementary nonlinear decoupling (END. Input saturation can have serious consequences particularly in multivariable control because it may lead to very undesirable system behaviour and quite often system instability. Many authors have searched for systematic techniques for designing multivariable control systems in which saturation may occur in any of the control variables (inputs, manipulated variables. No generally accepted method seems to have been presented so far which gives a solution in closed form. The method of elementary nonlinear decoupling (END can be applied directly to the case of saturation control variables by deriving as many control strategies as there are combinations of saturating control variables. The method is demonstrated by the multivariable control of a simulated Fluidized Catalytic Cracker (FCC with very convincing results.
Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain
Directory of Open Access Journals (Sweden)
Victor Kravets
2016-05-01
Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.
Non-parametric Bayesian inference for inhomogeneous Markov point processes
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper; Johansen, Per Michael
is a shot noise process, and the interaction function for a pair of points depends only on the distance between the two points and is a piecewise linear function modelled by a marked Poisson process. Simulation of the resulting posterior using a Metropolis-Hastings algorithm in the "conventional" way...
Chen, Baojiang; Zhou, Xiao-Hua
2013-05-01
Life history data arising in clusters with prespecified assessment time points for patients often feature incomplete data since patients may choose to visit the clinic based on their needs. Markov process models provide a useful tool describing disease progression for life history data. The literature mainly focuses on time homogeneous process. In this paper we develop methods to deal with non-homogeneous Markov process with incomplete clustered life history data. A correlated random effects model is developed to deal with the nonignorable missingness, and a time transformation is employed to address the non-homogeneity in the transition model. Maximum likelihood estimate based on the Monte-Carlo EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well in many situations. We also apply this method to an Alzheimer's disease study.
Burkatovskaya, Yuliya Borisovna; Kabanova, T.; Khaustov, Pavel Aleksandrovich
2016-01-01
CUSUM algorithm for controlling chain state switching in the Markov modulated Poissonprocess was investigated via simulation. Recommendations concerning the parameter choice were givensubject to characteristics of the process. Procedure of the process parameter estimation was described.
Generalization bounds of ERM-based learning processes for continuous-time Markov chains.
Zhang, Chao; Tao, Dacheng
2012-12-01
Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.
The Langevin Approach: An R Package for Modeling Markov Processes
Directory of Open Access Journals (Sweden)
Philip Rinn
2016-08-01
Full Text Available We describe an 'R' package developed by the research group 'Turbulence, Wind energy' 'and Stochastics' (TWiSt at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
The Markov process admits a consistent steady-state thermodynamic formalism
Peng, Liangrong; Zhu, Yi; Hong, Liu
2018-01-01
The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.
A fast exact simulation method for a class of Markov jump processes.
Li, Yao; Hu, Lili
2015-11-14
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.
Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process
International Nuclear Information System (INIS)
Skorobogatov, G.A.; Svertilov, S.I.
1999-01-01
The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru
Scalable approximate policies for Markov decision process models of hospital elective admissions.
Zhu, George; Lizotte, Dan; Hoey, Jesse
2014-05-01
To demonstrate the feasibility of using stochastic simulation methods for the solution of a large-scale Markov decision process model of on-line patient admissions scheduling. The problem of admissions scheduling is modeled as a Markov decision process in which the states represent numbers of patients using each of a number of resources. We investigate current state-of-the-art real time planning methods to compute solutions to this Markov decision process. Due to the complexity of the model, traditional model-based planners are limited in scalability since they require an explicit enumeration of the model dynamics. To overcome this challenge, we apply sample-based planners along with efficient simulation techniques that given an initial start state, generate an action on-demand while avoiding portions of the model that are irrelevant to the start state. We also propose a novel variant of a popular sample-based planner that is particularly well suited to the elective admissions problem. Results show that the stochastic simulation methods allow for the problem size to be scaled by a factor of almost 10 in the action space, and exponentially in the state space. We have demonstrated our approach on a problem with 81 actions, four specialities and four treatment patterns, and shown that we can generate solutions that are near-optimal in about 100s. Sample-based planners are a viable alternative to state-based planners for large Markov decision process models of elective admissions scheduling. Copyright © 2014 Elsevier B.V. All rights reserved.
Yamada, Yuhei; Yamazaki, Yoshihiro
2018-04-01
This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.
Assistive system for people with Apraxia using a Markov decision process.
Jean-Baptiste, Emilie M D; Russell, Martin; Rothstein, Pia
2014-01-01
CogWatch is an assistive system to re-train stroke survivors suffering from Apraxia or Action Disorganization Syndrome (AADS) to complete activities of daily living (ADLs). This paper describes the approach to real-time planning based on a Markov Decision Process (MDP), and demonstrates its ability to improve task's performance via user simulation. The paper concludes with a discussion of the remaining challenges and future enhancements.
«Concurrency» in M-L-Parallel Semi-Markov Process
Directory of Open Access Journals (Sweden)
Larkin Eugene
2017-01-01
Full Text Available This article investigates the functioning of a swarm of robots, each of which receives instructions from the external human operator and autonomously executes them. An abstract model of functioning of a robot, a group of robots and multiple groups of robots was obtained using the notion of semi-Markov process. The concepts of aggregated initial and aggregated absorbing states were introduced. Correspondences for calculation of time parameters of concurrency were obtained.
The Green-Kubo formula for general Markov processes with a continuous time parameter
International Nuclear Information System (INIS)
Yang Fengxia; Liu Yong; Chen Yong
2010-01-01
For general Markov processes, the Green-Kubo formula is shown to be valid under a mild condition. A class of stochastic evolution equations on a separable Hilbert space and three typical infinite systems of locally interacting diffusions on Z d (irreversible in most cases) are shown to satisfy the Green-Kubo formula, and the Einstein relations for these stochastic evolution equations are shown explicitly as a corollary.
Image processing with a cellular nonlinear network
International Nuclear Information System (INIS)
Morfu, S.
2005-01-01
A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented
Generalization of the Wide-Sense Markov Concept to a Widely Linear Processing
International Nuclear Information System (INIS)
Espinosa-Pulido, Juan Antonio; Navarro-Moreno, Jesús; Fernández-Alcalá, Rosa María; Ruiz-Molina, Juan Carlos; Oya-Lechuga, Antonia; Ruiz-Fuentes, Nuria
2014-01-01
In this paper we show that the classical definition and the associated characterizations of wide-sense Markov (WSM) signals are not valid for improper complex signals. For that, we propose an extension of the concept of WSM to a widely linear (WL) setting and the study of new characterizations. Specifically, we introduce a new class of signals, called widely linear Markov (WLM) signals, and we analyze some of their properties based either on second-order properties or on state-space models from a WL processing standpoint. The study is performed in both the forwards and backwards directions of time. Thus, we provide two forwards and backwards Markovian representations for WLM signals. Finally, different estimation recursive algorithms are obtained for these models
A reward semi-Markov process with memory for wind speed modeling
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. The primary goal of this analysis is the study of the time history of the wind in order to assess its reliability as a source of power and to determine the associated storage levels required. In order to assess this issue we use a probabilistic model based on indexed semi-Markov process [4] to which a reward structure is attached. Our model is used to calculate the expected energy produced by a given turbine and its variability expressed by the variance of the process. Our results can be used to compare different wind farms based on their reward and also on the risk of missed production due to the intrinsic variability of the wind speed process. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and backtesting procedure is used to compare results on first and second oder moments of rewards between real and synthetic data. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic gen- eration of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Re- newable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribu- tion, Renewable Energy 28 (2003) 1787-1802. [4]F. Petroni, G. D'Amico, F. Prattico, Indexed semi-Markov process for wind speed modeling. To be submitted.
Availability Control for Means of Transport in Decisive Semi-Markov Models of Exploitation Process
Migawa, Klaudiusz
2012-12-01
The issues presented in this research paper refer to problems connected with the control process for exploitation implemented in the complex systems of exploitation for technical objects. The article presents the description of the method concerning the control availability for technical objects (means of transport) on the basis of the mathematical model of the exploitation process with the implementation of the decisive processes by semi-Markov. The presented method means focused on the preparing the decisive for the exploitation process for technical objects (semi-Markov model) and after that specifying the best control strategy (optimal strategy) from among possible decisive variants in accordance with the approved criterion (criteria) of the activity evaluation of the system of exploitation for technical objects. In the presented method specifying the optimal strategy for control availability in the technical objects means a choice of a sequence of control decisions made in individual states of modelled exploitation process for which the function being a criterion of evaluation reaches the extreme value. In order to choose the optimal control strategy the implementation of the genetic algorithm was chosen. The opinions were presented on the example of the exploitation process of the means of transport implemented in the real system of the bus municipal transport. The model of the exploitation process for the means of transports was prepared on the basis of the results implemented in the real transport system. The mathematical model of the exploitation process was built taking into consideration the fact that the model of the process constitutes the homogenous semi-Markov process.
van Otterlo, M.
2008-01-01
Learning and reasoning in large, structured, probabilistic worlds is at the heart of artificial intelligence. Markov decision processes have become the de facto standard in modeling and solving sequential decision making problems under uncertainty. Many efficient reinforcement learning and dynamic
Reduced equations of motion for quantum systems driven by diffusive Markov processes.
Sarovar, Mohan; Grace, Matthew D
2012-09-28
The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.
A hierarchical Markov decision process modeling feeding and marketing decisions of growing pigs
DEFF Research Database (Denmark)
Pourmoayed, Reza; Nielsen, Lars Relund; Kristensen, Anders Ringgaard
2016-01-01
Feeding is the most important cost in the production of growing pigs and has a direct impact on the marketing decisions, growth and the final quality of the meat. In this paper, we address the sequential decision problem of when to change the feed-mix within a finisher pig pen and when to pick pigs...... for marketing. We formulate a hierarchical Markov decision process with three levels representing the decision process. The model considers decisions related to feeding and marketing and finds the optimal decision given the current state of the pen. The state of the system is based on information from on...
Markov-modulated infinite-server queues driven by a common background process
Mandjes , Michel; De Turck , Koen
2016-01-01
International audience; This paper studies a system with multiple infinite-server queues which are modulated by a common background process. If this background process, being modeled as a finite-state continuous-time Markov chain, is in state j, then the arrival rate into the i-th queue is λi,j, whereas the service times of customers present in this queue are exponentially distributed with mean µ −1 i,j ; at each of the individual queues all customers present are served in parallel (thus refl...
Ultrafast Nonlinear Signal Processing in Silicon Waveguides
DEFF Research Database (Denmark)
Oxenløwe, Leif Katsuo; Mulvad, Hans Christian Hansen; Hu, Hao
2012-01-01
We describe recent demonstrations of exploiting highly nonlinear silicon waveguides for ultrafast optical signal processing. We describe wavelength conversion and serial-to-parallel conversion of 640 Gbit/s data signals and 1.28 Tbit/s demultiplexing and all-optical sampling.......We describe recent demonstrations of exploiting highly nonlinear silicon waveguides for ultrafast optical signal processing. We describe wavelength conversion and serial-to-parallel conversion of 640 Gbit/s data signals and 1.28 Tbit/s demultiplexing and all-optical sampling....
A Multi-stage Representation of Cell Proliferation as a Markov Process.
Yates, Christian A; Ford, Matthew J; Mort, Richard L
2017-12-01
The stochastic simulation algorithm commonly known as Gillespie's algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie's algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular
Graph theoretical calculation of systems reliability with semi-Markov processes
International Nuclear Information System (INIS)
Widmer, U.
1984-06-01
The determination of the state probabilities and related quantities of a system characterized by an SMP (or a homogeneous MP) can be performed by means of graph-theoretical methods. The calculation procedures for semi-Markov processes based on signal flow graphs are reviewed. Some methods from electrotechnics are adapted in order to obtain a representation of the state probabilities by means of trees. From this some formulas are derived for the asymptotic state probabilities and for the mean life-time in reliability considerations. (Auth.)
International Nuclear Information System (INIS)
Lemons, Don S.
2012-01-01
We develop a Markov process theory of charged particle scattering from stationary, transverse, magnetic waves. We examine approximations that lead to quasilinear theory, in particular the resonant diffusion approximation. We find that, when appropriate, the resonant diffusion approximation simplifies the result of the weak turbulence approximation without significant further restricting the regime of applicability. We also explore a theory generated by expanding drift and diffusion rates in terms of a presumed small correlation time. This small correlation time expansion leads to results valid for relatively small pitch angle and large wave energy density - a regime that may govern pitch angle scattering of high-energy electrons into the geomagnetic loss cone.
Detection of Text Lines of Handwritten Arabic Manuscripts using Markov Decision Processes
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Youssef Boulid
2016-09-01
Full Text Available In a character recognition systems, the segmentation phase is critical since the accuracy of the recognition depend strongly on it. In this paper we present an approach based on Markov Decision Processes to extract text lines from binary images of Arabic handwritten documents. The proposed approach detects the connected components belonging to the same line by making use of knowledge about features and arrangement of those components. The initial results show that the system is promising for extracting Arabic handwritten lines.
Energy Technology Data Exchange (ETDEWEB)
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Institut de Mathématiques de Bordeaux, INRIA Bordeaux Sud Ouest, Team: CQFD, and IMB (France); Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es [UNED, Department of Statistics and Operations Research (Spain)
2016-08-15
We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.
Quantum Information Processing using Nonlinear Optical Effects
DEFF Research Database (Denmark)
Andersen, Lasse Mejling
This PhD thesis treats applications of nonlinear optical effects for quantum information processing. The two main applications are four-wave mixing in the form of Bragg scattering (BS) for quantum-state-preserving frequency conversion, and sum-frequency generation (SFG) in second-order nonlinear......-chirping the pumps. In the high-conversion regime without the effects of NPM, exact Green functions for BS are derived. In this limit, separability is possible for conversion efficiencies up to 60 %. However, the system still allows for selective frequency conversion as well as re-shaping of the output. One way...
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
Recent advances in nonlinear speech processing
Faundez-Zanuy, Marcos; Esposito, Antonietta; Cordasco, Gennaro; Drugman, Thomas; Solé-Casals, Jordi; Morabito, Francesco
2016-01-01
This book presents recent advances in nonlinear speech processing beyond nonlinear techniques. It shows that it exploits heuristic and psychological models of human interaction in order to succeed in the implementations of socially believable VUIs and applications for human health and psychological support. The book takes into account the multifunctional role of speech and what is “outside of the box” (see Björn Schuller’s foreword). To this aim, the book is organized in 6 sections, each collecting a small number of short chapters reporting advances “inside” and “outside” themes related to nonlinear speech research. The themes emphasize theoretical and practical issues for modelling socially believable speech interfaces, ranging from efforts to capture the nature of sound changes in linguistic contexts and the timing nature of speech; labors to identify and detect speech features that help in the diagnosis of psychological and neuronal disease, attempts to improve the effectiveness and performa...
Chen, Baojiang; Zhou, Xiao-Hua
2011-05-01
Identifying risk factors for transition rates among normal cognition, mildly cognitive impairment, dementia and death in an Alzheimer's disease study is very important. It is known that transition rates among these states are strongly time dependent. While Markov process models are often used to describe these disease progressions, the literature mainly focuses on time homogeneous processes, and limited tools are available for dealing with non-homogeneity. Further, patients may choose when they want to visit the clinics, which creates informative observations. In this paper, we develop methods to deal with non-homogeneous Markov processes through time scale transformation when observation times are pre-planned with some observations missing. Maximum likelihood estimation via the EM algorithm is derived for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. An application to the Alzheimer's disease study identifies that there is a significant increase in transition rates as a function of time. Furthermore, our models reveal that the non-ignorable missing mechanism is perhaps reasonable. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
International Nuclear Information System (INIS)
Costa, O. L. V.; Dufour, F.
2011-01-01
This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP’s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ n . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.
Detection of bursts in extracellular spike trains using hidden semi-Markov point process models.
Tokdar, Surya; Xi, Peiyi; Kelly, Ryan C; Kass, Robert E
2010-08-01
Neurons in vitro and in vivo have epochs of bursting or "up state" activity during which firing rates are dramatically elevated. Various methods of detecting bursts in extracellular spike trains have appeared in the literature, the most widely used apparently being Poisson Surprise (PS). A natural description of the phenomenon assumes (1) there are two hidden states, which we label "burst" and "non-burst," (2) the neuron evolves stochastically, switching at random between these two states, and (3) within each state the spike train follows a time-homogeneous point process. If in (2) the transitions from non-burst to burst and burst to non-burst states are memoryless, this becomes a hidden Markov model (HMM). For HMMs, the state transitions follow exponential distributions, and are highly irregular. Because observed bursting may in some cases be fairly regular-exhibiting inter-burst intervals with small variation-we relaxed this assumption. When more general probability distributions are used to describe the state transitions the two-state point process model becomes a hidden semi-Markov model (HSMM). We developed an efficient Bayesian computational scheme to fit HSMMs to spike train data. Numerical simulations indicate the method can perform well, sometimes yielding very different results than those based on PS.
Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes
Directory of Open Access Journals (Sweden)
Tomoaki Nakamura
2017-12-01
Full Text Available Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM, the emission distributions of which are Gaussian processes (GPs. Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods.
Internal Decoupling in Nonlinear Process Control
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Jens G. Balchen
1988-07-01
Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.
Combining experimental and simulation data of molecular processes via augmented Markov models.
Olsson, Simon; Wu, Hao; Paul, Fabian; Clementi, Cecilia; Noé, Frank
2017-08-01
Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few [Formula: see text], which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.
Data-Driven Markov Decision Process Approximations for Personalized Hypertension Treatment Planning
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Greggory J. Schell PhD
2016-10-01
Full Text Available Background: Markov decision process (MDP models are powerful tools. They enable the derivation of optimal treatment policies but may incur long computational times and generate decision rules that are challenging to interpret by physicians. Methods: In an effort to improve usability and interpretability, we examined whether Poisson regression can approximate optimal hypertension treatment policies derived by an MDP for maximizing a patient’s expected discounted quality-adjusted life years. Results: We found that our Poisson approximation to the optimal treatment policy matched the optimal policy in 99% of cases. This high accuracy translates to nearly identical health outcomes for patients. Furthermore, the Poisson approximation results in 104 additional quality-adjusted life years per 1000 patients compared to the Seventh Joint National Committee’s treatment guidelines for hypertension. The comparative health performance of the Poisson approximation was robust to the cardiovascular disease risk calculator used and calculator calibration error. Limitations: Our results are based on Markov chain modeling. Conclusions: Poisson model approximation for blood pressure treatment planning has high fidelity to optimal MDP treatment policies, which can improve usability and enhance transparency of more personalized treatment policies.
Directory of Open Access Journals (Sweden)
Yanfeng Wang
2017-01-01
Full Text Available This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay and the time-delay from controller to actuator (C-A delay, respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.
A Novel Analytical Model for Network-on-Chip using Semi-Markov Process
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WANG, J.
2011-02-01
Full Text Available Network-on-Chip (NoC communication architecture is proposed to resolve the bottleneck of Multi-processor communication in a single chip. In this paper, a performance analytical model using Semi-Markov Process (SMP is presented to obtain the NoC performance. More precisely, given the related parameters, SMP is used to describe the behavior of each channel and the header flit routing time on each channel can be calculated by analyzing the SMP. Then, the average packet latency in NoC can be calculated. The accuracy of our model is illustrated through simulation. Indeed, the experimental results show that the proposed model can be used to obtain NoC performance and it performs better than the state-of-art models. Therefore, our model can be used as a useful tool to guide the NoC design process.
Numerical construction of the p(fold) (committor) reaction coordinate for a Markov process.
Krivov, Sergei V
2011-10-06
To simplify the description of a complex multidimensional dynamical process, one often projects it onto a single reaction coordinate. In protein folding studies, the folding probability p(fold) is an optimal reaction coordinate which preserves many important properties of the dynamics. The construction of the coordinate is difficult. Here, an efficient numerical approach to construct the p(fold) reaction coordinate for a Markov process (satisfying the detailed balance) is described. The coordinate is obtained by optimizing parameters of a chosen functional form to make a generalized cut-based free energy profile the highest. The approach is illustrated by constructing the p(fold) reaction coordinate for the equilibrium folding simulation of FIP35 protein reported by Shaw et al. (Science 2010, 330, 341-346). © 2011 American Chemical Society
Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Bordeaux INP, IMB, UMR CNRS 5251 (France); Piunovskiy, A. B., E-mail: piunov@liv.ac.uk [University of Liverpool, Department of Mathematical Sciences (United Kingdom)
2016-08-15
In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.
First Passage Moments of Finite-State Semi-Markov Processes
Energy Technology Data Exchange (ETDEWEB)
Warr, Richard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Cordeiro, James [Air Force Research Lab. (AFRL), Wright-Patterson AFB, OH (United States)
2014-03-31
In this paper, we discuss the computation of first-passage moments of a regular time-homogeneous semi-Markov process (SMP) with a finite state space to certain of its states that possess the property of universal accessibility (UA). A UA state is one which is accessible from any other state of the SMP, but which may or may not connect back to one or more other states. An important characteristic of UA is that it is the state-level version of the oft-invoked process-level property of irreducibility. We adapt existing results for irreducible SMPs to the derivation of an analytical matrix expression for the first passage moments to a single UA state of the SMP. In addition, consistent point estimators for these first passage moments, together with relevant R code, are provided.
Modeling treatment of ischemic heart disease with partially observable Markov decision processes.
Hauskrecht, M; Fraser, H
1998-01-01
Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead they are very often dependent and interleaved over time, mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of Partially observable Markov decision processes (POMDPs) developed and used in operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In the paper, we show how the POMDP framework could be used to model and solve the problem of the management of patients with ischemic heart disease, and point out modeling advantages of the framework over standard decision formalisms.
Planning treatment of ischemic heart disease with partially observable Markov decision processes.
Hauskrecht, M; Fraser, H
2000-03-01
Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead, they are very often dependent and interleaved over time. This is mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of partially observable Markov decision processes (POMDPs) developed and used in the operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In this paper, we show how the POMDP framework can be used to model and solve the problem of the management of patients with ischemic heart disease (IHD), and demonstrate the modeling advantages of the framework over standard decision formalisms.
A high-fidelity weather time series generator using the Markov Chain process on a piecewise level
Hersvik, K.; Endrerud, O.-E. V.
2017-12-01
A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.
Dynamic Request Routing for Online Video-on-Demand Service: A Markov Decision Process Approach
Directory of Open Access Journals (Sweden)
Jianxiong Wan
2014-01-01
Full Text Available We investigate the request routing problem in the CDN-based Video-on-Demand system. We model the system as a controlled queueing system including a dispatcher and several edge servers. The system is formulated as a Markov decision process (MDP. Since the MDP formulation suffers from the so-called “the curse of dimensionality” problem, we then develop a greedy heuristic algorithm, which is simple and can be implemented online, to approximately solve the MDP model. However, we do not know how far it deviates from the optimal solution. To address this problem, we further aggregate the state space of the original MDP model and use the bounded-parameter MDP (BMDP to reformulate the system. This allows us to obtain a suboptimal solution with a known performance bound. The effectiveness of two approaches is evaluated in a simulation study.
Sieve estimation in a Markov illness-death process under dual censoring.
Boruvka, Audrey; Cook, Richard J
2016-04-01
Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Wind Farm Reliability Modelling Using Bayesian Networks and Semi-Markov Processes
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Robert Adam Sobolewski
2015-09-01
Full Text Available Technical reliability plays an important role among factors affecting the power output of a wind farm. The reliability is determined by an internal collection grid topology and reliability of its electrical components, e.g. generators, transformers, cables, switch breakers, protective relays, and busbars. A wind farm reliability’s quantitative measure can be the probability distribution of combinations of operating and failed states of the farm’s wind turbines. The operating state of a wind turbine is its ability to generate power and to transfer it to an external power grid, which means the availability of the wind turbine and other equipment necessary for the power transfer to the external grid. This measure can be used for quantitative analysis of the impact of various wind farm topologies and the reliability of individual farm components on the farm reliability, and for determining the expected farm output power with consideration of the reliability. This knowledge may be useful in an analysis of power generation reliability in power systems. The paper presents probabilistic models that quantify the wind farm reliability taking into account the above-mentioned technical factors. To formulate the reliability models Bayesian networks and semi-Markov processes were used. Using Bayesian networks the wind farm structural reliability was mapped, as well as quantitative characteristics describing equipment reliability. To determine the characteristics semi-Markov processes were used. The paper presents an example calculation of: (i probability distribution of the combination of both operating and failed states of four wind turbines included in the wind farm, and (ii expected wind farm output power with consideration of its reliability.
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.
Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J
2018-03-01
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.
Transportation and concentration inequalities for bifurcating Markov chains
DEFF Research Database (Denmark)
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Mo Zhou; Joseph Buongiorno
2011-01-01
Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...
Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process.
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.
Lerner, Vladimir S.
2012-01-01
The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information ...
Mapping absorption processes onto a Markov chain, conserving the mean first passage time
International Nuclear Information System (INIS)
Biswas, Katja
2013-01-01
The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k′; t, t + dt) between a set of states {k} represented by the regions {ζ k } in phase or discrete state space. Depending on the dynamics Γ i (t) of the original process and the choice of ζ k , the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates W-bar (k→k ' ) can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities p-bar (k ' |k) is derived based on either time-discrete measurements {t i } with variable time stepping Δ (i+1)i = t i+1 − t i or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory. (paper)
Kinjo, Ken; Uchibe, Eiji; Doya, Kenji
2013-01-01
Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.
Nonlinear dynamic processes in modified ionospheric plasma
Kochetov, A.; Terina, G.
Presented work is a contribution to the experimental and theoretical study of nonlinear effects arising on ionospheric plasma under the action of powerful radio emission (G.I. Terina, J. Atm. Terr. Phys., 1995, v.57, p.273; A.V. Kochetov et. al., Advances in Space Research, 2002, in press). The experimental results were obtained by the method of sounding of artificially disturbed ionosphere by short radio pulses. The amplitude and phase characteristics of scattered signal as of "caviton" type (CS) (analogy of narrow-band component of stimulation electromagnetic emission (SEE)) as the main signal (MS) of probing transmitter are considered. The theoretical model is based on numerical solution of driven nonlinear Shrödinger equation (NSE) in inhomogeneous plasma. The simulation allows us to study a self-consistent spatial-temporal dynamics of field and plasma. The observed evolution of phase characteristics of MS and CS qualitatively correspond to the results of numerical simulation and demonstrate the penetration processes of powerful electromagnetic wave in supercritical (in linear approach) plasma regions. The modeling results explain also the periodic generation of CS, the travel CS maximum down to density gradient, the aftereffect of CS. The obtained results show the excitation of strong turbulence and allow us to interpret CS, NC and so far inexplicable phenomena as "spikes" too. The work was supported in part by Russian Foundation for Basic Research (grants Nos. 99-02-16642, 99-02- 16399).
Corrugated Membrane Nonlinear Deformation Process Calculation
Directory of Open Access Journals (Sweden)
A. S. Nikolaeva
2015-01-01
Full Text Available Elastic elements are widely used in instrumentation. They are used to create a particular interference between the parts, for accumulating mechanical energy, as the motion transmission elements, elastic supports, and sensing elements of measuring devices. Device reliability and quality depend on the calculation accuracy of the elastic elements. A corrugated membrane is rather common embodiment of the elastic element.The corrugated membrane properties depend largely on its profile i.e. a generatrix of the meridian surface.Unlike other types of pressure elastic members (bellows, tube spring, the elastic characteristics of which are close to linear, an elastic characteristic of the corrugated membrane (typical movement versus external load is nonlinear. Therefore, the corrugated membranes can be used to measure quantities, nonlinearly related to the pressure (e.g., aircraft air speed, its altitude, pipeline fluid or gas flow rate. Another feature of the corrugated membrane is that significant movements are possible within the elastic material state. However, a significant non-linearity of membrane characteristics leads to severe complicated calculation.This article is aimed at calculating the corrugated membrane to obtain the elastic characteristics and the deformed shape of the membrane meridian, as well as at investigating the processes of buckling. As the calculation model, a thin-walled axisymmetric shell rotation is assumed. The material properties are linearly elastic. We consider a corrugated membrane of sinusoidal profile. The membrane load is a uniform pressure.The algorithm for calculating the mathematical model of an axisymmetric corrugated membrane of constant thickness, based on the Reissner’s theory of elastic thin shells, was realized as the author's program in C language. To solve the nonlinear problem were used a method of changing the subspace of control parameters, developed by S.S., Gavriushin, and a parameter marching method
Directory of Open Access Journals (Sweden)
Gerich M. S.
2012-12-01
Full Text Available Let ${xi(t, x(t}$ be a homogeneous semi-continuous lattice Poisson process on the Markov chain.The jumps of one sign are geometrically distributed, and jumps of the opposite sign are arbitrary latticed distribution. For a suchprocesses the relations for the components of two-sided matrix factorization are established.This relations define the moment genereting functions for extremumf of the process and their complements.
Markov-CA model using analytical hierarchy process and multiregression technique
International Nuclear Information System (INIS)
Omar, N Q; Sanusi, S A M; Hussin, W M W; Samat, N; Mohammed, K S
2014-01-01
The unprecedented increase in population and rapid rate of urbanisation has led to extensive land use changes. Cellular automata (CA) are increasingly used to simulate a variety of urban dynamics. This paper introduces a new CA based on an integration model built-in multi regression and multi-criteria evaluation to improve the representation of CA transition rule. This multi-criteria evaluation is implemented by utilising data relating to the environmental and socioeconomic factors in the study area in order to produce suitability maps (SMs) using an analytical hierarchical process, which is a well-known method. Before being integrated to generate suitability maps for the periods from 1984 to 2010 based on the different decision makings, which have become conditioned for the next step of CA generation. The suitability maps are compared in order to find the best maps based on the values of the root equation (R 2 ). This comparison can help the stakeholders make better decisions. Thus, the resultant suitability map derives a predefined transition rule for the last step for CA model. The approach used in this study highlights a mechanism for monitoring and evaluating land-use and land-cover changes in Kirkuk city, Iraq owing changes in the structures of governments, wars, and an economic blockade over the past decades. The present study asserts the high applicability and flexibility of Markov-CA model. The results have shown that the model and its interrelated concepts are performing rather well
Directory of Open Access Journals (Sweden)
Eric A Zilli
2008-12-01
Full Text Available Behavioral tasks are often used to study the different memory systems present in humans and animals. Such tasks are usually designed to isolate and measure some aspect of a single memory system. However, it is not necessarily clear that any given task actually does isolate a system or that the strategy used by a subject in the experiment is the one desired by the experimenter. We have previously shown that when tasks are written mathematically as a form of partially-observable Markov decision processes, the structure of the tasks provide information regarding the possible utility of certain memory systems. These previous analyses dealt with the disambiguation problem: given a specific ambiguous observation of the environment, is there information provided by a given memory strategy that can disambiguate that observation to allow a correct decisionµ Here we extend this approach to cases where multiple memory systems can be strategically combined in different ways. Specifically, we analyze the disambiguation arising from three ways by which episodic-like memory retrieval might be cued (by another episodic-like memory, by a semantic association, or by working memory for some earlier observation. We also consider the disambiguation arising from holding earlier working memories, episodic-like memories or semantic associations in working memory. From these analyses we can begin to develop a quantitative hierarchy among memory systems in which stimulus-response memories and semantic associations provide no disambiguation while the episodic memory system provides the most flexible
Markov model of fatigue of a composite material with the poisson process of defect initiation
Paramonov, Yu.; Chatys, R.; Andersons, J.; Kleinhofs, M.
2012-05-01
As a development of the model where only one weak microvolume (WMV) and only a pulsating cyclic loading are considered, in the current version of the model, we take into account the presence of several weak sites where fatigue damage can accumulate and a loading with an arbitrary (but positive) stress ratio. The Poisson process of initiation of WMVs is considered, whose rate depends on the size of a specimen. The cumulative distribution function (cdf) of the fatigue life of every individual WMV is calculated using the Markov model of fatigue. For the case where this function is approximated by a lognormal distribution, a formula for calculating the cdf of fatigue life of the specimen (modeled as a chain of WMVs) is obtained. Only a pulsating cyclic loading was considered in the previous version of the model. Now, using the modified energy method, a loading cycle with an arbitrary stress ratio is "transformed" into an equivalent cycle with some other stress ratio. In such a way, the entire probabilistic fatigue diagram for any stress ratio with a positive cycle stress can be obtained. Numerical examples are presented.
Composition of web services using Markov decision processes and dynamic programming.
Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael
2015-01-01
We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity.
Robust path planning for flexible needle insertion using Markov decision processes.
Tan, Xiaoyu; Yu, Pengqian; Lim, Kah-Bin; Chui, Chee-Kong
2018-05-11
Flexible needle has the potential to accurately navigate to a treatment region in the least invasive manner. We propose a new planning method using Markov decision processes (MDPs) for flexible needle navigation that can perform robust path planning and steering under the circumstance of complex tissue-needle interactions. This method enhances the robustness of flexible needle steering from three different perspectives. First, the method considers the problem caused by soft tissue deformation. The method then resolves the common needle penetration failure caused by patterns of targets, while the last solution addresses the uncertainty issues in flexible needle motion due to complex and unpredictable tissue-needle interaction. Computer simulation and phantom experimental results show that the proposed method can perform robust planning and generate a secure control policy for flexible needle steering. Compared with a traditional method using MDPs, the proposed method achieves higher accuracy and probability of success in avoiding obstacles under complicated and uncertain tissue-needle interactions. Future work will involve experiment with biological tissue in vivo. The proposed robust path planning method can securely steer flexible needle within soft phantom tissues and achieve high adaptability in computer simulation.
A test of multiple correlation temporal window characteristic of non-Markov processes
Arecchi, F. T.; Farini, A.; Megna, N.
2016-03-01
We introduce a sensitive test of memory effects in successive events. The test consists of a combination K of binary correlations at successive times. K decays monotonically from K = 1 for uncorrelated events as a Markov process. For a monotonic memory fading, K1 temporal window in cognitive tasks consisting of the visual identification of the front face of the Necker cube after a previous presentation of the same. We speculate that memory effects provide a temporal window with K>1 and this experiment could be a possible first step towards a better comprehension of this phenomenon. The K>1 behaviour is maximal at an inter-measurement time τ around 2s with inter-subject differences. The K>1 persists over a time window of 1s around τ; outside this window the K1 window in pairs of successive perceptions suggests that, at variance with single visual stimuli eliciting a suitable response, a pair of stimuli shortly separated in time displays mutual correlations.
Gedik, Ridvan; Zhang, Shengfan; Rainwater, Chase
2017-06-01
A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated from different categories satisfy desired mix percentages. Deviations from these percentages and their impacts on operational capabilities are of particular interest to healthcare planners. In this study, we investigate intelligent ways of admitting patients to a proton therapy facility that maximize the total expected number of treatment sessions (fractions) delivered to patients in a planning period with stochastic patient arrivals and penalize the deviation from the patient mix restrictions. We propose a Markov Decision Process (MDP) model that provides very useful insights in determining the best patient admission policies in the case of an unexpected opening in the facility (i.e., no-shows, appointment cancellations, etc.). In order to overcome the curse of dimensionality for larger and more realistic instances, we propose an aggregate MDP model that is able to approximate optimal patient admission policies using the worded weight aggregation technique. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI).
Directory of Open Access Journals (Sweden)
Jae Joon Suh
2017-01-01
Full Text Available We consider the distance-based registration (DBR which is a kind of dynamic location registration scheme in a mobile communication network. In the DBR, the location of a mobile station (MS is updated when it enters a base station more than or equal to a specified distance away from the base station where the location registration for the MS was done last. In this study, we first investigate the existing performance-evaluation methods on the DBR with implicit registration (DBIR presented to improve the performance of the DBR and point out some problems of the evaluation methods. We propose a new performance-evaluation method for the DBIR scheme using a semi-Markov process (SMP which can resolve the controversial issues of the existing methods. The numerical results obtained with the proposed SMP model are compared with those from previous models. It is shown that the SMP model should be considered to get an accurate performance of the DBIR scheme.
Balancing Long Lifetime and Satisfying Fairness in WBAN Using a Constrained Markov Decision Process
Directory of Open Access Journals (Sweden)
Yingqi Yin
2015-01-01
Full Text Available As an important part of the Internet of Things (IOT and the special case of device-to-device (D2D communication, wireless body area network (WBAN gradually becomes the focus of attention. Since WBAN is a body-centered network, the energy of sensor nodes is strictly restrained since they are supplied by battery with limited power. In each data collection, only one sensor node is scheduled to transmit its measurements directly to the access point (AP through the fading channel. We formulate the problem of dynamically choosing which sensor should communicate with the AP to maximize network lifetime under the constraint of fairness as a constrained markov decision process (CMDP. The optimal lifetime and optimal policy are obtained by Bellman equation in dynamic programming. The proposed algorithm defines the limiting performance in WBAN lifetime under different degrees of fairness constraints. Due to the defect of large implementation overhead in acquiring global channel state information (CSI, we put forward a distributed scheduling algorithm that adopts local CSI, which saves the network overhead and simplifies the algorithm. It was demonstrated via simulation that this scheduling algorithm can allocate time slot reasonably under different channel conditions to balance the performances of network lifetime and fairness.
A markov decision process model for the optimal dispatch of military medical evacuation assets.
Keneally, Sean K; Robbins, Matthew J; Lunday, Brian J
2016-06-01
We develop a Markov decision process (MDP) model to examine aerial military medical evacuation (MEDEVAC) dispatch policies in a combat environment. The problem of deciding which aeromedical asset to dispatch to each service request is complicated by the threat conditions at the service locations and the priority class of each casualty event. We assume requests for MEDEVAC support arrive sequentially, with the location and the priority of each casualty known upon initiation of the request. The United States military uses a 9-line MEDEVAC request system to classify casualties as being one of three priority levels: urgent, priority, and routine. Multiple casualties can be present at a single casualty event, with the highest priority casualty determining the priority level for the casualty event. Moreover, an armed escort may be required depending on the threat level indicated by the 9-line MEDEVAC request. The proposed MDP model indicates how to optimally dispatch MEDEVAC helicopters to casualty events in order to maximize steady-state system utility. The utility gained from servicing a specific request depends on the number of casualties, the priority class for each of the casualties, and the locations of both the servicing ambulatory helicopter and casualty event. Instances of the dispatching problem are solved using a relative value iteration dynamic programming algorithm. Computational examples are used to investigate optimal dispatch policies under different threat situations and armed escort delays; the examples are based on combat scenarios in which United States Army MEDEVAC units support ground operations in Afghanistan.
Simari, Gerardo I
2011-01-01
In this work, we provide a treatment of the relationship between two models that have been widely used in the implementation of autonomous agents: the Belief DesireIntention (BDI) model and Markov Decision Processes (MDPs). We start with an informal description of the relationship, identifying the common features of the two approaches and the differences between them. Then we hone our understanding of these differences through an empirical analysis of the performance of both models on the TileWorld testbed. This allows us to show that even though the MDP model displays consistently better behavior than the BDI model for small worlds, this is not the case when the world becomes large and the MDP model cannot be solved exactly. Finally we present a theoretical analysis of the relationship between the two approaches, identifying mappings that allow us to extract a set of intentions from a policy (a solution to an MDP), and to extract a policy from a set of intentions.
PLASMA EMISSION BY NONLINEAR ELECTROMAGNETIC PROCESSES
Energy Technology Data Exchange (ETDEWEB)
Ziebell, L. F.; Petruzzellis, L. T.; Gaelzer, R. [Instituto de Física, UFRGS, Porto Alegre, RS (Brazil); Yoon, P. H. [Institute for Physical Science and Technology, University of Maryland, College Park (United States); Pavan, J., E-mail: luiz.ziebell@ufrgs.br, E-mail: laripetruzzellis@yahoo.com.br, E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: joel.pavan@ufpel.edu.br [Instituto de Física e Matemática, UFPel, Pelotas, RS (Brazil)
2015-06-20
The plasma emission, or electromagnetic (EM) radiation at the plasma frequency and/or its harmonic(s), is generally accepted as the radiation mechanism responsible for solar type II and III radio bursts. Identification and characterization of these solar radio burst phenomena were done in the 1950s. Despite many decades of theoretical research since then, a rigorous demonstration of the plasma emission process based upon first principles was not available until recently, when, in a recent Letter, Ziebell et al. reported the first complete numerical solution of EM weak turbulence equations; thus, quantitatively analyzing the plasma emission process starting from the initial electron beam and the associated beam-plasma (or Langmuir wave) instability, as well as the subsequent nonlinear conversion of electrostatic Langmuir turbulence into EM radiation. In the present paper, the same problem is revisited in order to elucidate the detailed physical mechanisms that could not be reported in the brief Letter format. Findings from the present paper may be useful for interpreting observations and full-particle numerical simulations.
DEFF Research Database (Denmark)
Kristensen, Anders Ringgaard; Søllested, Thomas Algot
2004-01-01
that really uses all these methodological improvements. In this paper, the biological model describing the performance and feed intake of sows is presented. In particular, estimation of herd specific parameters is emphasized. The optimization model is described in a subsequent paper......Several replacement models have been presented in literature. In other applicational areas like dairy cow replacement, various methodological improvements like hierarchical Markov processes and Bayesian updating have been implemented, but not in sow models. Furthermore, there are methodological...... improvements like multi-level hierarchical Markov processes with decisions on multiple time scales, efficient methods for parameter estimations at herd level and standard software that has been hardly implemented at all in any replacement model. The aim of this study is to present a sow replacement model...
Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.
2016-06-01
We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.
International Nuclear Information System (INIS)
Younmyoung Lee; Kunjai Lee
1995-01-01
A model using continuous time Markov process for nuclide transport of decay chain of arbitrary length in the fractured rock medium has been developed. Considering the fracture in the rock matrix as a finite number of compartments, the transition probability for nuclide from the transition intensity between and out of the compartments is represented utilizing Chapman-Kolmogorov equation, with which the expectation and the variance of nuclide distribution for the fractured rock medium could be obtained. A comparison between continuous time Markov process model and available analytical solutions for the nuclide transport of three decay chains without rock matrix diffusion has been made showing comparatively good agreement. Fittings with experimental breakthrough curves obtained with nonsorbing materials such as NaLS and uranine in the artificial fractured rock are also made. (author)
Projected metastable Markov processes and their estimation with observable operator models
International Nuclear Information System (INIS)
Wu, Hao; Prinz, Jan-Hendrik; Noé, Frank
2015-01-01
The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning
Borchers, D L; Langrock, R
2015-12-01
We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markov-modulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a mark-recapture component arising from the independent-observer survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multiple-detection estimators with estimators that use only initial detections of individuals, and with a single-observer estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and double-observer data but not with single-observer data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a double-observer survey of North Atlantic minke whales, and find that double-observer data greatly improve estimator precision here too. © 2015 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.
Bozhalkina, Yana
2017-12-01
Mathematical model of the loan portfolio structure change in the form of Markov chain is explored. This model considers in one scheme both the process of customers attraction, their selection based on the credit score, and loans repayment. The model describes the structure and volume of the loan portfolio dynamics, which allows to make medium-term forecasts of profitability and risk. Within the model corrective actions of bank management in order to increase lending volumes or to reduce the risk are formalized.
Optoelectronic and nonlinear optical processes in low dimensional ...
Indian Academy of Sciences (India)
Optoelectronic process; nonlinear optical process; semiconductor. Quest for ever faster and intelligent information processing technologies has sparked ..... Schematic energy level diagram for the proposed 4-level model. States other than the.
A competitive Markov decision process model for the energy–water–climate change nexus
International Nuclear Information System (INIS)
Nanduri, Vishnu; Saavedra-Antolínez, Ivan
2013-01-01
Highlights: • Developed a CMDP model for the energy–water–climate change nexus. • Solved the model using a reinforcement learning algorithm. • Study demonstrated on 30-bus IEEE electric power network using DCOPF formulation. • Sixty percentage drop in CO 2 and 40% drop in H 2 O use when coal replaced by wind (over 10 years). • Higher profits for nuclear and wind as well as higher LMPs under CO 2 and H 2 O taxes. - Abstract: Drought-like conditions in some parts of the US and around the world are causing water shortages that lead to power failures, becoming a source of concern to independent system operators. Water shortages can cause significant challenges in electricity production and thereby a direct socioeconomic impact on the surrounding region. Our paper presents a new, comprehensive quantitative model that examines the electricity–water–climate change nexus. We investigate the impact of a joint water and carbon tax proposal on the operation of a transmission-constrained power network operating in a wholesale power market setting. We develop a competitive Markov decision process (CMDP) model for the dynamic competition in wholesale electricity markets, and solve the model using reinforcement learning. Several cases, including the impact of different tax schemes, integration of stochastic wind energy resources, and capacity disruptions due to droughts are investigated. Results from the analysis on the sample power network show that electricity prices increased with the adoption of water and carbon taxes compared with locational marginal prices without taxes. As expected, wind energy integration reduced both CO 2 emissions and water usage. Capacity disruptions also caused locational marginal prices to increase. Other detailed analyses and results obtained using a 30-bus IEEE network are discussed in detail
Learning to maximize reward rate: a model based on semi-Markov decision processes.
Khodadadi, Arash; Fakhari, Pegah; Busemeyer, Jerome R
2014-01-01
WHEN ANIMALS HAVE TO MAKE A NUMBER OF DECISIONS DURING A LIMITED TIME INTERVAL, THEY FACE A FUNDAMENTAL PROBLEM: how much time they should spend on each decision in order to achieve the maximum possible total outcome. Deliberating more on one decision usually leads to more outcome but less time will remain for other decisions. In the framework of sequential sampling models, the question is how animals learn to set their decision threshold such that the total expected outcome achieved during a limited time is maximized. The aim of this paper is to provide a theoretical framework for answering this question. To this end, we consider an experimental design in which each trial can come from one of the several possible "conditions." A condition specifies the difficulty of the trial, the reward, the penalty and so on. We show that to maximize the expected reward during a limited time, the subject should set a separate value of decision threshold for each condition. We propose a model of learning the optimal value of decision thresholds based on the theory of semi-Markov decision processes (SMDP). In our model, the experimental environment is modeled as an SMDP with each "condition" being a "state" and the value of decision thresholds being the "actions" taken in those states. The problem of finding the optimal decision thresholds then is cast as the stochastic optimal control problem of taking actions in each state in the corresponding SMDP such that the average reward rate is maximized. Our model utilizes a biologically plausible learning algorithm to solve this problem. The simulation results show that at the beginning of learning the model choses high values of decision threshold which lead to sub-optimal performance. With experience, however, the model learns to lower the value of decision thresholds till finally it finds the optimal values.
Directory of Open Access Journals (Sweden)
Rajesh P N Rao
2010-11-01
Full Text Available A fundamental problem faced by animals is learning to select actions based on noisy sensory information and incomplete knowledge of the world. It has been suggested that the brain engages in Bayesian inference during perception but how such probabilistic representations are used to select actions has remained unclear. Here we propose a neural model of action selection and decision making based on the theory of partially observable Markov decision processes (POMDPs. Actions are selected based not on a single optimal estimate of state but on the posterior distribution over states (the belief state. We show how such a model provides a unified framework for explaining experimental results in decision making that involve both information gathering and overt actions. The model utilizes temporal difference (TD learning for maximizing expected reward. The resulting neural architecture posits an active role for the neocortex in belief computation while ascribing a role to the basal ganglia in belief representation, value computation, and action selection. When applied to the random dots motion discrimination task, model neurons representing belief exhibit responses similar to those of LIP neurons in primate neocortex. The appropriate threshold for switching from information gathering to overt actions emerges naturally during reward maximization. Additionally, the time course of reward prediction error in the model shares similarities with dopaminergic responses in the basal ganglia during the random dots task. For tasks with a deadline, the model learns a decision making strategy that changes with elapsed time, predicting a collapsing decision threshold consistent with some experimental studies. The model provides a new framework for understanding neural decision making and suggests an important role for interactions between the neocortex and the basal ganglia in learning the mapping between probabilistic sensory representations and actions that maximize
International Nuclear Information System (INIS)
Lee, Youn Myoung
1995-02-01
As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured
International Nuclear Information System (INIS)
Csenki, A.
1995-01-01
The interval reliability for a repairable system which alternates between working and repair periods is defined as the probability of the system being functional throughout a given time interval. In this paper, a set of integral equations is derived for this dependability measure, under the assumption that the system is modelled by an irreducible finite semi-Markov process. The result is applied to the semi-Markov model of a two-unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two-point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results are discussed and compared with those from simulation
Haesaert, S.; Cauchi, N.; Abate, A.
2017-01-01
In this paper, we present an industrial application of new approximate similarity relations for Markov models, and show that they are key for the synthesis of control strategies. Typically, modern engineering systems are modelled using complex and high-order models which make the correct-by-design
Directory of Open Access Journals (Sweden)
Eldon Glen Caldwell Marin
2015-01-01
Full Text Available The Markov Chains Model was proposed to analyze stochastic events when recursive cycles occur; for example, when rework in a continuous flow production affects the overall performance. Typically, the analysis of rework and scrap is done through a wasted material cost perspective and not from the perspective of waste capacity that reduces throughput and economic value added (EVA. Also, we can not find many cases of this application in agro-industrial production in Latin America, given the complexity of the calculations and the need for robust applications. This scientific work presents the results of a quasi-experimental research approach in order to explain how to apply DOE methods and Markov analysis in a rice production process located in Central America, evaluating the global effects of a single reduction in rework and scrap in a part of the whole line. The results show that in this case it is possible to evaluate benefits from Global Throughput and EVA perspective and not only from the saving costs perspective, finding a relationship between operational indicators and corporate performance. However, it was found that it is necessary to analyze the markov chains configuration with many rework points, also it is still relevant to take into account the effects on takt time and not only scrap´s costs.
janssen, Anja; Segers, Johan
2013-01-01
The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in Rd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In ...
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Keywords. Markov chain; state space; stationary transition probability; stationary distribution; irreducibility; aperiodicity; stationarity; M-H algorithm; proposal distribution; acceptance probability; image processing; Gibbs sampler.
Results of nonlinear and nonstationary image processing
International Nuclear Information System (INIS)
Pizer, S.M.; Correla, J.A.; Chesler, D.A.; Metz, C.E.
1973-01-01
A nonstationary method, multiple z-divided filtering, and a nonlinear method, biased smearing have been applied to scintigrams. Biased smearing does not appear to hold much promise. Multiple z-divided filtering, on the other hand, appears to be justified, and initial results at minimum encourage further research into the possibility that this technique may become a method of choice
2017-03-23
POLICIES THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force Institute of Technology...dispatching policy and three practitioner-friendly myopic baseline policies. Two computational experiments, a two-level, five-factor screening design and a...over, an open question exists concerning the best exact solution approach for solving Markov decision problems due to recent advances in performance by
Bennett, Casey C; Hauser, Kris
2013-01-01
In the modern healthcare system, rapidly expanding costs/complexity, the growing myriad of treatment options, and exploding information streams that often do not effectively reach the front lines hinder the ability to choose optimal treatment decisions over time. The goal in this paper is to develop a general purpose (non-disease-specific) computational/artificial intelligence (AI) framework to address these challenges. This framework serves two potential functions: (1) a simulation environment for exploring various healthcare policies, payment methodologies, etc., and (2) the basis for clinical artificial intelligence - an AI that can "think like a doctor". This approach combines Markov decision processes and dynamic decision networks to learn from clinical data and develop complex plans via simulation of alternative sequential decision paths while capturing the sometimes conflicting, sometimes synergistic interactions of various components in the healthcare system. It can operate in partially observable environments (in the case of missing observations or data) by maintaining belief states about patient health status and functions as an online agent that plans and re-plans as actions are performed and new observations are obtained. This framework was evaluated using real patient data from an electronic health record. The results demonstrate the feasibility of this approach; such an AI framework easily outperforms the current treatment-as-usual (TAU) case-rate/fee-for-service models of healthcare. The cost per unit of outcome change (CPUC) was $189 vs. $497 for AI vs. TAU (where lower is considered optimal) - while at the same time the AI approach could obtain a 30-35% increase in patient outcomes. Tweaking certain AI model parameters could further enhance this advantage, obtaining approximately 50% more improvement (outcome change) for roughly half the costs. Given careful design and problem formulation, an AI simulation framework can approximate optimal
Barbu, Vlad
2008-01-01
Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes
Bubble nonlinear dynamics and stimulated scattering process
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
SILVA R. G.
1999-01-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Risk-Sensitive and Mean Variance Optimality in Markov Decision Processes
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2013-01-01
Roč. 7, č. 3 (2013), s. 146-161 ISSN 0572-3043 R&D Projects: GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Grant - others:AVČR a CONACyT(CZ) 171396 Institutional support: RVO:67985556 Keywords : Discrete-time Markov decision chains * exponential utility functions * certainty equivalent * mean-variance optimality * connections between risk -sensitive and risk -neutral models Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-0399099.pdf
On some Filtration Procedure for Jump Markov Process Observed in White Gaussian Noise
Khas'minskii, Rafail Z.; Lazareva, Betty V.
1992-01-01
The importance of optimal filtration problem for Markov chain with two states observed in Gaussian white noise (GWN) for a lot of concrete technical problems is well known. The equation for a posterior probability $\\pi(t)$ of one of the states was obtained many years ago. The aim of this paper is to study a simple filtration method. It is shown that this simplified filtration is asymptotically efficient in some sense if the diffusion constant of the GWN goes to 0. Some advantages of this proc...
Nonlinear signal processing using neural networks: Prediction and system modelling
Energy Technology Data Exchange (ETDEWEB)
Lapedes, A.; Farber, R.
1987-06-01
The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.
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.
Stifter, Cynthia A; Rovine, Michael
2015-01-01
The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at two and six months of age, used hidden Markov modeling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a 4-state model for the dyadic responses to a two-month inoculation whereas a 6-state model best described the dyadic process at six months. Two of the states at two months and three of the states at six months suggested a progression from high intensity crying to no crying with parents using vestibular and auditory soothing methods. The use of feeding and/or pacifying to soothe the infant characterized one two-month state and two six-month states. These data indicate that with maturation and experience, the mother-infant dyad is becoming more organized around the soothing interaction. Using hidden Markov modeling to describe individual differences, as well as normative processes, is also presented and discussed.
Post processing of optically recognized text via second order hidden Markov model
Poudel, Srijana
In this thesis, we describe a postprocessing system on Optical Character Recognition(OCR) generated text. Second Order Hidden Markov Model (HMM) approach is used to detect and correct the OCR related errors. The reason for choosing the 2nd order HMM is to keep track of the bigrams so that the model can represent the system more accurately. Based on experiments with training data of 159,733 characters and testing of 5,688 characters, the model was able to correct 43.38 % of the errors with a precision of 75.34 %. However, the precision value indicates that the model introduced some new errors, decreasing the correction percentage to 26.4%.
MARKOV PROCESSES IN MODELING LAND USE AND LAND COVER CHANGES IN SINTRA-CASCAIS, PORTUGAL
Directory of Open Access Journals (Sweden)
PEDRO CABRAL
2009-01-01
Full Text Available En este artículo los procesos de alteración de la utilización y ocupación del suelo (LUCC son investigados recorriendo-se a técnicas de teledetección y a cadenas de Markov en lasmunicipalidades de Sintra y Cascais (Portugal entre los anos de 1989 y 2000. El papel del Parque Natural de Sintra-Cascais (PNSC es evaluado.Los resultados demuestran que, dentro del PNSC, el LUCC presente depende del pasadoinmediato del uso y ocupación del suelo siguiendo un comportamiento Markoviano. Fuera del PNSC, LUCC es aleatorio y no sigue un proceso Markoviano. Estimativas del LUCC para el ano de 2006 son presentadas para el área dentro del PNSC. Estos resultados refuerzan el papel del PNSC como una herramienta indispensable para preservar la estabilidad del LUCC y garantizar sus funciones.
Multi-state reliability for pump group in system based on UGF and semi-Markov process
International Nuclear Information System (INIS)
Shang Yanlong; Cai Qi; Zhao Xinwen; Chen Ling
2012-01-01
In this paper, multi-state reliability value of pump group in nuclear power system is obtained by the combination method of the universal generating function (UGF) and Semi-Markov process. UGF arithmetic model of multi-state system reliability is studied, and the performance state probability expression of multi-state component is derived using semi-Markov theory. A quantificational model is defined to express the performance rate of the system and component. Different availability results by multi-state and binary state analysis method are compared under the condition whether the performance rate can satisfy the demanded value, and the mean value of system instantaneous output performance is also obtained. It shows that this combination method is an effective and feasible one which can quantify the effect of the partial failure on the system reliability, and the result of multi-state system reliability by this method deduces the modesty of the reliability value obtained by binary reliability analysis method. (authors)
International Nuclear Information System (INIS)
Piriou, Pierre-Yves; Faure, Jean-Marc; Lesage, Jean-Jacques
2017-01-01
This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.
Nonlinear partial least squares with Hellinger distance for nonlinear process monitoring
Harrou, Fouzi
2017-02-16
This paper proposes an efficient data-based anomaly detection method that can be used for monitoring nonlinear processes. The proposed method merges advantages of nonlinear projection to latent structures (NLPLS) modeling and those of Hellinger distance (HD) metric to identify abnormal changes in highly correlated multivariate data. Specifically, the HD is used to quantify the dissimilarity between current NLPLS-based residual and reference probability distributions. The performances of the developed anomaly detection using NLPLS-based HD technique is illustrated using simulated plug flow reactor data.
Nonlinear partial least squares with Hellinger distance for nonlinear process monitoring
Harrou, Fouzi; Madakyaru, Muddu; Sun, Ying
2017-01-01
This paper proposes an efficient data-based anomaly detection method that can be used for monitoring nonlinear processes. The proposed method merges advantages of nonlinear projection to latent structures (NLPLS) modeling and those of Hellinger distance (HD) metric to identify abnormal changes in highly correlated multivariate data. Specifically, the HD is used to quantify the dissimilarity between current NLPLS-based residual and reference probability distributions. The performances of the developed anomaly detection using NLPLS-based HD technique is illustrated using simulated plug flow reactor data.
Ultra-Fast Optical Signal Processing in Nonlinear Silicon Waveguides
DEFF Research Database (Denmark)
Oxenløwe, Leif Katsuo; Galili, Michael; Pu, Minhao
2011-01-01
We describe recent demonstrations of exploiting highly nonlinear silicon nanowires for processing Tbit/s optical data signals. We perform demultiplexing and optical waveform sampling of 1.28 Tbit/s and wavelength conversion of 640 Gbit/s data signals.......We describe recent demonstrations of exploiting highly nonlinear silicon nanowires for processing Tbit/s optical data signals. We perform demultiplexing and optical waveform sampling of 1.28 Tbit/s and wavelength conversion of 640 Gbit/s data signals....
DEFF Research Database (Denmark)
Kristensen, Anders Ringgaard; Søllested, Thomas Algot
2004-01-01
improvements. The biological model of the replacement model is described in a previous paper and in this paper the optimization model is described. The model is developed as a prototype for use under practical conditions. The application of the model is demonstrated using data from two commercial Danish sow......Recent methodological improvements in replacement models comprising multi-level hierarchical Markov processes and Bayesian updating have hardly been implemented in any replacement model and the aim of this study is to present a sow replacement model that really uses these methodological...... herds. It is concluded that the Bayesian updating technique and the hierarchical structure decrease the size of the state space dramatically. Since parameter estimates vary considerably among herds it is concluded that decision support concerning sow replacement only makes sense with parameters...
International Nuclear Information System (INIS)
Ruiz-Castro, Juan Eloy
2016-01-01
In this paper, a discrete complex reliability system subject to internal failures and external shocks, is modelled algorithmically. Two types of internal failure are considered: repairable and non-repairable. When a repairable failure occurs, the unit goes to corrective repair. In addition, the unit is subject to external shocks that may produce an aggravation of the internal degradation level, cumulative damage or extreme failure. When a damage threshold is reached, the unit must be removed. When a non-repairable failure occurs, the device is replaced by a new, identical one. The internal performance and the external damage are partitioned in performance levels. Random inspections are carried out. When an inspection takes place, the internal performance of the system and the damage caused by external shocks are observed and if necessary the unit is sent to preventive maintenance. If the inspection observes minor state for the internal performance and/or external damage, then these states remain in memory when the unit goes to corrective or preventive maintenance. Transient and stationary analyses are performed. Markov counting and reward processes are developed in computational form to analyse the performance and profitability of the system with and without preventive maintenance. These aspects are implemented computationally with Matlab. - Highlights: • A multi-state device is modelled in an algorithmic and computational form. • The performance is partitioned in multi-states and degradation levels. • Several types of failures with repair times according to degradation levels. • Preventive maintenance as response to random inspection is introduced. • The performance-profitable is analysed through Markov counting and reward processes.
Composable Markov Building Blocks
Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.; Prade, H.; Subrahmanian, V.S.
2007-01-01
In situations where disjunct parts of the same process are described by their own first-order Markov models and only one model applies at a time (activity in one model coincides with non-activity in the other models), these models can be joined together into one. Under certain conditions, nearly all
Composable Markov Building Blocks
Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.
2007-01-01
In situations where disjunct parts of the same process are described by their own first-order Markov models, these models can be joined together under the constraint that there can only be one activity at a time, i.e. the activities of one model coincide with non-activity in the other models. Under
Fannes, Mark; Wouters, Jeroen
2012-01-01
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.
A Markov decision process for managing habitat for Florida scrub-jays
Johnson, Fred A.; Breininger, David R.; Duncan, Brean W.; Nichols, James D.; Runge, Michael C.; Williams, B. Ken
2011-01-01
Florida scrub-jays Aphelocoma coerulescens are listed as threatened under the Endangered Species Act due to loss and degradation of scrub habitat. This study concerned the development of an optimal strategy for the restoration and management of scrub habitat at Merritt Island National Wildlife Refuge, which contains one of the few remaining large populations of scrub-jays in Florida. There are documented differences in the reproductive and survival rates of scrubjays among discrete classes of scrub height (Markov models to estimate annual transition probabilities among the four scrub-height classes under three possible management actions: scrub restoration (mechanical cutting followed by burning), a prescribed burn, or no intervention. A strategy prescribing the optimal management action for management units exhibiting different proportions of scrub-height classes was derived using dynamic programming. Scrub restoration was the optimal management action only in units dominated by mixed and tall scrub, and burning tended to be the optimal action for intermediate levels of short scrub. The optimal action was to do nothing when the amount of short scrub was greater than 30%, because short scrub mostly transitions to optimal height scrub (i.e., that state with the highest demographic success of scrub-jays) in the absence of intervention. Monte Carlo simulation of the optimal policy suggested that some form of management would be required every year. We note, however, that estimates of scrub-height transition probabilities were subject to several sources of uncertainty, and so we explored the management implications of alternative sets of transition probabilities. Generally, our analysis demonstrated the difficulty of managing for a species that requires midsuccessional habitat, and suggests that innovative management tools may be needed to help ensure the persistence of scrub-jays at Merritt Island National Wildlife Refuge. The development of a tailored monitoring
Nonlinear signal processing for ultrasonic imaging of material complexity
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk
2010-01-01
Roč. 59, č. 2 (2010), s. 108-117 ISSN 1736-6046 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear signal processing * TR-NEWS * symmetry analysis * DORT Subject RIV: BI - Acoustics Impact factor: 0.464, year: 2010 www.eap.ee/proceedings
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
Bhulai, S.; Brooms, A.C.; Spieksma, F.M.
2014-01-01
The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the
Kana, A.A.; Harrison, B.M.
2017-01-01
A Monte Carlo approach to the ship-centric Markov decision process (SC-MDP) is presented for analyzing whether a container ship should convert to LNG power in the face of evolving Emission Control Area regulations. The SC-MDP model was originally developed as a means to analyze uncertain,
Photonic single nonlinear-delay dynamical node for information processing
Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel
2012-06-01
An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Nonlinear transport processes in tokamak plasmas. I. The collisional regimes
International Nuclear Information System (INIS)
Sonnino, Giorgio; Peeters, Philippe
2008-01-01
An application of the thermodynamic field theory (TFT) to transport processes in L-mode tokamak plasmas is presented. The nonlinear corrections to the linear ('Onsager') transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the Pfirsch-Schlueter (P-S) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for Joint European Torus (JET) plasmas are also reported. It is found that the nonlinear electron P-S transport coefficients exceed the values provided by neoclassical theory by a factor that may be of the order 10 2 . The nonlinear classical coefficients exceed the neoclassical ones by a factor that may be of order 2. For JET, the discrepancy between experimental and theoretical results for the electron losses is therefore significantly reduced by a factor 10 2 when the nonlinear contributions are duly taken into account but, there is still a factor of 10 2 to be explained. This is most likely due to turbulence. The expressions of the ion transport coefficients, determined by the neoclassical theory in these two regimes, remain unaltered. The low-collisional regimes, i.e., the plateau and the banana regimes, are analyzed in the second part of this work
A Markov decision process for managing habitat for Florida scrub-jays
Johnson, Fred A.; Breininger, David R.; Duncan, Brean W.; Nichols, James D.; Runge, Michael C.; Williams, B. Ken
2011-01-01
Florida scrub-jays Aphelocoma coerulescens are listed as threatened under the Endangered Species Act due to loss and degradation of scrub habitat. This study concerned the development of an optimal strategy for the restoration and management of scrub habitat at Merritt Island National Wildlife Refuge, which contains one of the few remaining large populations of scrub-jays in Florida. There are documented differences in the reproductive and survival rates of scrubjays among discrete classes of scrub height (strategy that would maximize the long-term growth rate of the resident scrub-jay population. We used aerial imagery with multistate Markov models to estimate annual transition probabilities among the four scrub-height classes under three possible management actions: scrub restoration (mechanical cutting followed by burning), a prescribed burn, or no intervention. A strategy prescribing the optimal management action for management units exhibiting different proportions of scrub-height classes was derived using dynamic programming. Scrub restoration was the optimal management action only in units dominated by mixed and tall scrub, and burning tended to be the optimal action for intermediate levels of short scrub. The optimal action was to do nothing when the amount of short scrub was greater than 30%, because short scrub mostly transitions to optimal height scrub (i.e., that state with the highest demographic success of scrub-jays) in the absence of intervention. Monte Carlo simulation of the optimal policy suggested that some form of management would be required every year. We note, however, that estimates of scrub-height transition probabilities were subject to several sources of uncertainty, and so we explored the management implications of alternative sets of transition probabilities. Generally, our analysis demonstrated the difficulty of managing for a species that requires midsuccessional habitat, and suggests that innovative management tools may be needed to
Confluence reduction for Markov automata
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
Confluence Reduction for Markov Automata
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Braberman, Victor; Fribourg, Laurent
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Nonlinear wave-mixing processes in the extreme ultraviolet
International Nuclear Information System (INIS)
Misoguti, L.; Christov, I. P.; Backus, S.; Murnane, M. M.; Kapteyn, H. C.
2005-01-01
We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an 800 nm laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths
Nonlinear processes of magnons in insulating ferromagnetic materials
International Nuclear Information System (INIS)
Araujo, C.B. de.
1975-04-01
The representation of coherent states is used to investigate the excitation of magnons by 'parallel pumping', 'perpendicular pumping' and 'phonon pumping'. The stationary regime of the processes is studied with respect to the magnon population and the statistic behavior of the system below and just above the threshold. Particular attention is given to the thermodynamic and the coherence properties of the parametric states. The results show that just above the threshold the generated states become coherent. Also, it is shown that the non-linear processes have characteristics of a second-order phase transition with the pumping power as the 'reservoir variable' and the transverse dynamical magnetization as the 'order parameter'. Finally, the possibilities to extend the theory, its experimental check, and its convenience to study the other nonlinear processes of magnons and phonons in magnetic insulators are discussed. (author) [pt
International Nuclear Information System (INIS)
Choi, K.Y.; Yoon, Y.K.; Chang, S.H.
1991-01-01
This paper reports on a new statistical fuel failure model developed to take into account the effects of damaging environmental conditions and the overall operating history of the fuel elements. The degradation of material properties and damage resistance of the fuel cladding is mainly caused by the combined effects of accumulated dynamic stresses, neutron irradiation, and chemical and stress corrosion at operating temperature. Since the degradation of material properties due to these effects can be considered as a stochastic process, a dynamic reliability function is derived based on the Markov process. Four damage parameters, namely, dynamic stresses, magnitude of power increase from the preceding power level and with ramp rate, and fatigue cycles, are used to build this model. The dynamic reliability function and damage parameters are used to obtain effective damage parameters. The entropy maximization principle is used to generate a probability density function of the effective damage parameters. The entropy minimization principle is applied to determine weighting factors for amalgamation of the failure probabilities due to the respective failure modes. In this way, the effects of operating history, damaging environmental conditions, and damage sequence are taken into account
D'Onofrio, Giuseppe; Pirozzi, Enrica
2017-05-01
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen
2017-09-25
In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.
Regeneration and general Markov chains
Directory of Open Access Journals (Sweden)
Vladimir V. Kalashnikov
1994-01-01
Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Photonic Crystal Nanocavity Devices for Nonlinear Signal Processing
DEFF Research Database (Denmark)
Yu, Yi
, membranization of InP/InGaAs structure and wet etching. Experimental investigation of the switching dynamics of InP photonic crystal nanocavity structures are carried out using short-pulse homodyne pump-probe techniques, both in the linear and nonlinear region where the cavity is perturbed by a relatively small......This thesis deals with the investigation of InP material based photonic crystal cavity membrane structures, both experimentally and theoretically. The work emphasizes on the understanding of the physics underlying the structures’ nonlinear properties and their applications for all-optical signal...... processing. Based on the previous fabrication recipe developed in our III-V platform, several processing techniques are developed and optimized for the fabrication of InP photonic crystal membrane structures. Several key issues are identified to ensure a good device quality such as air hole size control...
Preface "Nonlinear processes in oceanic and atmospheric flows"
Directory of Open Access Journals (Sweden)
E. García-Ladona
2010-05-01
Full Text Available Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows" contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Niño Southern Oscillation.
Nonlinear Silicon Photonic Signal Processing Devices for Future Optical Networks
Directory of Open Access Journals (Sweden)
Cosimo Lacava
2017-01-01
Full Text Available In this paper, we present a review on silicon-based nonlinear devices for all optical nonlinear processing of complex telecommunication signals. We discuss some recent developments achieved by our research group, through extensive collaborations with academic partners across Europe, on optical signal processing using silicon-germanium and amorphous silicon based waveguides as well as novel materials such as silicon rich silicon nitride and tantalum pentoxide. We review the performance of four wave mixing wavelength conversion applied on complex signals such as Differential Phase Shift Keying (DPSK, Quadrature Phase Shift Keying (QPSK, 16-Quadrature Amplitude Modulation (QAM and 64-QAM that dramatically enhance the telecom signal spectral efficiency, paving the way to next generation terabit all-optical networks.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Heterogeneous recurrence monitoring and control of nonlinear stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun [Complex Systems Monitoring, Modeling and Analysis Laboratory, University of South Florida, Tampa, Florida 33620 (United States)
2014-03-15
Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
DEFF Research Database (Denmark)
Häggström, Olle; Lieshout, Marie-Colette van; Møller, Jesper
1999-01-01
The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects...... is simpler to analyse and simulate. Using this correspondence we devise a two-component Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a Swendsen-Wang type algorithm. The relevance of the results within spatial statistics...
Directory of Open Access Journals (Sweden)
Jian Jiao
2017-09-01
Full Text Available The Ka-band and higher Q/V band channels can provide an appealing capacity for the future deep-space communications and Space Information Networks (SIN, which are viewed as a primary solution to satisfy the increasing demands for high data rate services. However, Ka-band channel is much more sensitive to the weather conditions than the conventional communication channels. Moreover, due to the huge distance and long propagation delay in SINs, the transmitter can only obtain delayed Channel State Information (CSI from feedback. In this paper, the noise temperature of time-varying rain attenuation at Ka-band channels is modeled to a two-state Gilbert–Elliot channel, to capture the channel capacity that randomly ranging from good to bad state. An optimal transmission scheme based on Partially Observable Markov Decision Processes (POMDP is proposed, and the key thresholds for selecting the optimal transmission method in the SIN communications are derived. Simulation results show that our proposed scheme can effectively improve the throughput.
Demeter, R M; Kristensen, A R; Dijkstra, J; Oude Lansink, A G J M; Meuwissen, M P M; van Arendonk, J A M
2011-12-01
Herd optimization models that determine economically optimal insemination and replacement decisions are valuable research tools to study various aspects of farming systems. The aim of this study was to develop a herd optimization and simulation model for dairy cattle. The model determines economically optimal insemination and replacement decisions for individual cows and simulates whole-herd results that follow from optimal decisions. The optimization problem was formulated as a multi-level hierarchic Markov process, and a state space model with Bayesian updating was applied to model variation in milk yield. Methodological developments were incorporated in 2 main aspects. First, we introduced an additional level to the model hierarchy to obtain a more tractable and efficient structure. Second, we included a recently developed cattle feed intake model. In addition to methodological developments, new parameters were used in the state space model and other biological functions. Results were generated for Dutch farming conditions, and outcomes were in line with actual herd performance in the Netherlands. Optimal culling decisions were sensitive to variation in milk yield but insensitive to energy requirements for maintenance and feed intake capacity. We anticipate that the model will be applied in research and extension. Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented.\\ud \\ud We then moved on to investigate the basic proper...
Distinguishing Hidden Markov Chains
Kiefer, Stefan; Sistla, A. Prasad
2015-01-01
Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HM...
Pemodelan Markov Switching Autoregressive
Ariyani, Fiqria Devi; Warsito, Budi; Yasin, Hasbi
2014-01-01
Transition from depreciation to appreciation of exchange rate is one of regime switching that ignored by classic time series model, such as ARIMA, ARCH, or GARCH. Therefore, economic variables are modeled by Markov Switching Autoregressive (MSAR) which consider the regime switching. MLE is not applicable to parameters estimation because regime is an unobservable variable. So that filtering and smoothing process are applied to see the regime probabilities of observation. Using this model, tran...
Nonlinear Statistical Signal Processing: A Particle Filtering Approach
International Nuclear Information System (INIS)
Candy, J.
2007-01-01
A introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations
Predicting speech intelligibility in conditions with nonlinearly processed noisy speech
DEFF Research Database (Denmark)
Jørgensen, Søren; Dau, Torsten
2013-01-01
The speech-based envelope power spectrum model (sEPSM; [1]) was proposed in order to overcome the limitations of the classical speech transmission index (STI) and speech intelligibility index (SII). The sEPSM applies the signal-tonoise ratio in the envelope domain (SNRenv), which was demonstrated...... to successfully predict speech intelligibility in conditions with nonlinearly processed noisy speech, such as processing with spectral subtraction. Moreover, a multiresolution version (mr-sEPSM) was demonstrated to account for speech intelligibility in various conditions with stationary and fluctuating...
Bifurcation and stability analysis of a nonlinear milling process
Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy
2018-01-01
Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.
Relative entropy and waiting time for continuous-time Markov processes
Chazottes, J.R.; Giardinà, C.; Redig, F.H.J.
2006-01-01
For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on
Distribution of chirality in the quantum walk: Markov process and entanglement
International Nuclear Information System (INIS)
Romanelli, Alejandro
2010-01-01
The asymptotic behavior of the quantum walk on the line is investigated, focusing on the probability distribution of chirality independently of position. It is shown analytically that this distribution has a longtime limit that is stationary and depends on the initial conditions. This result is unexpected in the context of the unitary evolution of the quantum walk as it is usually linked to a Markovian process. The asymptotic value of the entanglement between the coin and the position is determined by the chirality distribution. For given asymptotic values of both the entanglement and the chirality distribution, it is possible to find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions.
Probabilistic parameter estimation of activated sludge processes using Markov Chain Monte Carlo.
Sharifi, Soroosh; Murthy, Sudhir; Takács, Imre; Massoudieh, Arash
2014-03-01
One of the most important challenges in making activated sludge models (ASMs) applicable to design problems is identifying the values of its many stoichiometric and kinetic parameters. When wastewater characteristics data from full-scale biological treatment systems are used for parameter estimation, several sources of uncertainty, including uncertainty in measured data, external forcing (e.g. influent characteristics), and model structural errors influence the value of the estimated parameters. This paper presents a Bayesian hierarchical modeling framework for the probabilistic estimation of activated sludge process parameters. The method provides the joint probability density functions (JPDFs) of stoichiometric and kinetic parameters by updating prior information regarding the parameters obtained from expert knowledge and literature. The method also provides the posterior correlations between the parameters, as well as a measure of sensitivity of the different constituents with respect to the parameters. This information can be used to design experiments to provide higher information content regarding certain parameters. The method is illustrated using the ASM1 model to describe synthetically generated data from a hypothetical biological treatment system. The results indicate that data from full-scale systems can narrow down the ranges of some parameters substantially whereas the amount of information they provide regarding other parameters is small, due to either large correlations between some of the parameters or a lack of sensitivity with respect to the parameters. Copyright © 2013 Elsevier Ltd. All rights reserved.
Control of a nonlinear ice cream crystallization process
Casenave, Céline; Dochain, Denis; Alvarez, Graciela; Arellano, Marcela; Benkhelifa, Hayat; Leducq, Denis
2013-01-01
International audience; In the ice cream industry, the type of final desired product (large cartons (sqrounds) or ice creams on a stick) determine the viscosity at which the ice cream has to be produced. One of the objectives of the ice cream crystallization processes is therefore to produce an ice cream of specified viscosity. In this paper, a nonlinear control strategy is proposed for the control of the viscosity of the ice cream in a continuous crystallizer. It has been designed on the bas...
Directory of Open Access Journals (Sweden)
Eric A Zilli
2008-07-01
Full Text Available Researchers use a variety of behavioral tasks to analyze the effect of biological manipulations on memory function. This research will benefit from a systematic mathematical method for analyzing memory demands in behavioral tasks. In the framework of reinforcement learning theory, these tasks can be mathematically described as partially-observable Markov decision processes. While a wealth of evidence collected over the past 15 years relates the basal ganglia to the reinforcement learning framework, only recently has much attention been paid to including psychological concepts such as working memory or episodic memory in these models. This paper presents an analysis that provides a quantitative description of memory states sufficient for correct choices at specific decision points. Using information from the mathematical structure of the task descriptions, we derive measures that indicate whether working memory (for one or more cues or episodic memory can provide strategically useful information to an agent. In particular, the analysis determines which observed states must be maintained in or retrieved from memory to perform these specific tasks. We demonstrate the analysis on three simplified tasks as well as eight more complex memory tasks drawn from the animal and human literature (two alternation tasks, two sequence disambiguation tasks, two non-matching tasks, the 2-back task, and the 1-2-AX task. The results of these analyses agree with results from quantitative simulations of the task reported in previous publications and provide simple indications of the memory demands of the tasks which can require far less computation than a full simulation of the task. This may provide a basis for a quantitative behavioral stoichiometry of memory tasks.
Zilli, Eric A; Hasselmo, Michael E
2008-07-23
Researchers use a variety of behavioral tasks to analyze the effect of biological manipulations on memory function. This research will benefit from a systematic mathematical method for analyzing memory demands in behavioral tasks. In the framework of reinforcement learning theory, these tasks can be mathematically described as partially-observable Markov decision processes. While a wealth of evidence collected over the past 15 years relates the basal ganglia to the reinforcement learning framework, only recently has much attention been paid to including psychological concepts such as working memory or episodic memory in these models. This paper presents an analysis that provides a quantitative description of memory states sufficient for correct choices at specific decision points. Using information from the mathematical structure of the task descriptions, we derive measures that indicate whether working memory (for one or more cues) or episodic memory can provide strategically useful information to an agent. In particular, the analysis determines which observed states must be maintained in or retrieved from memory to perform these specific tasks. We demonstrate the analysis on three simplified tasks as well as eight more complex memory tasks drawn from the animal and human literature (two alternation tasks, two sequence disambiguation tasks, two non-matching tasks, the 2-back task, and the 1-2-AX task). The results of these analyses agree with results from quantitative simulations of the task reported in previous publications and provide simple indications of the memory demands of the tasks which can require far less computation than a full simulation of the task. This may provide a basis for a quantitative behavioral stoichiometry of memory tasks.
Directory of Open Access Journals (Sweden)
Ken eKinjo
2013-04-01
Full Text Available Linearly solvable Markov Decision Process (LMDP is a class of optimal control problem in whichthe Bellman’s equation can be converted into a linear equation by an exponential transformation ofthe state value function (Todorov, 2009. In an LMDP, the optimal value function and the correspondingcontrol policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunctionproblem in a continuous state using the knowledge of the system dynamics and the action, state, andterminal cost functions.In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in whichthe dynamics of the body and the environment have to be learned from experience. We first perform asimulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynam-ics model on the derived the action policy. The result shows that a crude linear approximation of thenonlinear dynamics can still allow solution of the task, despite with a higher total cost.We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robotplatform. The state is given by the position and the size of a battery in its camera view and two neck jointangles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servocontroller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state costfunctions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics modelperformed equivalently with the optimal linear quadratic controller (LQR. In the non-quadratic task, theLMDP controller with a linear dynamics model showed the best performance. The results demonstratethe usefulness of the LMDP framework in real robot control even when simple linear models are usedfor dynamics learning.
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Stifter, Cynthia A.; Rovine, Michael
2015-01-01
The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at 2 and 6?months of age, used hidden Markov modelling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a…
Spectral methods for quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Nonlinear identification of process dynamics using neural networks
International Nuclear Information System (INIS)
Parlos, A.G.; Atiya, A.F.; Chong, K.T.
1992-01-01
In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios
Some nonlinear processes relevant to the beat wave accelerator
International Nuclear Information System (INIS)
Bingham, R.; Mori, W.B.
1985-03-01
The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω 1 , k 1 ) and (ω 2 ,k 2 ) with ωsub(p) = ω 1 -ω 2 , ksub(p) = k 1 -k 2 . Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)
Hierarchical optimal control of large-scale nonlinear chemical processes.
Ramezani, Mohammad Hossein; Sadati, Nasser
2009-01-01
In this paper, a new approach is presented for optimal control of large-scale chemical processes. In this approach, the chemical process is decomposed into smaller sub-systems at the first level, and a coordinator at the second level, for which a two-level hierarchical control strategy is designed. For this purpose, each sub-system in the first level can be solved separately, by using any conventional optimization algorithm. In the second level, the solutions obtained from the first level are coordinated using a new gradient-type strategy, which is updated by the error of the coordination vector. The proposed algorithm is used to solve the optimal control problem of a complex nonlinear chemical stirred tank reactor (CSTR), where its solution is also compared with the ones obtained using the centralized approach. The simulation results show the efficiency and the capability of the proposed hierarchical approach, in finding the optimal solution, over the centralized method.
Recursive utility in a Markov environment with stochastic growth.
Hansen, Lars Peter; Scheinkman, José A
2012-07-24
Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.
Kapli, P; Lutteropp, S; Zhang, J; Kobert, K; Pavlidis, P; Stamatakis, A; Flouri, T
2017-06-01
In recent years, molecular species delimitation has become a routine approach for quantifying and classifying biodiversity. Barcoding methods are of particular importance in large-scale surveys as they promote fast species discovery and biodiversity estimates. Among those, distance-based methods are the most common choice as they scale well with large datasets; however, they are sensitive to similarity threshold parameters and they ignore evolutionary relationships. The recently introduced "Poisson Tree Processes" (PTP) method is a phylogeny-aware approach that does not rely on such thresholds. Yet, two weaknesses of PTP impact its accuracy and practicality when applied to large datasets; it does not account for divergent intraspecific variation and is slow for a large number of sequences. We introduce the multi-rate PTP (mPTP), an improved method that alleviates the theoretical and technical shortcomings of PTP. It incorporates different levels of intraspecific genetic diversity deriving from differences in either the evolutionary history or sampling of each species. Results on empirical data suggest that mPTP is superior to PTP and popular distance-based methods as it, consistently yields more accurate delimitations with respect to the taxonomy (i.e., identifies more taxonomic species, infers species numbers closer to the taxonomy). Moreover, mPTP does not require any similarity threshold as input. The novel dynamic programming algorithm attains a speedup of at least five orders of magnitude compared to PTP, allowing it to delimit species in large (meta-) barcoding data. In addition, Markov Chain Monte Carlo sampling provides a comprehensive evaluation of the inferred delimitation in just a few seconds for millions of steps, independently of tree size. mPTP is implemented in C and is available for download at http://github.com/Pas-Kapli/mptp under the GNU Affero 3 license. A web-service is available at http://mptp.h-its.org . : paschalia.kapli@h-its.org or
International Nuclear Information System (INIS)
Klemin, A.I.; Emel'yanov, V.S.; Rabchun, A.V.
1984-01-01
A technique is sugfested for estimating service life indices of equipment based on describing the process of the equipment ageing by continuous Markov diffusion process. It is noted that a number of problems on estimating durability indices of products is reduced to problems of estimating characteristics of the time of the first attainment of the preset boundary (boundaries) by a random process describing the ageing of a product. The methods of statistic estimation of the drift and diffusion coefficient in the continuous Markov diffusion process are considered formulae for their point and interval estimates are presented. A special description is given for a case of a stationary process and determining in this case mathematical expectation and dispersion of the time of the first attainment of a boundary (boundaries). The method of numerical simulation of the diffusion process with constant drift and diffusion coefficients is also described; results obtained on the basis of such a simulation are discussed. An example of using the suggested technique for quantitative estimate of the service life for the RBMK-1000 gate-regulating value is given
Nonlinear analysis and control of a continuous fermentation process
DEFF Research Database (Denmark)
Szederkényi, G.; Kristensen, Niels Rode; Hangos, K.M
2002-01-01
Different types of nonlinear controllers are designed and compared for a simple continuous bioreactor operating near optimal productivity. This operating point is located close to a fold bifurcation point. Nonlinear analysis of stability, controllability and zero dynamics is used to investigate o...... are recommended for the simple fermenter. Passivity based controllers have been found to be globally stable, not very sensitive to the uncertainties in the reaction rate and controller parameter but they require full nonlinear state feedback....
Markov stochasticity coordinates
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard
2007-01-01
We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Non-linear processes in the Earth atmosphere boundary layer
Grunskaya, Lubov; Valery, Isakevich; Dmitry, Rubay
2013-04-01
The work is connected with studying electromagnetic fields in the resonator Earth-Ionosphere. There is studied the interconnection of tide processes of geophysical and astrophysical origin with the Earth electromagnetic fields. On account of non-linear property of the resonator Earth-Ionosphere the tides (moon and astrophysical tides) in the electromagnetic Earth fields are kinds of polyharmonic nature. It is impossible to detect such non-linear processes with the help of the classical spectral analysis. Therefore to extract tide processes in the electromagnetic fields, the method of covariance matrix eigen vectors is used. Experimental investigations of electromagnetic fields in the atmosphere boundary layer are done at the distance spaced stations, situated on Vladimir State University test ground, at Main Geophysical Observatory (St. Petersburg), on Kamchatka pen., on Lake Baikal. In 2012 there was continued to operate the multichannel synchronic monitoring system of electrical and geomagnetic fields at the spaced apart stations: VSU physical experimental proving ground; the station of the Institute of Solar and Terrestrial Physics of Russian Academy of Science (RAS) at Lake Baikal; the station of the Institute of volcanology and seismology of RAS in Paratunka; the station in Obninsk on the base of the scientific and production society "Typhoon". Such investigations turned out to be possible after developing the method of scanning experimental signal of electromagnetic field into non- correlated components. There was used a method of the analysis of the eigen vectors ofthe time series covariance matrix for exposing influence of the moon tides on Ez. The method allows to distribute an experimental signal into non-correlated periodicities. The present method is effective just in the situation when energetical deposit because of possible influence of moon tides upon the electromagnetic fields is little. There have been developed and realized in program components
Nonlinear closure relations theory for transport processes in nonequilibrium systems
International Nuclear Information System (INIS)
Sonnino, Giorgio
2009-01-01
A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.
Directory of Open Access Journals (Sweden)
Francielly Hedler Staudt
2011-01-01
Full Text Available Todas as empresas em desenvolvimento passam pelo momento de decidir se há ou não necessidade de realizar novos investimentos para suprir uma demanda crescente. Para tomar tal decisão é imprescindível conhecer se o processo atual tem capacidade de produzir a nova demanda. Porém, são raras as empresas que têm a percepção de que os refugos e retrabalhos também consomem recursos da produção e, portanto, devem ser considerados no cálculo da capacidade produtiva. A proposta deste trabalho consiste em incluir esses fatores na análise de capacidade da fábrica, utilizando uma matriz de transição estocástica da cadeia absorvente de Markov como ferramenta para obtenção do fator de capacidade. Este fator, aliado ao índice de eficiência e a demanda desejada ao fim do processo, resulta na capacidade real necessária. Um estudo de caso exemplifica a metodologia, apresentando resultados que permitem o cálculo do índice de ocupação real de cada centro produtivo. O cálculo desse índice demonstrou que alguns centros de trabalho necessitam de análises sobre investimentos em capacitação, pois ultrapassaram 90% de ocupação.All developing companies must decide once in a while whether it is required to perform new investments to handle a growing demand. In order to make this decision, it is essential to know whether the current productive capacity is able to supply the new demand. However, just few companies realize that refuse and rework use production resources, which must be taken into account in the productive capacity calculation. The aim of this work was to include these factors in factory capacity analysis, using Markov chain stochastic transition matrix as a tool to obtain the capacity factor. This factor - used together with the efficiency index and the required demand in the end of the process - results in the necessary real capacity. A case study exemplifies the proposed methodology, presenting results that allow for the
Extracting Markov Models of Peptide Conformational Dynamics from Simulation Data.
Schultheis, Verena; Hirschberger, Thomas; Carstens, Heiko; Tavan, Paul
2005-07-01
A high-dimensional time series obtained by simulating a complex and stochastic dynamical system (like a peptide in solution) may code an underlying multiple-state Markov process. We present a computational approach to most plausibly identify and reconstruct this process from the simulated trajectory. Using a mixture of normal distributions we first construct a maximum likelihood estimate of the point density associated with this time series and thus obtain a density-oriented partition of the data space. This discretization allows us to estimate the transfer operator as a matrix of moderate dimension at sufficient statistics. A nonlinear dynamics involving that matrix and, alternatively, a deterministic coarse-graining procedure are employed to construct respective hierarchies of Markov models, from which the model most plausibly mapping the generating stochastic process is selected by consideration of certain observables. Within both procedures the data are classified in terms of prototypical points, the conformations, marking the various Markov states. As a typical example, the approach is applied to analyze the conformational dynamics of a tripeptide in solution. The corresponding high-dimensional time series has been obtained from an extended molecular dynamics simulation.
Energy Technology Data Exchange (ETDEWEB)
Sagdeev, R Z
1984-01-01
The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.
Corner-point criterion for assessing nonlinear image processing imagers
Landeau, Stéphane; Pigois, Laurent; Foing, Jean-Paul; Deshors, Gilles; Swiathy, Greggory
2017-10-01
Range performance modeling of optronics imagers attempts to characterize the ability to resolve details in the image. Today, digital image processing is systematically used in conjunction with the optoelectronic system to correct its defects or to exploit tiny detection signals to increase performance. In order to characterize these processing having adaptive and non-linear properties, it becomes necessary to stimulate the imagers with test patterns whose properties are similar to the actual scene image ones, in terms of dynamic range, contours, texture and singular points. This paper presents an approach based on a Corner-Point (CP) resolution criterion, derived from the Probability of Correct Resolution (PCR) of binary fractal patterns. The fundamental principle lies in the respectful perception of the CP direction of one pixel minority value among the majority value of a 2×2 pixels block. The evaluation procedure considers the actual image as its multi-resolution CP transformation, taking the role of Ground Truth (GT). After a spatial registration between the degraded image and the original one, the degradation is statistically measured by comparing the GT with the degraded image CP transformation, in terms of localized PCR at the region of interest. The paper defines this CP criterion and presents the developed evaluation techniques, such as the measurement of the number of CP resolved on the target, the transformation CP and its inverse transform that make it possible to reconstruct an image of the perceived CPs. Then, this criterion is compared with the standard Johnson criterion, in the case of a linear blur and noise degradation. The evaluation of an imaging system integrating an image display and a visual perception is considered, by proposing an analysis scheme combining two methods: a CP measurement for the highly non-linear part (imaging) with real signature test target and conventional methods for the more linear part (displaying). The application to
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
Two-stage nonlinear filter for processing of scintigrams
International Nuclear Information System (INIS)
Pistor, P.; Hoener, J.; Walch, G.
1973-01-01
Linear filters which have been successfully used to process scintigrams can be modified in a meaningful manner by a preceding non-linear point operator, the Anscombe-transform. The advantages are: The scintigraphic noise becomes quasi-stationary and thus independent of the image. By these means the noise can be readily allowed for in the design of the convolutional operators. Transformed images with a stationary signal-to-noise ratio and a non-constant background t correspond to untransformed images with a signal-to-noise ratio that varies in certain limits. The filter chain automatically adapts to these changes. Our filter has the advantage over the majority of space-varying filters of being realizable by Fast Fourier Transform techniques. These advantages have to be paid for by reduced signal amplitude to background ratios. If the background is known, this shortcoming can be easily by-passed by processing trendfree scintigrams. If not, the filter chain should be completed by a third operator which reverses the Anscombe-transform. The Anscombe-transform influences the signal-to-noise ratio of cold spots and of hot spots in a different way. It remains an open question if this fact can be utilized to directly influence the detectability of the different kinds of spots
Nonlinear quantum electrodynamic and electroweak processes in strong laser fields
Energy Technology Data Exchange (ETDEWEB)
Meuren, Sebastian
2015-06-24
Various nonlinear electrodynamic and electroweak processes in strong plane-wave laser fields are considered with an emphasis on short-pulse effects. In particular, the momentum distribution of photoproduced electron-positron pairs is calculated numerically and a semiclassical interpretation of its characteristic features is established. By proving the optical theorem, compact double-integral expressions for the total pair-creation probability are obtained and numerically evaluated. The exponential decay of the photon wave function in a plane wave is included by solving the Schwinger-Dyson equations to leading-order in the quasistatic approximation. In this respect, the polarization operator in a plane wave is investigated and its Ward-Takahashi identity verified. A classical analysis indicates that a photoproduced electron-positron pair recollides for certain initial conditions. The contributions of such recollision processes to the polarization operator are identified and calculated both analytically and numerically. Furthermore, the existence of nontrivial electron-spin dynamics induced by quantum fluctuations is verified for ultra-short laser pulses. Finally, the exchange of weak gauge bosons is considered, which is essential for neutrino-photon interactions. In particular, the axial-vector-vector coupling tensor is calculated and the so-called Adler-Bell-Jackiw (ABJ) anomaly investigated.
Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling
1999-12-31
incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown
International Nuclear Information System (INIS)
Shrier, O; Khachan, J; Bosi, S
2006-01-01
A Markov chain method is presented as an alternative approach to Monte Carlo simulations of charge exchange collisions by an energetic hydrogen ion beam with a cold background hydrogen gas. This method was used to determine the average energy of the resulting energetic neutrals along the path of the beam. A comparison with Monte Carlo modelling showed a good agreement but with the advantage that it required much less computing time and produced no numerical noise. In particular, the Markov chain method works well for monotonically increasing or decreasing electrostatic potentials. Finally, a good agreement is obtained with experimental results from Doppler shift spectroscopy on energetic beams from a hollow cathode discharge. In particular, the average energy of ions that undergo charge exchange reaches a plateau that can be well below the full energy that might be expected from the applied voltage bias, depending on the background gas pressure. For example, pressures of ∼20 mTorr limit the ion energy to ∼20% of the applied voltage
All-optical image processing with nonlinear liquid crystals
Hong, Kuan-Lun
Liquid crystals are fascinating materials because of several advantages such as large optical birefringence, dielectric anisotropic, and easily compatible to most kinds of materials. Compared to the electro-optical properties of liquid crystals widely applied in displays and switching application, transparency through most parts of wavelengths also makes liquid crystals a better candidate for all-optical processing. The fast response time of liquid crystals resulting from multiple nonlinear effects, such as thermal and density effect can even make real-time processing realized. In addition, blue phase liquid crystals with spontaneously self-assembled three dimensional cubic structures attracted academic attention. In my dissertation, I will divide the whole contents into six parts. In Chapter 1, a brief introduction of liquid crystals is presented, including the current progress and the classification of liquid crystals. Anisotropy and laser induced director axis reorientation is presented in Chapter 2. In Chapter 3, I will solve the electrostrictive coupled equation and analyze the laser induced thermal and density effect in both static and dynamic ways. Furthermore, a dynamic simulation of laser induced density fluctuation is proposed by applying finite element method. In Chapter 4, two image processing setups are presented. One is the intensity inversion experiment in which intensity dependent phase modulation is the mechanism. The other is the wavelength conversion experiment in which I can read the invisible image with a visible probe beam. Both experiments are accompanied with simulations to realize the matching between the theories and practical experiment results. In Chapter 5, optical properties of blue phase liquid crystals will be introduced and discussed. The results of grating diffractions and thermal refractive index gradient are presented in this chapter. In addition, fiber arrays imaging and switching with BPLCs will be included in this chapter
All-optical signal processing in quadratic nonlinear materials
DEFF Research Database (Denmark)
Johansen, Steffen Kjær
2002-01-01
of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....
Confluence reduction for Markov automata (extended version)
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
Nonlinear acoustic/seismic waves in earthquake processes
International Nuclear Information System (INIS)
Johnson, Paul A.
2012-01-01
Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.
Solution of the Markov chain for the dead time problem
International Nuclear Information System (INIS)
Degweker, S.B.
1997-01-01
A method for solving the equation for the Markov chain, describing the effect of a non-extendible dead time on the statistics of time correlated pulses, is discussed. The equation, which was derived in an earlier paper, describes a non-linear process and is not amenable to exact solution. The present method consists of representing the probability generating function as a factorial cumulant expansion and neglecting factorial cumulants beyond the second. This results in a closed set of non-linear equations for the factorial moments. Stationary solutions of these equations, which are of interest for calculating the count rate, are obtained iteratively. The method is applied to the variable dead time counter technique for estimation of system parameters in passive neutron assay of Pu and reactor noise analysis. Comparisons of results by this method with Monte Carlo calculations are presented. (author)
Nonlinear fluctuation-induced rate equations for linear birth-death processes
International Nuclear Information System (INIS)
Honkonen, J.
2008-01-01
The Fock-space approach to the solution of master equations for the one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov's ecological model and Lanchester's model of modern warfare
Nonlinear fluctuations-induced rate equations for linear birth-death processes
Honkonen, J.
2008-05-01
The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
The Photoplethismographic Signal Processed with Nonlinear Time Series Analysis Tools
International Nuclear Information System (INIS)
Hernandez Caceres, Jose Luis; Hong, Rolando; Garcia Lanz, Abel; Garcia Dominguez, Luis; Cabannas, Karelia
2001-01-01
Finger photoplethismography (PPG) signals were submitted to nonlinear time series analysis. The applied analytical techniques were: (i) High degree polynomial fitting for baseline estimation; (ii) FFT analysis for estimating power spectra; (iii) fractal dimension estimation via the Higuchi's time-domain method, and (iv) kernel nonparametric estimation for reconstructing noise free-attractors and also for estimating signal's stochastic components
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
Hsieh, Shang-Hsien
1993-01-01
The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. © 2015, The International Biometric Society.
Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo
2013-01-01
We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.
Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.
Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng
2017-09-15
Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability qu...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem.......The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
Stencil method: a Markov model for transport in porous media
Delgoshaie, A. H.; Tchelepi, H.; Jenny, P.
2016-12-01
In porous media the transport of fluid is dominated by flow-field heterogeneity resulting from the underlying transmissibility field. Since the transmissibility is highly uncertain, many realizations of a geological model are used to describe the statistics of the transport phenomena in a Monte Carlo framework. One possible way to avoid the high computational cost of physics-based Monte Carlo simulations is to model the velocity field as a Markov process and use Markov Chain Monte Carlo. In previous works multiple Markov models for discrete velocity processes have been proposed. These models can be divided into two general classes of Markov models in time and Markov models in space. Both of these choices have been shown to be effective to some extent. However some studies have suggested that the Markov property cannot be confirmed for a temporal Markov process; Therefore there is not a consensus about the validity and value of Markov models in time. Moreover, previous spacial Markov models have only been used for modeling transport on structured networks and can not be readily applied to model transport in unstructured networks. In this work we propose a novel approach for constructing a Markov model in time (stencil method) for a discrete velocity process. The results form the stencil method are compared to previously proposed spacial Markov models for structured networks. The stencil method is also applied to unstructured networks and can successfully describe the dispersion of particles in this setting. Our conclusion is that both temporal Markov models and spacial Markov models for discrete velocity processes can be valid for a range of model parameters. Moreover, we show that the stencil model can be more efficient in many practical settings and is suited to model dispersion both on structured and unstructured networks.
International Nuclear Information System (INIS)
Swinney, H.L.; Swift, J.
1987-01-01
This progress report summarizes the principal accomplishments dealing with perturbation and characterization of nonlinear processes. Topics of research include Lyapunov equations, mutual information and metric entropy, the dimensions, complex dynamics and transition sequences and spatial patterns
Azimuthal asymmetry in processes of nonlinear QED for linearly polarized photon
International Nuclear Information System (INIS)
Bajer, V.N.; Mil'shtejn, A.I.
1994-01-01
Cross sections of nonlinear QED processes (photon-photon scattering, photon splitting in a Coulomb field, and Delbrueck scattering) are considered for linearly polarized initial photon. The cross sections have sizeable azimuthal asymmetry. 15 refs.; 3 figs
MARKOV CHAIN PORTFOLIO LIQUIDITY OPTIMIZATION MODEL
Directory of Open Access Journals (Sweden)
Eder Oliveira Abensur
2014-05-01
Full Text Available The international financial crisis of September 2008 and May 2010 showed the importance of liquidity as an attribute to be considered in portfolio decisions. This study proposes an optimization model based on available public data, using Markov chain and Genetic Algorithms concepts as it considers the classic duality of risk versus return and incorporating liquidity costs. The work intends to propose a multi-criterion non-linear optimization model using liquidity based on a Markov chain. The non-linear model was tested using Genetic Algorithms with twenty five Brazilian stocks from 2007 to 2009. The results suggest that this is an innovative development methodology and useful for developing an efficient and realistic financial portfolio, as it considers many attributes such as risk, return and liquidity.
Nonlinear radiation generation processes in the auroral acceleration region
Directory of Open Access Journals (Sweden)
R. Pottelette
2017-11-01
Full Text Available It is known from laboratory plasma experiments that double layers (DLs radiate in the electromagnetic spectrum; but this is only known qualitatively. In these experiments, it was shown that the electron beam created on the high-potential side of a DL generates nonlinear structures which couple to electromagnetic waves and act as a sender antenna. In the Earth auroral region, observations performed by auroral spacecraft have shown that DLs occur naturally in the source region of intense radio emissions called auroral kilometric radiation (AKR. Very high time-, spatial-, and temporal-resolution measurements are needed in order to characterize waves and particle distributions in the vicinity of DLs, which are moving transient structures. We report observations from the FAST satellite of a localized large-amplitude parallel electric field (∼ 300 mV m−1 recorded at the edges of the auroral density cavity. In agreement with laboratory experiments, on the high-potential side of the DL, elementary radiation events are detected. They occur substantially above the local electron gyrofrequency and are associated with the presence of electron holes. The velocity of these nonlinear structures can be derived from the measurement of the Doppler-shifted AKR frequency spectrum above the electron gyrofrequency. The generated electron holes appear as the nonlinear evolution of electrostatic waves generated by the electron–electron two-stream instability because they propagate at about half the beam velocity. It is pointed out that, in the vicinity of a DL, the shape of the electron distribution gives rise to a significant power recorded in the left-hand polarized ordinary (LO mode.
An ultra-efficient nonlinear planar integrated platform for optical signal processing and generation
DEFF Research Database (Denmark)
Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta
2017-01-01
This paper will discuss the recently developed integrated platform: AlGaAs-oninsulator and its broad range of nonlinear applications. Recent demonstrations of broadband optical signal processing and efficient frequency comb generations in this platform will be reviewed.......This paper will discuss the recently developed integrated platform: AlGaAs-oninsulator and its broad range of nonlinear applications. Recent demonstrations of broadband optical signal processing and efficient frequency comb generations in this platform will be reviewed....
Real-Time Implementation of Nonlinear Optical Processing Functions.
1986-09-30
information capacity) with the nonlinear error correction properties of associative neural nets such as the Hopfield model. Analogies between holography...symnolic ma.Ip’:ation Th.e error correcting -apart" :ty of non" ;n-ar associative merTtnies is necessary for s’uch structu-res Experimerta. results... geometrica snapes in contact ’A,.n a c-:’:ser ’Figure 51a’ ., and a spher:cal 4:verg.ng reference -eam Upion :"um’latlon of t -" c-’gram by the object beam
Nonlinear dynamics of global atmospheric and earth system processes
Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu
1995-01-01
During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.
Fu, Yangyang; Parsey, Guy M.; Verboncoeur, John P.; Christlieb, Andrew J.
2017-11-01
In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.
Observation uncertainty in reversible Markov chains.
Metzner, Philipp; Weber, Marcus; Schütte, Christof
2010-09-01
In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the
Markov chains and mixing times
Levin, David A
2017-01-01
Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement. -Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises...
Transport processes in magnetically confined plasmas in the nonlinear regime.
Sonnino, Giorgio
2006-06-01
A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.
Nonlinear processes in laser heating of chemically active media
Energy Technology Data Exchange (ETDEWEB)
Bunkin, F V; Kirichenko, N A; Luk' yanchuk, B S
1984-08-01
After it had been discovered and in due measure physically comprehended that numerous nontrivial phenomena observed during laser heating of chemically active media are caused primarily by self-stress of laser radiation due to the chemical intertial nonlinearity of the medium, an approach was found for solving problems of laser thermochemistry that is most adequate from the mathematical (and physical) standpoint: the approach of the theory of nonlinear oscillations in point systems and distributed systems. This approach has provided a uniform viewpoint for examination of a variety of phenomena of spatiotemporal self-organization of chemically active media under the effect of laser radiation, qualitative, and in some cases quantitative description of such phenomena as the onset of thermochemical instability, self-oscillations, various spatial structures and the like. Evidently it can be rightly considered that at this juncture a definite stage has been completed in the development of laser thermochemistry marked by the creation of an ideology, method and overall approach to interpretation of the most diverse phenomena under conditions of actual physical experiments. References to the numerous studies that make up the content of this stage of development of laser thermochemistry are to be found in survey papers. 48 references, 10 figures.
Nonlinear model predictive control for chemical looping process
Joshi, Abhinaya; Lei, Hao; Lou, Xinsheng
2017-08-22
A control system for optimizing a chemical looping ("CL") plant includes a reduced order mathematical model ("ROM") that is designed by eliminating mathematical terms that have minimal effect on the outcome. A non-linear optimizer provides various inputs to the ROM and monitors the outputs to determine the optimum inputs that are then provided to the CL plant. An estimator estimates the values of various internal state variables of the CL plant. The system has one structure adapted to control a CL plant that only provides pressure measurements in the CL loops A and B, a second structure adapted to a CL plant that provides pressure measurements and solid levels in both loops A, and B, and a third structure adapted to control a CL plant that provides full information on internal state variables. A final structure provides a neural network NMPC controller to control operation of loops A and B.
Unusual nonlinear absorption response of graphene oxide in the presence of a reduction process
International Nuclear Information System (INIS)
Karimzadeh, Rouhollah; Arandian, Alireza
2015-01-01
The nonlinear absorption responses of graphene, graphene oxide and reduced graphene oxide are investigated using the Z-scan technique and laser beams at 405, 532 and 635 nm in a continuous wave regime. Results show that graphene, graphene oxide and reduced graphene oxide do not show any open Z-scan signals at wavelengths of 532 and 635 nm. At the same time, fresh graphene oxide suspension is found to exhibit a nonlinear absorption process in the case of a laser light at 405 nm. Moreover, it can be observed that the reduction of graphene oxide by 405 nm laser irradiation decreases its nonlinear absorption value significantly. These findings highlight the important role of the reduction process on the nonlinear absorption performance of graphene oxide. (letter)
Acoustic wave focusing in complex media using Nonlinear Time Reversal coded signal processing
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Lints, M.; Kůs, V.; Salupere, A.; Převorovský, Zdeněk
2014-01-01
Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] Institutional support: RVO:61388998 Keywords : ultrasonic testing (UT) * signal processing * TR- NEWS * nonlinear time reversal * NDT * nonlinear acoustics Subject RIV: BI - Acoustics http://www.ndt.net/events/ECNDT2014/app/content/Slides/590_DosSantos_Rev1.pdf
Tamaki, Takashi; Ogawa, Takuji
2017-09-05
This review highlights molecular design for nonlinear and nonsymmetric single-molecule electronic properties such as rectification, negative differential resistance, and switching, which are important components of future single-molecule information processing devices. Perspectives on integrated "molecular circuits" are also provided. Nonlinear and nonsymmetric single-molecule electronics can be designed by utilizing (1) asymmetric molecular cores, (2) asymmetric anchoring groups, (3) an asymmetric junction environment, and (4) asymmetric electrode materials. This review mainly focuses on the design of molecular cores.
Simulations of the Ocean Response to a Hurricane: Nonlinear Processes
Zedler, Sarah E.
2009-10-01
Superinertial internal waves generated by a tropical cyclone can propagate vertically and laterally away from their local generation site and break, contributing to turbulent vertical mixing in the deep ocean and maintenance of the stratification of the main thermocline. In this paper, the results of a modeling study are reported to investigate the mechanism by which superinertial fluctuations are generated in the deep ocean. The general properties of the superinertial wave wake were also characterized as a function of storm speed and central latitude. The Massachusetts Institute of Technology (MIT) Ocean General Circulation Model (OGCM) was used to simulate the open ocean response to realistic westward-tracking hurricane-type surface wind stress and heat and net freshwater buoyancy forcing for regions representative of midlatitudes in the Atlantic, the Caribbean, and low latitudes in the eastern Pacific. The model had high horizontal [Δ(x, y) = 1/6°] and vertical (Δz = 5 m in top 100 m) resolution and employed a parameterization for vertical mixing induced by shear instability. In the horizontal momentum equation, the relative size of the nonlinear advection terms, which had a dominant frequency near twice the inertial, was large only in the upper 200 m of water. Below 200 m, the linear momentum equations obeyed a linear balance to 2%. Fluctuations at nearly twice the inertial frequency (2f) were prevalent throughout the depth of the water column, indicating that these nonlinear advection terms in the upper 200 m forced a linear mode below at nearly twice the inertial frequency via vorticity conservation. Maximum variance at 2f in horizontal velocity occurred on the south side of the track. This was in response to vertical advection of northward momentum, which in the north momentum equation is an oscillatory positive definite term that constituted a net force to the south at a frequency near 2f. The ratio of this term to the Coriolis force was larger on the
Nonlinearities in the quantum measurement process of superconducting qubits
International Nuclear Information System (INIS)
Serban, Ioana
2008-05-01
The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on
Nonlinearities in the quantum measurement process of superconducting qubits
Energy Technology Data Exchange (ETDEWEB)
Serban, Ioana
2008-05-15
The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on
Consistent Estimation of Partition Markov Models
Directory of Open Access Journals (Sweden)
Jesús E. García
2017-04-01
Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.
Directory of Open Access Journals (Sweden)
Mohammad Saber Fallah Nezhad
2012-03-01
Full Text Available For a manufacturing organization to compete effectively in the global marketplace, cutting costs and improving overall efficiency is essential. A single-stage production system with two independent quality characteristics and different costs associated with each quality characteristic that falls below a lower specification limit (scrap or above an upper specification limit (rework is presented in this paper. The amount of reworks and scraps are assumed to be depending on the process parameters such as process mean and standard deviation thus the expected total profit is significantly dependent on the process parameters. This paper develops a Markovian decision making model for determining the process means. Sensitivity analyzes is performed to validate, and a numerical example is given to illustrate the proposed model. The results showed that the optimal process means extremely effects on the quality characteristics’ parameters.
International Nuclear Information System (INIS)
Lambropoulos, P.
1998-01-01
The work on the grant for the entire period of its duration concentrated on two different but related areas, namely coherent control of photoabsorption processes and the calculation of non linear optical processes with short wavelength radiation. On the first topic, the work dealt with the problem of controlling the population transfer from one to another bound state of a system in a route that passes through a continuum. This question is most important in the context of transferring populations between vibrational states of a molecule through a sequence of two pulses taking the system via the dissociation continuum. On the second topic, their work was motivated by the availability of XUV and soft X-ray coherent radiation sources obtained through high order harmonic generation. In addition, a few other techniques based on schemes of photo-pumped X-ray lasers promise to provide in the near-future similarly coherent sources. It is thus important to have an assessment of the possibility of extending non-linear optical processes to this range of wavelengths. This means assessing the relevant magnitude of the susceptibilities for third harmonic generation, stimulated Raman scattering, two-photon absorption, etc
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Portfolio allocation under the vendor managed inventory: A Markov ...
African Journals Online (AJOL)
Portfolio allocation under the vendor managed inventory: A Markov decision process. ... Journal of Applied Sciences and Environmental Management ... This study provides a review of Markov decision processes and investigates its suitability for solutions to portfolio allocation problems under vendor managed inventory in ...
Logics and Models for Stochastic Analysis Beyond Markov Chains
DEFF Research Database (Denmark)
Zeng, Kebin
, because of the generality of ME distributions, we have to leave the world of Markov chains. To support ME distributions with multiple exits, we introduce a multi-exits ME distribution together with a process algebra MEME to express the systems having the semantics as Markov renewal processes with ME...
Energy Technology Data Exchange (ETDEWEB)
Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin [East China University of Science and Technology, Shanghai (China)
2013-06-15
Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring.
International Nuclear Information System (INIS)
Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin
2013-01-01
Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring
Noise removal in extended depth of field microscope images through nonlinear signal processing.
Zahreddine, Ramzi N; Cormack, Robert H; Cogswell, Carol J
2013-04-01
Extended depth of field (EDF) microscopy, achieved through computational optics, allows for real-time 3D imaging of live cell dynamics. EDF is achieved through a combination of point spread function engineering and digital image processing. A linear Wiener filter has been conventionally used to deconvolve the image, but it suffers from high frequency noise amplification and processing artifacts. A nonlinear processing scheme is proposed which extends the depth of field while minimizing background noise. The nonlinear filter is generated via a training algorithm and an iterative optimizer. Biological microscope images processed with the nonlinear filter show a significant improvement in image quality and signal-to-noise ratio over the conventional linear filter.
International Nuclear Information System (INIS)
Xiao Li; Zhang Wei; Huang Yidong; Peng Jiangde
2008-01-01
High nonlinear microstructure fibre (HNMF) is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability (MI) method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum (SC) generation. On one axis MI sidebands with symmetric frequency detunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift
International Nuclear Information System (INIS)
Lacasa, Lucas
2014-01-01
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein–Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments. (paper)
Hartfiel, Darald J
1998-01-01
In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.
Context Tree Estimation in Variable Length Hidden Markov Models
Dumont, Thierry
2011-01-01
We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exp...
Impurity-defect induced noncentrosymmetricity in nonlinear optical processes
International Nuclear Information System (INIS)
Miah, M. Idrish
2009-01-01
Noncentrosymmetric nanosize-material processes in cadmium iodide are formed by doping it with the impurity copper. The noncentrosymmetricity in the processes are probed by the observation of the second-order optical susceptibility χ ijk (2) . The value of χ ijk (2) is found to depend fashionably on the impurity content of the nanomaterials. The results also show that a significant enhancement in the noncentrosymmetric response is achieved in nanomaterials with reduced sizes and at low temperatures.
Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process
Directory of Open Access Journals (Sweden)
Dazi Li
2015-01-01
Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.
Confluence reduction for Markov automata
Timmer, Mark; Katoen, Joost P.; van de Pol, Jaco; Stoelinga, Mariëlle Ida Antoinette
2016-01-01
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. As expected, the state space explosion threatens the analysability of these models. We therefore introduce confluence reduction for Markov automata, a powerful reduction
A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes.
Savran, Aydogan; Kahraman, Gokalp
2014-03-01
We develop a novel adaptive tuning method for classical proportional-integral-derivative (PID) controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in industry, to the control of nonlinear processes, we introduce a method which can readily be used by the industry. In this method, controller design does not require a first principal model of the process which is usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from the measured input-output data of the process. A soft limiter is used to impose industrial limits on the control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear process involving instabilities. Several tests showed the method's success in tracking, robustness to noise, and adaptation properties. We as well compared our system's performance to those of a plant with altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude, we present a novel adaptive control method that is built upon the well-known PID architecture that successfully controls highly nonlinear industrial processes, even under conditions such as strong parameter variations, noise, and instabilities. © 2013 Published by ISA on behalf of ISA.
Study on the Evolution of Weights on the Market of Competitive Products using Markov Chains
Directory of Open Access Journals (Sweden)
Daniel Mihai Amariei
2016-10-01
Full Text Available In this paper aims the application through the Markov Process mode, within the software product WinQSB, Markov chain in the establishment of the development on the market of five brands of athletic shoes.
Impurity-defect induced noncentrosymmetricity in nonlinear optical processes
Energy Technology Data Exchange (ETDEWEB)
Miah, M. Idrish, E-mail: m.miah@griffith.edu.au [Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Department of Physics, University of Chittagong, Chittagong 4331 (Bangladesh)
2009-12-15
Noncentrosymmetric nanosize-material processes in cadmium iodide are formed by doping it with the impurity copper. The noncentrosymmetricity in the processes are probed by the observation of the second-order optical susceptibility {chi}{sub ijk}{sup (2)}. The value of {chi}{sub ijk}{sup (2)} is found to depend fashionably on the impurity content of the nanomaterials. The results also show that a significant enhancement in the noncentrosymmetric response is achieved in nanomaterials with reduced sizes and at low temperatures.
Nonlinear Lagrangian and the π N → π π π N process
International Nuclear Information System (INIS)
Pinto, F.A.
1976-02-01
A nonlinear Lagrangian is constructed involving only pions and nucleons consisting of a part invariant under the transformations of the group SU(2) (X) SU(2) and of a part which breaks this symmetry and contains an arbitrary parameter zeta introduced in order to allow the breaking of exact PCAC. The total cross-section for the process π N → π π π N at low incident energies of the incident pion, in the threshold approximation, is calculated utilizing this nonlinear Lagrangian. The parameter zeta appears in the total cross-section of the process π N → π π N also [pt
Aburas, Maher Milad; Ho, Yuek Ming; Ramli, Mohammad Firuz; Ash'aari, Zulfa Hanan
2017-07-01
The creation of an accurate simulation of future urban growth is considered one of the most important challenges in urban studies that involve spatial modeling. The purpose of this study is to improve the simulation capability of an integrated CA-Markov Chain (CA-MC) model using CA-MC based on the Analytical Hierarchy Process (AHP) and CA-MC based on Frequency Ratio (FR), both applied in Seremban, Malaysia, as well as to compare the performance and accuracy between the traditional and hybrid models. Various physical, socio-economic, utilities, and environmental criteria were used as predictors, including elevation, slope, soil texture, population density, distance to commercial area, distance to educational area, distance to residential area, distance to industrial area, distance to roads, distance to highway, distance to railway, distance to power line, distance to stream, and land cover. For calibration, three models were applied to simulate urban growth trends in 2010; the actual data of 2010 were used for model validation utilizing the Relative Operating Characteristic (ROC) and Kappa coefficient methods Consequently, future urban growth maps of 2020 and 2030 were created. The validation findings confirm that the integration of the CA-MC model with the FR model and employing the significant driving force of urban growth in the simulation process have resulted in the improved simulation capability of the CA-MC model. This study has provided a novel approach for improving the CA-MC model based on FR, which will provide powerful support to planners and decision-makers in the development of future sustainable urban planning.
Indian Academy of Sciences (India)
be obtained as a limiting value of a sample path of a suitable ... makes a mathematical model of chance and deals with the problem by .... Is the Markov chain aperiodic? It is! Here is how you can see it. Suppose that after you do the cut, you hold the top half in your right hand, and the bottom half in your left. Then there.
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 3. Markov Chain Monte Carlo - Examples. Arnab Chakraborty. General Article Volume 7 Issue 3 March 2002 pp 25-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/03/0025-0034. Keywords.
Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rissanen, Jorma
1996-01-01
Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where...
Markov chain of distances between parked cars
International Nuclear Information System (INIS)
Seba, Petr
2008-01-01
We describe the distribution of distances between parked cars as a solution of certain Markov processes and show that its solution is obtained with the help of a distributional fixed point equation. Under certain conditions the process is solved explicitly. The resulting probability density is compared with the actual parking data measured in the city. (fast track communication)
Markov and mixed models with applications
DEFF Research Database (Denmark)
Mortensen, Stig Bousgaard
This thesis deals with mathematical and statistical models with focus on applications in pharmacokinetic and pharmacodynamic (PK/PD) modelling. These models are today an important aspect of the drug development in the pharmaceutical industry and continued research in statistical methodology within...... or uncontrollable factors in an individual. Modelling using SDEs also provides new tools for estimation of unknown inputs to a system and is illustrated with an application to estimation of insulin secretion rates in diabetic patients. Models for the eect of a drug is a broader area since drugs may affect...... for non-parametric estimation of Markov processes are proposed to give a detailed description of the sleep process during the night. Statistically the Markov models considered for sleep states are closely related to the PK models based on SDEs as both models share the Markov property. When the models...
Simultaneous spatial and temporal focusing: a route towards confined nonlinear materials processing
Kammel, Robert; Bergner, Klaus; Thomas, Jens; Ackermann, Roland; Skupin, Stefan; Nolte, Stefan
2016-03-01
Ultrashort pulse lasers enable reliable and versatile high precision ablation and surface processing of various materials such as metals, polymers and semiconductors. However, when modifications deep inside the bulk of transparent media are required, nonlinear pulse material interactions can decrease the precision, since weak focusing and the long propagation of the intense pulses within the nonlinear media may induce Kerr self-focusing, filamentation and white light generation. In order to improve the precision of those modifications, simultaneous spatial and temporal focusing (SSTF) allows to reduce detrimental nonlinear interactions, because the ultrashort pulse duration is only obtained at the focus, while outside of the focal region the continuously increasing pulse duration strongly reduces the pulse intensity. In this paper, we review the fundamental concepts of this technology and provide an overview of its applications for purposes of multiphoton microscopy and laser materials processing. Moreover, numerical simulations on the nonlinear pulse propagation within transparent media illustrate the linear and nonlinear pulse propagation, highlighting the differences between conventional focusing and SSTF. Finally, fs-laser induced modifications in gelatine are presented to compare nonlinear side-effects caused by conventional focusing and SSTF. With conventional focusing the complex interplay of self-focusing and filamentation induces strongly inhomogeneous, elongated disruptions. In contrast, disruptions induced by SSTF are homogeneously located at the focal plane and reduced in length by a factor >2, which is in excellent agreement with the numerical simulations of the nonlinear pulse propagation and might favor SSTF for demanding applications such as intraocular fs-laser surgery.
Time evolution of absorption process in nonlinear metallic photonic crystals
Energy Technology Data Exchange (ETDEWEB)
Singh, Mahi R.; Hatef, Ali [Department of Physics and Astronomy, University of Western Ontario, London (Canada)
2009-05-15
The time evolution of the absorption coefficient in metallic photonic crystals has been studied numerically. These crystals are made from metallic spheres which are arranged periodically in air. The refractive index of the metallic spheres depends on the plasma frequency. Probe and pump fields are applied to monitor the absorption process. Ensembles of three-level particles are embedded in the crystal. Nanoparticles are interacting with the metallic crystals via the electron-photon interaction. It is found that when the resonance states lie away from the band edges system goes to transparent state. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Recursive smoothers for hidden discrete-time Markov chains
Directory of Open Access Journals (Sweden)
Lakhdar Aggoun
2005-01-01
Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.
A Markov decision model for optimising economic production lot size ...
African Journals Online (AJOL)
Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces ...
Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1994-05-01
Let E=L p , p≥2 and let T:E→ E be a Lipschitzian and strongly accretive mapping. Let S:E → E be defined by Sx=f-Tx+x. It is proved that under suitable conditions on the real sequences {α n } ∞ n=0 and {β n } ∞ n=0 , the iteration process, x 0 is an element of E, x n+1 =(1-α n ) x n +α n S[(1-β n ) x n +β n Sx n ], n≥0, converges strongly to the unique solution of Tx=f. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our results gives an affirmative answer to a problem posed by one of the authors in 1990. (J. Math. Anal. Appl. 151, 2 (1990) p. 460). (author). 36 refs
Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunqi; Gong, Yungui [School of Physics, Huazhong University of Science and Technology,Wuhan, Hubei 430074 (China); Wang, Bin [IFSA Collaborative Innovation Center, Department of Physics and Astronomy, Shanghai Jiao Tong University,Shanghai 200240 (China)
2016-02-17
We study the non-equilibrium condensation process in a holographic superconductor with nonlinear corrections to the U(1) gauge field. We start with an asymptotic Anti-de-Sitter(AdS) black hole against a complex scalar perturbation at the initial time, and solve the dynamics of the gravitational systems in the bulk. When the black hole temperature T is smaller than a critical value T{sub c}, the scalar perturbation grows exponentially till saturation, the final state of spacetime approaches to a hairy black hole. In the bulk theory, we find the clue of the influence of nonlinear corrections in the gauge filed on the process of the scalar field condensation. We show that the bulk dynamics in the non-equilibrium process is completely consistent with the observations on the boundary order parameter. Furthermore we examine the time evolution of horizons in the bulk non-equilibrium transformation process from the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent and event horizons show that the original AdS black hole configuration requires more time to finish the transformation to become a hairy black hole if there is nonlinear correction to the electromagnetic field. We generalize our non-equilibrium discussions to the holographic entanglement entropy and find that the holographic entanglement entropy can give us further understanding of the influence of the nonlinearity in the gauge field on the scalar condensation.
International Nuclear Information System (INIS)
Swinney, H.L.; Swift, J.
1985-01-01
Methods of characterizing nonperiodic processes in nonlinear systems are being developed and tested on low dimensional mathematical models and applied to laboratory data for nonequilibrium systems, particularly the Belousov--Zhabotinskii (BZ) reaction. Methods developed for characterizing dynamical behavior are described first, followed by a discussion of the experimental work
Scene matching based on non-linear pre-processing on reference image and sensed image
Institute of Scientific and Technical Information of China (English)
Zhong Sheng; Zhang Tianxu; Sang Nong
2005-01-01
To solve the heterogeneous image scene matching problem, a non-linear pre-processing method for the original images before intensity-based correlation is proposed. The result shows that the proper matching probability is raised greatly. Especially for the low S/N image pairs, the effect is more remarkable.
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia
2014-01-01
We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...
Markov bridges, bisection and variance reduction
DEFF Research Database (Denmark)
Asmussen, Søren; Hobolth, Asger
. In this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are presented......Time-continuous Markov jump processes is a popular modelling tool in disciplines ranging from computational finance and operations research to human genetics and genomics. The data is often sampled at discrete points in time, and it can be useful to simulate sample paths between the datapoints...
Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay
2017-11-01
Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.
NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND
Energy Technology Data Exchange (ETDEWEB)
Shoda, M.; Yokoyama, T., E-mail: shoda@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2016-04-01
Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wave with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.
Equivalent Markov-Renewal Processes.
1979-12-01
a Fa P(X0 - JON Joml(t I’Q m-lim (tm 0 J 0 A0 jA rm A- Let td be the semi algebra of sets of the form (X0 cA 0 ,-*.,Xnc An, T1 < t l,..*,Tn < t n... IHQ (tl)Q(t 2 )"Q(tn)U - Y(tI)Y(t 2). "’Y(tn). If 0 - wy then Bl - wjjl - w, so (tl)Q(t2)... Q(tn)U - WnQ(tl)Q(t 2) ... Q(tn)U - 1O¥(t )¥(t,) ..•.y
Nonlinear Pulse Shaping in Fibres for Pulse Generation and Optical Processing
Directory of Open Access Journals (Sweden)
Sonia Boscolo
2012-01-01
Full Text Available The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science. Nonlinear phenomena occurring in optical fibres have many attractive features and great, but not yet fully explored, potential in signal processing. Here, we review recent progress on the use of fibre nonlinearities for the generation and shaping of optical pulses and on the applications of advanced pulse shapes in all-optical signal processing. Amongst other topics, we will discuss ultrahigh repetition rate pulse sources, the generation of parabolic shaped pulses in active and passive fibres, the generation of pulses with triangular temporal profiles, and coherent supercontinuum sources. The signal processing applications will span optical regeneration, linear distortion compensation, optical decision at the receiver in optical communication systems, spectral and temporal signal doubling, and frequency conversion.
Ragain, Stephen; Ugander, Johan
2016-01-01
As datasets capturing human choices grow in richness and scale---particularly in online domains---there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansio...
Suppression of two-photon resonantly enhanced nonlinear processes in extended media
International Nuclear Information System (INIS)
Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.
1988-11-01
On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs
Rius, Manuel; Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José
2015-05-18
We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.
Nonlinearities in Drug Release Process from Polymeric Microparticles: Long-Time-Scale Behaviour
Directory of Open Access Journals (Sweden)
Elena Simona Bacaita
2012-01-01
Full Text Available A theoretical model of the drug release process from polymeric microparticles (a particular type of polymer matrix, through dispersive fractal approximation of motion, is built. As a result, the drug release process takes place through cnoidal oscillations modes of a normalized concentration field. This indicates that, in the case of long-time-scale evolutions, the drug particles assemble in a lattice of nonlinear oscillators occur macroscopically, through variations of drug concentration. The model is validated by experimental results.
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful fo...
Bisimulation and Simulation Relations for Markov Chains
Baier, Christel; Hermanns, H.; Katoen, Joost P.; Wolf, Verena; Aceto, L.; Gordon, A.
2006-01-01
Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete- or continuous-time Markov chains.
Fracture Mechanical Markov Chain Crack Growth Model
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
1991-01-01
propagation process can be described by a discrete space Markov theory. The model is applicable to deterministic as well as to random loading. Once the model parameters for a given material have been determined, the results can be used for any structure as soon as the geometrical function is known....
Efficient Modelling and Generation of Markov Automata
Koutny, M.; Timmer, Mark; Ulidowski, I.; Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
This paper introduces a framework for the efficient modelling and generation of Markov automata. It consists of (1) the data-rich process-algebraic language MAPA, allowing concise modelling of systems with nondeterminism, probability and Markovian timing; (2) a restricted form of the language, the
Some applications of nonlinear diffusion to processing of dynamic evolution images
International Nuclear Information System (INIS)
Goltsov, Alexey N.; Nikishov, Sergey A.
1997-01-01
Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung
Effects of noise, nonlinear processing, and linear filtering on perceived music quality.
Arehart, Kathryn H; Kates, James M; Anderson, Melinda C
2011-03-01
The purpose of this study was to determine the relative impact of different forms of hearing aid signal processing on quality ratings of music. Music quality was assessed using a rating scale for three types of music: orchestral classical music, jazz instrumental, and a female vocalist. The music stimuli were subjected to a wide range of simulated hearing aid processing conditions including, (1) noise and nonlinear processing, (2) linear filtering, and (3) combinations of noise, nonlinear, and linear filtering. Quality ratings were measured in a group of 19 listeners with normal hearing and a group of 15 listeners with sensorineural hearing impairment. Quality ratings in both groups were generally comparable, were reliable across test sessions, were impacted more by noise and nonlinear signal processing than by linear filtering, and were significantly affected by the genre of music. The average quality ratings for music were reasonably well predicted by the hearing aid speech quality index (HASQI), but additional work is needed to optimize the index to the wide range of music genres and processing conditions included in this study.
Adaptive Markov Chain Monte Carlo
Jadoon, Khan
2016-08-08
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In the MCMC simulations, posterior distribution was computed using Bayes rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD mini-Explorer. The model parameters and uncertainty for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness are not well estimated as compared to layers electrical conductivity because layer thicknesses in the model exhibits a low sensitivity to the EMI measurements, and is hence difficult to resolve. Application of the proposed MCMC based inversion to the field measurements in a drip irrigation system demonstrate that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provide useful insight about parameter uncertainty for the assessment of the model outputs.
Mallak, Saed
1996-01-01
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...
DEFF Research Database (Denmark)
Peucheret, Christophe; Da Ros, Francesco; Vukovic, Dragana
Parametric processes in materials presenting a second- or third-order nonlinearity have been widely used to demonstrate a wide range of all-optical signal processing functionalities, including amplication, wavelength conversion, regeneration, sampling, switching, modulation format conver- sion, o...
Observations of linear and nonlinear processes in the foreshock wave evolution
Directory of Open Access Journals (Sweden)
Y. Narita
2007-07-01
Full Text Available Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.
D. Schertzer; S. Lovejoy; S. Lovejoy
1994-01-01
1. The conference The third conference on "Nonlinear VAriability in Geophysics: scaling and multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993. NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first specialist conference jointly sponsored by the two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988; Schertzer and Lovejoy, 1991), five consecutive annual ...
Schertzer , D; Lovejoy , S.
1994-01-01
International audience; 1. The conference The third conference on "Nonlinear VAriability in Geophysics: scaling and multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993. NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first specialist conference jointly sponsored by the two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988; Schertzer and Lovejoy, 1991), five conse...
Volchenkov, Dima; Dawin, Jean René
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
DEFF Research Database (Denmark)
Kohlenbach, Ulrich Wilhelm
2002-01-01
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within...... the framework of Bishop-style mathematics (which has been open for about 20 years). The underivability even holds if the ine.ective schema of full comprehension (in all types) for negated formulas (in particular for -free formulas) is added, which allows one to derive the law of excluded middle...
Valenza, G; Romigi, A; Citi, L; Placidi, F; Izzi, F; Albanese, M; Scilingo, E P; Marciani, M G; Duggento, A; Guerrisi, M; Toschi, N; Barbieri, R
2016-08-01
Symptoms of temporal lobe epilepsy (TLE) are frequently associated with autonomic dysregulation, whose underlying biological processes are thought to strongly contribute to sudden unexpected death in epilepsy (SUDEP). While abnormal cardiovascular patterns commonly occur during ictal events, putative patterns of autonomic cardiac effects during pre-ictal (PRE) periods (i.e. periods preceding seizures) are still unknown. In this study, we investigated TLE-related heart rate variability (HRV) through instantaneous, nonlinear estimates of cardiovascular oscillations during inter-ictal (INT) and PRE periods. ECG recordings from 12 patients with TLE were processed to extract standard HRV indices, as well as indices of instantaneous HRV complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra) obtained through definition of inhomogeneous point-process nonlinear models, employing Volterra-Laguerre expansions of linear, quadratic, and cubic kernels. Experimental results demonstrate that the best INT vs. PRE classification performance (balanced accuracy: 73.91%) was achieved only when retaining the time-varying, nonlinear, and non-stationary structure of heartbeat dynamical features. The proposed approach opens novel important avenues in predicting ictal events using information gathered from cardiovascular signals exclusively.
Sub-wavelength patterning of organic monolayers via nonlinear processing with continuous-wave lasers
Energy Technology Data Exchange (ETDEWEB)
Mathieu, Mareike; Hartmann, Nils, E-mail: nils.hartmann@uni-due.de [Fakultaet fuer Chemie, Universitaet Duisburg-Essen, 45117 Essen (Germany); CeNIDE-Center for Nanointegration Duisburg-Essen, 47048 Duisburg (Germany); NETZ-NanoEnergieTechnikZentrum, 47048 Duisburg (Germany)
2010-12-15
In recent years, nonlinear processing with continuous-wave lasers has been demonstrated to be a facile means of rapid nanopatterning of organic monolayers down to the sub-100 nm range. In this study, we report on laser patterning of thiol-based organic monolayers with sub-wavelength resolution. Au-coated silicon substrates are functionalized with 1-hexadecanethiol. Irradiation with a focused beam of an Ar{sup +} laser operating at {lambda}=514 nm allows one to locally remove the monolayer. Subsequently, the patterns are transferred into the Au film via selective etching in a ferri-/ferrocyanide solution. Despite a 1/e{sup 2} spot diameter of about 2.8 {mu}m, structures with lateral dimensions down to 250 nm are fabricated. The underlying nonlinear dependence of the patterning process on laser intensity is traced back to the interplay between the laser-induced transient local temperature rise and the thermally activated desorption of the thiol molecules. A simple thermokinetic analysis of the data allows us to determine the effective kinetic parameters. These results complement our previous work on photothermal laser patterning of ultrathin organic coatings, such as silane-based organic monolayers, organo/silicon interfaces and supported membranes. A general introduction to nonlinear laser processing of organic monolayers is presented.
Data-driven design of fault diagnosis systems nonlinear multimode processes
Haghani Abandan Sari, Adel
2014-01-01
In many industrial applications early detection and diagnosis of abnormal behavior of the plant is of great importance. During the last decades, the complexity of process plants has been drastically increased, which imposes great challenges in development of model-based monitoring approaches and it sometimes becomes unrealistic for modern large-scale processes. The main objective of Adel Haghani Abandan Sari is to study eﬃcient fault diagnosis techniques for complex industrial systems using process historical data and considering the nonlinear behavior of the process. To this end, diﬀerent methods are presented to solve the fault diagnosis problem based on the overall behavior of the process and its dynamics. Moreover, a novel technique is proposed for fault isolation and determination of the root-cause of the faults in the system, based on the fault impacts on the process measurements. Contents Process monitoring Fault diagnosis and fault-tolerant control Data-driven approaches and decision making Target...
Ultrafast nonlinear optical processes in metal-dielectric nanocomposites and nanostructures
Energy Technology Data Exchange (ETDEWEB)
Kim, Kwang-Hyon
2012-04-13
This work reports results of a theoretical study of nonlinear optical processes in metal-dielectric nanocomposites used for the increase of the nonlinear coefficients and for plasmonic field enhancement. The main results include the study of the transient saturable nonlinearity in dielectric composites doped with metal nanoparticles, its physical mechanism as well its applications in nonlinear optics. For the study of the transient response, a time-depending equation for the dielectric function of the nanocomposite using the semi-classical two-temperature model is derived. By using this approach, we study the transient nonlinear characteristics of these materials in comparison with preceding experimental measurements. The results show that these materials behave as efficient saturable absorbers for passive mode-locking of lasers in the spectral range from the visible to near IR. We present results for the modelocked dynamics in short-wavelength solid-state and semiconductor disk lasers; in this spectral range other efficient saturable absorbers do not exist. We suggest a new mechanism for the realization of slow light phenomenon by using glasses doped with metal nanoparticles in a pump-probe regime near the plasmonic resonance. Furthermore, we study femtosecond plasmon generation by mode-locked surface plasmon polariton lasers with Bragg reflectors and metal-gain-absorber layered structures. In the final part of the thesis, we present results for high-order harmonic generation near a metallic fractal rough surface. The results show a possible reduction of the pump intensities by three orders of magnitudes and two orders of magnitudes higher efficiency compared with preceding experimental results by using bow-tie nanostructures.
Noise can speed convergence in Markov chains.
Franzke, Brandon; Kosko, Bart
2011-10-01
A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.
The Bacterial Sequential Markov Coalescent.
De Maio, Nicola; Wilson, Daniel J
2017-05-01
Bacteria can exchange and acquire new genetic material from other organisms directly and via the environment. This process, known as bacterial recombination, has a strong impact on the evolution of bacteria, for example, leading to the spread of antibiotic resistance across clades and species, and to the avoidance of clonal interference. Recombination hinders phylogenetic and transmission inference because it creates patterns of substitutions (homoplasies) inconsistent with the hypothesis of a single evolutionary tree. Bacterial recombination is typically modeled as statistically akin to gene conversion in eukaryotes, i.e. , using the coalescent with gene conversion (CGC). However, this model can be very computationally demanding as it needs to account for the correlations of evolutionary histories of even distant loci. So, with the increasing popularity of whole genome sequencing, the need has emerged for a faster approach to model and simulate bacterial genome evolution. We present a new model that approximates the coalescent with gene conversion: the bacterial sequential Markov coalescent (BSMC). Our approach is based on a similar idea to the sequential Markov coalescent (SMC)-an approximation of the coalescent with crossover recombination. However, bacterial recombination poses hurdles to a sequential Markov approximation, as it leads to strong correlations and linkage disequilibrium across very distant sites in the genome. Our BSMC overcomes these difficulties, and shows a considerable reduction in computational demand compared to the exact CGC, and very similar patterns in simulated data. We implemented our BSMC model within new simulation software FastSimBac. In addition to the decreased computational demand compared to previous bacterial genome evolution simulators, FastSimBac provides more general options for evolutionary scenarios, allowing population structure with migration, speciation, population size changes, and recombination hotspots. FastSimBac is
Parametric amplification and cascaded-nonlinearity processes in common atomic system.
Zheng, Huaibin; Zhang, Xun; Zhang, Zhaoyang; Tian, Yaling; Chen, Haixia; Li, Changbiao; Zhang, Yanpeng
2013-01-01
For the first time, we study the parametric amplification process of multi-wave mixing (PA-MWM) signal and cascaded-nonlinearity process (CNP) in sodium vapors both theoretically and experimentally, based on a conventional phase-conjugate MWM and a self-diffraction four-wave mixing (SD-FWM) processes, which are pumped by laser or amplified spontaneous emission (ASE), respectively. For laser pumping case, SD-FWM process serves as a quantum linear amplifier (a CNP) out (inside) of the resonant absorption region. While for ASE case, only the CNP occurs and the output linewidth is much narrower than that of the MWM signal due to the second selected effect of its electromagnetically induced transparency window. In addition, the phase-sensitive amplifying process seeded by two MWM processes is discussed for the first time. Theoretical fittings agree well with the experiment. The investigations have important potential applications in quantum communication.
Photo-physics of third-order nonlinear optical processes in organic dyes
International Nuclear Information System (INIS)
Delysse, Stephane
1997-01-01
We study some aspects of the nonlinear picosecond photo-physics in organic dyes using Kerr ellipsometry. The aim is to establish link between the photo-physics and nonlinear optics in these compounds. First, we study coherent processes directly linked to the third-order susceptibility. Thus, we measure two-photon absorption spectra of large internal charge transfer dyes. We take into account all coupling between three electronic states which can interfere to explain the particular response of some stilbene dyes. On the second hand, we expose a more photophysical approach to determine the S 1 → S n transition energies and moments using the measurement of excited state absorption cross sections. These results allow the prediction of the susceptibilities relevant to alternative nonlinear optical methods. Nevertheless, the stationary approach hides the complex relaxation processes which can take place in organic dyes. As an illustration, we study the formation and disappearance of a TICT (Twisted intramolecular charge transfer) in a pyrylium salt in solvents of increasing viscosity. (author) [fr
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Truccolo, Wilson
2016-11-01
This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.
Study of a multivariable nonlinear process by the phase space method
International Nuclear Information System (INIS)
Tomei, Alain
1969-02-01
This paper concerns the study of the properties of a multivariate nonlinear process using the phase space method. Based on the example of the Rapsodie reactor, a fast sodium reactor, the authors have established the simplified differential equations with the analogical study of partial differential equations (in order to replace them with ordinary differential equations), a mathematical study of dynamic properties and stability of the simplified model by the phase space method, and the verification of the model properties using an analog calculator. The reactor, with all its thermal circuits, has been considered as a nonlinear system with two inputs and one output (reactor power). The great stability of a fast reactor such as Rapsodie, in the normal operating conditions, has been verified. The same method could be applied to any other type of reactor
Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet
Energy Technology Data Exchange (ETDEWEB)
Cunha, R. O. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Interdisciplinar de Ciências da Natureza, Universidade Federal da Integração Latino-Americana, 85867-970 Foz do Iguaçu, PR (Brazil); Holanda, J.; Azevedo, A.; Rezende, S. M., E-mail: rezende@df.ufpe.br [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Vilela-Leão, L. H. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Acadêmico do Agreste, Universidade Federal de Pernambuco, 55002-970 Caruaru, PE (Brazil); Rodríguez-Suárez, R. L. [Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago (Chile)
2015-05-11
We report an investigation of the dynamics of the three-magnon splitting process associated with the ferromagnetic resonance (FMR) in films of the insulating ferrimagnet yttrium iron garnet (YIG). The experiments are performed with a 6 μm thick YIG film close to a microstrip line fed by a microwave generator operating in the 2–6 GHz range. The magnetization precession is driven by the microwave rf magnetic field perpendicular to the static magnetic field, and its dynamics is observed by monitoring the amplitude of the FMR absorption peak. The time evolution of the amplitude reveals that if the frequency is lowered below a critical value of 3.3 GHz, the FMR mode pumps two magnons with opposite wave vectors that react back on the FMR, resulting in a nonlinear dynamics of the magnetization. The results are explained by a model with coupled nonlinear equations describing the time evolution of the magnon modes.
DEFF Research Database (Denmark)
Porto da Silva, Edson
Digital signal processing (DSP) has become one of the main enabling technologies for the physical layer of coherent optical communication networks. The DSP subsystems are used to implement several functionalities in the digital domain, from synchronization to channel equalization. Flexibility...... nonlinearity compensation, (II) spectral shaping, and (III) adaptive equalization. For (I), original contributions are presented to the study of the nonlinearity compensation (NLC) with digital backpropagation (DBP). Numerical and experimental performance investigations are shown for different application...... scenarios. Concerning (II), it is demonstrated how optical and electrical (digital) pulse shaping can be allied to improve the spectral confinement of a particular class of optical time-division multiplexing (OTDM) signals that can be used as a building block for fast signaling single-carrier transceivers...
Directory of Open Access Journals (Sweden)
Dan Selişteanu
2015-01-01
Full Text Available Monoclonal antibodies (mAbs are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies.
Directory of Open Access Journals (Sweden)
N. Jaya
2008-10-01
Full Text Available In this work, a design and implementation of a Conventional PI controller, single region fuzzy logic controller, two region fuzzy logic controller and Globally Linearized Controller (GLC for a two capacity interacting nonlinear process is carried out. The performance of this process using single region FLC, two region FLC and GLC are compared with the performance of conventional PI controller about an operating point of 50 %. It has been observed that GLC and two region FLC provides better performance. Further, this procedure is also validated by real time experimentation using dSPACE.
International Nuclear Information System (INIS)
Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel
2016-01-01
Highlights: • The flux through a Markov chain of a conserved quantity (mass) is studied. • Mass is supplied by an external source and ends in the absorbing states of the chain. • Meaningful for modeling open systems whose dynamics has a Markov property. • The analytical expression of mass distribution is given for a constant source. • The expression of mass distribution is given for periodic or random sources. - Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.
International Nuclear Information System (INIS)
Zhang, Hao; Chen, Diyi; Xu, Beibei; Wang, Feifei
2015-01-01
Graphical abstract: Nonlinear dynamic transfer coefficients are introduced to the hydro-turbine governing system. In the process of load reject ion transient, the nonlinear dynamical behaviors of the system are studied in detail. - Highlights: • A novel mathematical model of a hydro-turbine governing system is established. • The process of load rejection transient is considered. • Nonlinear dynamic transfer coefficients are introduced to the system. • The bifurcation diagram with the variable t has better engineering significance. • The nonlinear dynamical behaviors of the system are studied in detail. - Abstract: This article pays attention to the mathematical modeling of a hydro-turbine governing system in the process of load rejection transient. As a pioneer work, the nonlinear dynamic transfer coefficients are introduced in a penstock system. Considering a generator system, a turbine system and a governor system, we present a novel nonlinear dynamical model of a hydro-turbine governing system. Fortunately, for the unchanged of PID parameters, we acquire the stable regions of the governing system in the process of load rejection transient by numerical simulations. Moreover, the nonlinear dynamic behaviors of the governing system are illustrated by bifurcation diagrams, Poincare maps, time waveforms and phase orbits. More importantly, these methods and analytic results will present theoretical groundwork for allowing a hydropower station in the process of load rejection transient
When high working memory capacity is and is not beneficial for predicting nonlinear processes.
Fischer, Helen; Holt, Daniel V
2017-04-01
Predicting the development of dynamic processes is vital in many areas of life. Previous findings are inconclusive as to whether higher working memory capacity (WMC) is always associated with using more accurate prediction strategies, or whether higher WMC can also be associated with using overly complex strategies that do not improve accuracy. In this study, participants predicted a range of systematically varied nonlinear processes based on exponential functions where prediction accuracy could or could not be enhanced using well-calibrated rules. Results indicate that higher WMC participants seem to rely more on well-calibrated strategies, leading to more accurate predictions for processes with highly nonlinear trajectories in the prediction region. Predictions of lower WMC participants, in contrast, point toward an increased use of simple exemplar-based prediction strategies, which perform just as well as more complex strategies when the prediction region is approximately linear. These results imply that with respect to predicting dynamic processes, working memory capacity limits are not generally a strength or a weakness, but that this depends on the process to be predicted.
Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium
Kapfer, Sebastian C.; Krauth, Werner
2017-12-01
We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.
Nonlinear dynamics of regenerative cutting processes-Comparison of two models
International Nuclear Information System (INIS)
Wang, X.S.; Hu, J.; Gao, J.B.
2006-01-01
Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons and Fractals 2002;13:1531-5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak's model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed
Definition of distance for nonlinear time series analysis of marked point process data
Energy Technology Data Exchange (ETDEWEB)
Iwayama, Koji, E-mail: koji@sat.t.u-tokyo.ac.jp [Research Institute for Food and Agriculture, Ryukoku Univeristy, 1-5 Yokotani, Seta Oe-cho, Otsu-Shi, Shiga 520-2194 (Japan); Hirata, Yoshito; Aihara, Kazuyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan)
2017-01-30
Marked point process data are time series of discrete events accompanied with some values, such as economic trades, earthquakes, and lightnings. A distance for marked point process data allows us to apply nonlinear time series analysis to such data. We propose a distance for marked point process data which can be calculated much faster than the existing distance when the number of marks is small. Furthermore, under some assumptions, the Kullback–Leibler divergences between posterior distributions for neighbors defined by this distance are small. We performed some numerical simulations showing that analysis based on the proposed distance is effective. - Highlights: • A new distance for marked point process data is proposed. • The distance can be computed fast enough for a small number of marks. • The method to optimize parameter values of the distance is also proposed. • Numerical simulations indicate that the analysis based on the distance is effective.
Zhao, Haiquan; Zeng, Xiangping; Zhang, Jiashu; Liu, Yangguang; Wang, Xiaomin; Li, Tianrui
2011-01-01
To eliminate nonlinear channel distortion in chaotic communication systems, a novel joint-processing adaptive nonlinear equalizer based on a pipelined recurrent neural network (JPRNN) is proposed, using a modified real-time recurrent learning (RTRL) algorithm. Furthermore, an adaptive amplitude RTRL algorithm is adopted to overcome the deteriorating effect introduced by the nesting process. Computer simulations illustrate that the proposed equalizer outperforms the pipelined recurrent neural network (PRNN) and recurrent neural network (RNN) equalizers. Copyright © 2010 Elsevier Ltd. All rights reserved.
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Embedded algorithms within an FPGA-based system to process nonlinear time series data
Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.
2008-03-01
This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane
2013-01-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Modeling human auditory evoked brainstem responses based on nonlinear cochlear processing
DEFF Research Database (Denmark)
Harte, James; Rønne, Filip Munch; Dau, Torsten
2010-01-01
. To generate AEPs recorded at remote locations, a convolution was made on an empirically obtained elementary unit waveform with the instantaneous discharge rate function for the corresponding AN unit. AEPs to click-trains, as well as to tone pulses at various frequencies, were both modelled and recorded...... at different stimulation levels and repetition rates. The observed nonlinearities in the recorded potential patterns, with respect to ABR wave V latencies and amplitudes, could be largely accounted for by level-dependent BM processing as well as effects of short-term neural adaptation. The present study...
Intrinsic Nonlinearities and Layout Impacts of 100 V Integrated Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Knott, Arnold; Jørgensen, Ivan Harald Holger
Parasitic capacitances of power semiconductors are a part of the key design parameters of state-of-the-art very high frequency (VHF) power supplies. In this poster, four 100 V integrated power MOSFETs with different layout structures are designed, implemented, and analyzed in a 0.18 ȝm partial...... Silicon-on-Insulator (SOI) process with a die area 2.31 mm2. A small-signal model of power MOSFETs is proposed to systematically analyze the nonlinear parasitic capacitances in different transistor states: off-state, sub-threshold region, and on-state in the linear region. 3D plots are used to summarize...
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
Reliability estimation of semi-Markov systems: a case study
International Nuclear Information System (INIS)
Ouhbi, Brahim; Limnios, Nikolaos
1997-01-01
In this article, we are concerned with the estimation of the reliability and the availability of a turbo-generator rotor using a set of data observed in a real engineering situation provided by Electricite De France (EDF). The rotor is modeled by a semi-Markov process, which is used to estimate the rotor's reliability and availability. To do this, we present a method for estimating the semi-Markov kernel from a censored data
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Strategies for Enhancing Nonlinear Internal Model Control of pH Processes
Energy Technology Data Exchange (ETDEWEB)
Hu, Qiuping.; Rangaiah, G.P. [The National University of Singapore, Singapore (Singapore). Dept. of Chemical and Environmental Engineering
1999-02-01
Control of neutralization processes is very difficult due to nonlinear dynamics, different types of disturbances and modeling errors. The objective of the paper is to evaluate two strategies (augmented internal model control, AuIMC and adaptive internal model control, AdIMC) for enhancing pH control by nonlinear internal model control (NIMC). A NIMC controller is derived directly form input output linearization. The AuIMC is composed of NIMC and an additional loop through which the difference between the process and model outputs is fed back and added to the input of the controller. For the AdIMC, and adaptive law with two tuning parameters is proposed for estimating the unknown parameter. Both AuIMC and AdIMC are extensively tested via simulation for pH neutralization. The theoretical and simulation results show that both the proposed strategies can reduce the effect of modeling errors and disturbances, and thereby enhance the performance of NIMC for pH processes. (author)
An integrated nonlinear optical loop mirror in silicon photonics for all-optical signal processing
Directory of Open Access Journals (Sweden)
Zifei Wang
2018-02-01
Full Text Available The nonlinear optical loop mirror (NOLM has been studied for several decades and has attracted considerable attention for applications in high data rate optical communications and all-optical signal processing. The majority of NOLM research has focused on silica fiber-based implementations. While various fiber designs have been considered to increase the nonlinearity and manage dispersion, several meters to hundreds of meters of fiber are still required. On the other hand, there is increasing interest in developing photonic integrated circuits for realizing signal processing functions. In this paper, we realize the first-ever passive integrated NOLM in silicon photonics and demonstrate its application for all-optical signal processing. In particular, we show wavelength conversion of 10 Gb/s return-to-zero on-off keying (RZ-OOK signals over a wavelength range of 30 nm with error-free operation and a power penalty of less than 2.5 dB, we achieve error-free nonreturn to zero (NRZ-to-RZ modulation format conversion at 10 Gb/s also with a power penalty of less than 2.8 dB, and we obtain error-free all-optical time-division demultiplexing of a 40 Gb/s RZ-OOK data signal into its 10 Gb/s tributary channels with a maximum power penalty of 3.5 dB.
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Systat Software Asia-Pacific. Ltd., in Bangalore, where the technical work for the development of the statistical software Systat takes ... In Part 4, we discuss some applications of the Markov ... one can construct the joint probability distribution of.
Constructing Dynamic Event Trees from Markov Models
International Nuclear Information System (INIS)
Paolo Bucci; Jason Kirschenbaum; Tunc Aldemir; Curtis Smith; Ted Wood
2006-01-01
In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA. In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE. To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: (a) partitioning the process variable state space into magnitude intervals (cells), (b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, (c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree. As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank
A non-linear decision making process for public involvement in environmental management activities
International Nuclear Information System (INIS)
Harper, M.R.; Kastenberg, W.
1995-01-01
The international industrial and governmental institutions involved in radioactive waste management and environmental remediation are now entering a new era in which they must significantly expand public involvement. Thus the decision making processes formerly utilized to direct and guide these institutions must now be shifted to take into consideration the needs of many more stakeholders than ever before. To meet this challenge, they now have the job of developing and creating a new set of accurate, sufficient and continuous self-regulating and self-correcting information pathways between themselves and the many divergent stakeholder groups in order to establish sustainable, trusting and respectful relationships. In this paper the authors introduce a new set of non-linear, practical and effective strategies for interaction. These self-regulating strategies provide timely feedback to a system, establishing trust and creating a viable vehicle for staying open and responsive to the needs out of which change and balanced adaptation can continually emerge for all stakeholders. The authors present a decision making process for public involvement which is congruent with the non-linear ideas of holographic and fractal relationships -- the mutual influence between related parts of the whole and the self-symmetry of systems at every level of complexity
Nuclear security assessment with Markov model approach
International Nuclear Information System (INIS)
Suzuki, Mitsutoshi; Terao, Norichika
2013-01-01
Nuclear security risk assessment with the Markov model based on random event is performed to explore evaluation methodology for physical protection in nuclear facilities. Because the security incidences are initiated by malicious and intentional acts, expert judgment and Bayes updating are used to estimate scenario and initiation likelihood, and it is assumed that the Markov model derived from stochastic process can be applied to incidence sequence. Both an unauthorized intrusion as Design Based Threat (DBT) and a stand-off attack as beyond-DBT are assumed to hypothetical facilities, and performance of physical protection and mitigation and minimization of consequence are investigated to develop the assessment methodology in a semi-quantitative manner. It is shown that cooperation between facility operator and security authority is important to respond to the beyond-DBT incidence. (author)
Hu, Ming-Lie; Wang, Ching-Yue; Song, You-Jian; Li, Yan-Feng; Chai, Lu; Serebryannikov, Evgenii; Zheltikov, Aleksei
2006-02-06
We demonstrate an experimental technique that allows a mapping of vectorial nonlinear-optical processes in multimode photonic-crystal fibers (PCFs). Spatial and polarization modes of PCFs are selectively excited in this technique by varying the tilt angle of the input beam and rotating the polarization of the input field. Intensity spectra of the PCF output plotted as a function of the input field power and polarization then yield mode-resolved maps of nonlinear-optical interactions in multimode PCFs, facilitating the analysis and control of nonlinear-optical transformations of ultrashort laser pulses in such fibers.
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
Pincus, S.
1996-01-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics
The Application of Linear and Nonlinear Water Tanks Case Study in Teaching of Process Control
Li, Xiangshun; Li, Zhiang
2018-02-01
In the traditional process control teaching, the importance of passing knowledge is emphasized while the development of creative and practical abilities of students is ignored. Traditional teaching methods are not very helpful to breed a good engineer. Case teaching is a very useful way to improve students’ innovative and practical abilities. In the traditional case teaching, knowledge points are taught separately based on different examples or no examples, thus it is very hard to setup the whole knowledge structure. Though all the knowledge is learned, how to use the knowledge to solve engineering problems keeps challenging for students. In this paper, the linear and nonlinear tanks are taken as illustrative examples which involves several knowledge points of process control. The application method of each knowledge point is discussed in detail and simulated. I believe the case-based study will be helpful for students.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Markov Chain Modelling for Short-Term NDVI Time Series Forecasting
Directory of Open Access Journals (Sweden)
Stepčenko Artūrs
2016-12-01
Full Text Available In this paper, the NDVI time series forecasting model has been developed based on the use of discrete time, continuous state Markov chain of suitable order. The normalised difference vegetation index (NDVI is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation; therefore, it is an important variable for vegetation forecasting. A Markov chain is a stochastic process that consists of a state space. This stochastic process undergoes transitions from one state to another in the state space with some probabilities. A Markov chain forecast model is flexible in accommodating various forecast assumptions and structures. The present paper discusses the considerations and techniques in building a Markov chain forecast model at each step. Continuous state Markov chain model is analytically described. Finally, the application of the proposed Markov chain model is illustrated with reference to a set of NDVI time series data.
Prognostics for Steam Generator Tube Rupture using Markov Chain model
International Nuclear Information System (INIS)
Kim, Gibeom; Heo, Gyunyoung; Kim, Hyeonmin
2016-01-01
This paper will describe the prognostics method for evaluating and forecasting the ageing effect and demonstrate the procedure of prognostics for the Steam Generator Tube Rupture (SGTR) accident. Authors will propose the data-driven method so called MCMC (Markov Chain Monte Carlo) which is preferred to the physical-model method in terms of flexibility and availability. Degradation data is represented as growth of burst probability over time. Markov chain model is performed based on transition probability of state. And the state must be discrete variable. Therefore, burst probability that is continuous variable have to be changed into discrete variable to apply Markov chain model to the degradation data. The Markov chain model which is one of prognostics methods was described and the pilot demonstration for a SGTR accident was performed as a case study. The Markov chain model is strong since it is possible to be performed without physical models as long as enough data are available. However, in the case of the discrete Markov chain used in this study, there must be loss of information while the given data is discretized and assigned to the finite number of states. In this process, original information might not be reflected on prediction sufficiently. This should be noted as the limitation of discrete models. Now we will be studying on other prognostics methods such as GPM (General Path Model) which is also data-driven method as well as the particle filer which belongs to physical-model method and conducting comparison analysis
Ju, Seongmin; Watekar, Pramod R; Han, Won-Taek
2011-01-31
Germano-silicate glass optical fiber incorporated with PbTe semiconductor quantum dots (SQDs) in the core was fabricated by using the atomization process in modified chemical vapor deposition (MCVD) process. The absorption bands attributed to PbTe semiconductor quantum dots in the fiber core were found to appear at around 687 nm and 1055 nm. The nonlinear refractive index measured by the long-period fiber grating (LPG) pair method upon pumping with laser diode at 976.4 nm was estimated to be ~1.5 × 10(-16) m2/W.
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)
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
Tornadoes and related damage costs: statistical modeling with a semi-Markov approach
Corini, Chiara; D'Amico, Guglielmo; Petroni, Filippo; Prattico, Flavio; Manca, Raimondo
2015-01-01
We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reprod...
Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes
DEFF Research Database (Denmark)
Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo
2012-01-01
In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...... our algorithm on the same data that was used in [5], where the authors use motion capture devices to record the demonstrations. As further validation we test our approach on novel data acquired on our iCub in a different demonstration scenario in which the robot is physically driven by the human...
Directory of Open Access Journals (Sweden)
Luiz Augusto da Cruz Meleiro
2005-06-01
Full Text Available In this work a MIMO non-linear predictive controller was developed for an extractive alcoholic fermentation process. The internal model of the controller was represented by two MISO Functional Link Networks (FLNs, identified using simulated data generated from a deterministic mathematical model whose kinetic parameters were determined experimentally. The FLN structure presents as advantages fast training and guaranteed convergence, since the estimation of the weights is a linear optimization problem. Besides, the elimination of non-significant weights generates parsimonious models, which allows for fast execution in an MPC-based algorithm. The proposed algorithm showed good potential in identification and control of non-linear processes.Neste trabalho um controlador preditivo não linear multivariável foi desenvolvido para um processo de fermentação alcoólica extrativa. O modelo interno do controlador foi representado por duas redes do tipo Functional Link (FLN, identificadas usando dados de simulação gerados a partir de um modelo validado experimentalmente. A estrutura FLN apresenta como vantagem o treinamento rápido e convergência garantida, já que a estimação dos seus pesos é um problema de otimização linear. Além disso, a eliminação de pesos não significativos gera modelos parsimoniosos, o que permite a rápida execução em algoritmos de controle preditivo baseado em modelo. Os resultados mostram que o algoritmo proposto tem grande potencial para identificação e controle de processos não lineares.
A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes
Directory of Open Access Journals (Sweden)
Qi-Zhi Zhang
2005-01-01
Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.
Markov Networks in Evolutionary Computation
Shakya, Siddhartha
2012-01-01
Markov networks and other probabilistic graphical modes have recently received an upsurge in attention from Evolutionary computation community, particularly in the area of Estimation of distribution algorithms (EDAs). EDAs have arisen as one of the most successful experiences in the application of machine learning methods in optimization, mainly due to their efficiency to solve complex real-world optimization problems and their suitability for theoretical analysis. This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current researc...
Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)
2001-01-01
A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.
The Havriliak-Negami susceptibility as a nonlinear and nonlocal process
International Nuclear Information System (INIS)
Miskinis, Paulius
2009-01-01
A theoretical substantiation of the Cole-Cole, Cole-Davidson and Havriliak-Negami types of susceptibilities is presented. These types of susceptibility are shown to be a manifestation of weak nonlocality and nonlinearity. The Debye susceptibility corresponds to linear and local relaxation, the Cole-Cole susceptibility being linear and nonlocal; the Cole-Davidson susceptibility is nonlinear and local and the Havriliak-Negami susceptibility corresponds to nonlinear and nonlocal relaxation.
Maglev Train Signal Processing Architecture Based on Nonlinear Discrete Tracking Differentiator
Directory of Open Access Journals (Sweden)
Zhiqiang Wang
2018-05-01
Full Text Available In a maglev train levitation system, signal processing plays an important role for the reason that some sensor signals are prone to be corrupted by noise due to the harsh installation and operation environment of sensors and some signals cannot be acquired directly via sensors. Based on these concerns, an architecture based on a new type of nonlinear second-order discrete tracking differentiator is proposed. The function of this signal processing architecture includes filtering signal noise and acquiring needed signals for levitation purposes. The proposed tracking differentiator possesses the advantages of quick convergence, no fluttering, and simple calculation. Tracking differentiator’s frequency characteristics at different parameter values are studied in this paper. The performance of this new type of tracking differentiator is tested in a MATLAB simulation and this tracking-differentiator is implemented in Very-High-Speed Integrated Circuit Hardware Description Language (VHDL. In the end, experiments are conducted separately on a test board and a maglev train model. Simulation and experiment results show that the performance of this novel signal processing architecture can fulfill the real system requirement.
Maglev Train Signal Processing Architecture Based on Nonlinear Discrete Tracking Differentiator.
Wang, Zhiqiang; Li, Xiaolong; Xie, Yunde; Long, Zhiqiang
2018-05-24
In a maglev train levitation system, signal processing plays an important role for the reason that some sensor signals are prone to be corrupted by noise due to the harsh installation and operation environment of sensors and some signals cannot be acquired directly via sensors. Based on these concerns, an architecture based on a new type of nonlinear second-order discrete tracking differentiator is proposed. The function of this signal processing architecture includes filtering signal noise and acquiring needed signals for levitation purposes. The proposed tracking differentiator possesses the advantages of quick convergence, no fluttering, and simple calculation. Tracking differentiator's frequency characteristics at different parameter values are studied in this paper. The performance of this new type of tracking differentiator is tested in a MATLAB simulation and this tracking-differentiator is implemented in Very-High-Speed Integrated Circuit Hardware Description Language (VHDL). In the end, experiments are conducted separately on a test board and a maglev train model. Simulation and experiment results show that the performance of this novel signal processing architecture can fulfill the real system requirement.
Markov chains and mixing times
Levin, David A; Wilmer, Elizabeth L
2009-01-01
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of r
Markov Models for Handwriting Recognition
Plotz, Thomas
2011-01-01
Since their first inception, automatic reading systems have evolved substantially, yet the recognition of handwriting remains an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic handwriting recognition. However, no standard procedures for building Markov model-based recognizers have yet been established. This text provides a comprehensive overview of the application of Markov models in the field of handwriting recognition, covering both hidden
International Nuclear Information System (INIS)
Mogaddam, Mehran Wahdani; Shuvalov, Vladimir V
2005-01-01
The dynamics of formation of a nonlinear response of a double phase-conjugate (PC) BaTiO 3 mirror is calculated. It is shown that because of competition between processes of different types (related to the presence of several PC channels, the local and nonlocal components of the photorefractive nonlinearity), the transient and dynamic lasing regimes for this mirror can be substantially different. It is found that the development of lasing begins with the successive formation and phasing of dynamic holograms of two different types (two PC channels). It is shown that even under optimal conditions, the lasing regime is not stationary due to competition between processes of different types, and the parameters of output fields fluctuate in time in a nontrivial way (due to the presence of the in-phase and out-of-phase components). Several scenarios of transition to the dynamic chaos are described. (nonlinear optical phenomena)
Digital signals processing using non-linear orthogonal transformation in frequency domain
Directory of Open Access Journals (Sweden)
Ivanichenko E.V.
2017-12-01
Full Text Available The rapid progress of computer technology in recent decades led to a wide introduction of methods of digital information processing practically in all fields of scientific research. In this case, among various applications of computing one of the most important places is occupied by digital processing systems signals (DSP that are used in data processing remote solution tasks of navigation of aerospace and marine objects, communications, radiophysics, digital optics and in a number of other applications. Digital Signal Processing (DSP is a dynamically developing an area that covers both technical and software tools. Related areas for digital signal processing are theory information, in particular, the theory of optimal signal reception and theory pattern recognition. In the first case, the main problem is signal extraction against a background of noise and interference of a different physical nature, and in the second - automatic recognition, i.e. classification and signal identification. In the digital processing of signals under a signal, we mean its mathematical description, i.e. a certain real function, containing information on the state or behavior of a physical system under an event that can be defined on a continuous or discrete space of time variation or spatial coordinates. In the broad sense, DSP systems mean a complex algorithmic, hardware and software. As a rule, systems contain specialized technical means of preliminary (or primary signal processing and special technical means for secondary processing of signals. Means of pretreatment are designed to process the original signals observed in general case against a background of random noise and interference of a different physical nature and represented in the form of discrete digital samples, for the purpose of detecting and selection (selection of the useful signal and evaluation characteristics of the detected signal. A new method of digital signal processing in the frequency
Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo
2015-01-01
Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.
Markov Modeling with Soft Aggregation for Safety and Decision Analysis; TOPICAL
International Nuclear Information System (INIS)
COOPER, J. ARLIN
1999-01-01
The methodology in this report improves on some of the limitations of many conventional safety assessment and decision analysis methods. A top-down mathematical approach is developed for decomposing systems and for expressing imprecise individual metrics as possibilistic or fuzzy numbers. A ''Markov-like'' model is developed that facilitates combining (aggregating) inputs into overall metrics and decision aids, also portraying the inherent uncertainty. A major goal of Markov modeling is to help convey the top-down system perspective. One of the constituent methodologies allows metrics to be weighted according to significance of the attribute and aggregated nonlinearly as to contribution. This aggregation is performed using exponential combination of the metrics, since the accumulating effect of such factors responds less and less to additional factors. This is termed ''soft'' mathematical aggregation. Dependence among the contributing factors is accounted for by incorporating subjective metrics on ''overlap'' of the factors as well as by correspondingly reducing the overall contribution of these combinations to the overall aggregation. Decisions corresponding to the meaningfulness of the results are facilitated in several ways. First, the results are compared to a soft threshold provided by a sigmoid function. Second, information is provided on input ''Importance'' and ''Sensitivity,'' in order to know where to place emphasis on considering new controls that may be necessary. Third, trends in inputs and outputs are tracked in order to obtain significant information% including cyclic information for the decision process. A practical example from the air transportation industry is used to demonstrate application of the methodology. Illustrations are given for developing a structure (along with recommended inputs and weights) for air transportation oversight at three different levels, for developing and using cycle information, for developing Importance and
Mamdani-Fuzzy Modeling Approach for Quality Prediction of Non-Linear Laser Lathing Process
Sivaraos; Khalim, A. Z.; Salleh, M. S.; Sivakumar, D.; Kadirgama, K.
2018-03-01
Lathing is a process to fashioning stock materials into desired cylindrical shapes which usually performed by traditional lathe machine. But, the recent rapid advancements in engineering materials and precision demand gives a great challenge to the traditional method. The main drawback of conventional lathe is its mechanical contact which brings to the undesirable tool wear, heat affected zone, finishing, and dimensional accuracy especially taper quality in machining of stock with high length to diameter ratio. Therefore, a novel approach has been devised to investigate in transforming a 2D flatbed CO2 laser cutting machine into 3D laser lathing capability as an alternative solution. Three significant design parameters were selected for this experiment, namely cutting speed, spinning speed, and depth of cut. Total of 24 experiments were performed with eight (8) sequential runs where they were then replicated three (3) times. The experimental results were then used to establish Mamdani - Fuzzy predictive model where it yields the accuracy of more than 95%. Thus, the proposed Mamdani - Fuzzy modelling approach is found very much suitable and practical for quality prediction of non-linear laser lathing process for cylindrical stocks of 10mm diameter.
International Nuclear Information System (INIS)
Naimzada, Ahmad K.; Sbragia, Lucia
2006-01-01
We consider a Cournot oligopoly game, where firms produce an homogenous good and the demand and cost functions are nonlinear. These features make the classical best reply solution difficult to be obtained, even if players have full information about their environment. We propose two different kinds of repeated games based on a lower degree of rationality of the firms, on a reduced information set and reduced computational capabilities. The first adjustment mechanism is called 'Local Monopolistic Approximation' (LMA). First firms get the correct local estimate of the demand function and then they use such estimate in a linear approximation of the demand function where the effects of the competitors' outputs are ignored. On the basis of this subjective demand function they solve their profit maximization problem. By using the second adjustment process, that belongs to a class of adaptive mechanisms known in the literature as 'Gradient Dynamics' (GD), firms do not solve any optimization problem, but they adjust their production in the direction indicated by their (correct) estimate of the marginal profit. Both these repeated games may converge to a Cournot-Nash equilibrium, i.e. to the equilibrium of the best reply dynamics. We compare the properties of the two different dynamical systems that describe the time evolution of the oligopoly games under the two adjustment mechanisms, and we analyze the conditions that lead to non-convergence and complex dynamic behaviors. The paper extends the results of other authors that consider similar adjustment processes assuming linear cost functions or linear demand functions
Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi
2006-02-01
The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.
Gubin, V.; Firsov, A.
2018-03-01
As the title implies the article describes the nonlinear system identification of the reduction smelting process of nickel oxide in electric arc furnaces. It is suggested that for operational control ratio of components of the charge must be solved the problem of determining the qualitative composition of the melt in real time. The use of 0th harmonic of phase voltage AC furnace as an indirect measure of the melt composition is proposed. Brief description of the mechanism of occurrence and nature of the non-zero 0th harmonic of the AC voltage of the arc is given. It is shown that value of 0th harmonic of the arc voltage is not function of electrical parameters but depends of the material composition of the melt. Processed industrial data are given. Hammerstein-Wiener model is used for description of the dependence of 0th harmonic of the furnace voltage from the technical parameters of melting furnace: the melt composition and current. Recommendations are given about the practical use of the model.
Uncovering molecular relaxation processes with nonlinear spectroscopies in the deep UV
International Nuclear Information System (INIS)
West, Brantley A.; Molesky, Brian P.; Giokas, Paul G.; Moran, Andrew M.
2013-01-01
Highlights: • We discuss the outlook for multidimensional spectroscopies in the deep UV. • Photophysics are examined in small DNA components at cryogenic temperatures. • Wavepacket motions are detected in ring-opening systems with 2DUV spectroscopy. • Measurements of electronic wavepacket motions in molecules are proposed. - Abstract: Nonlinear laser spectroscopies in the deep UV spectral range are motivated by studies of biological systems and elementary processes in small molecules. This perspective article discusses recent technical advances in this area with a particular emphasis on diffractive optic based approaches to four-wave mixing spectroscopies. Applications to two classes of systems illustrate present experimental capabilities. First, experiments on DNA components at cryogenic temperatures are used to uncover features of excited state potential energy surfaces and vibrational cooling mechanisms. Second, sub-200 fs internal conversion processes and coherent wavepacket motions are investigated in cyclohexadiene and α-terpinene. Finally, we propose new experimental directions that combine methods for producing few-cycle UV laser pulses in noble gases with incoherent detection methods (e.g., photoionization) in experiments with time resolution near a singlefemtosecond. These measurements are motivated by knowledge of extremely fast non-adiabatic dynamics and the resolution of electronic wavepacket motions in molecules
Optimization of Nonlinear Figure-of-Merits of Integrated Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Jørgensen, Ivan Harald Holger; Knott, Arnold
2016-01-01
State-of-the-art power semiconductor industry uses figure-of-merits (FOMs) for technology-to-technology and/or device-to-device comparisons. However, the existing FOMs are fundamentally nonlinear due to the nonlinearities of the parameters such as the gate charge and the output charge versus...
Directory of Open Access Journals (Sweden)
S. I. Samsudin
2014-01-01
Full Text Available The wastewater treatment plant (WWTP is highly known with the nonlinearity of the control parameters, thus it is difficult to be controlled. In this paper, the enhancement of nonlinear PI controller (ENon-PI to compensate the nonlinearity of the activated sludge WWTP is proposed. The ENon-PI controller is designed by cascading a sector-bounded nonlinear gain to linear PI controller. The rate variation of the nonlinear gain kn is automatically updated based on adaptive interaction algorithm. Initiative to simplify the ENon-PI control structure by adapting kn has been proved by significant improvement under various dynamic influents. More than 30% of integral square error and 14% of integral absolute error are reduced compared to benchmark PI for DO control and nitrate in nitrogen removal control. Better average effluent qualities, less number of effluent violations, and lower aeration energy consumption resulted.
Consistency and refinement for Interval Markov Chains
DEFF Research Database (Denmark)
Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel
2012-01-01
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...
Stochastic processes and filtering theory
Jazwinski, Andrew H
1970-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
Katoen, Joost P.; Maneesh Khattri, M.; Zapreev, I.S.; Zapreev, I.S.
2005-01-01
This short tool paper introduces MRMC, a model checker for discrete-time and continuous-time Markov reward models. It supports reward extensions of PCTL and CSL, and allows for the automated verification of properties concerning long-run and instantaneous rewards as well as cumulative rewards. In
Adaptive Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rasmussen, Tage
1996-01-01
Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding....
DETERMINANTS OF FOREIGN DIRECT INVESTMENT IN NIGERIA: A MARKOV REGIME-SWITCHING APPROACH
Directory of Open Access Journals (Sweden)
Akinlo A. Enisan
2017-04-01
Full Text Available Several studies have analyzed the movement of foreign direct investment in Nigeria using linear approach. In contrast with all existing studies in Nigeria, this paper runs several non linear FDI equations where the main determinants of FDI are determined using Markov- Regime Switching Model (MSMs. The approach enables us to observe structural changes, where exist, in FDI equations through time. Asides, where FDI regression equation is truly nonlinear, MSMs fit data better than the linear models. The paper adopts maximum likelihood methodology of Markov-Regime Model (MSM to identify possible structural changes in level and/or trends and possible changes in parameters of independent variables through the transition probabilities. The results show that FDI process in Nigeria is governed by two different regimes and a shift from one regime to another regime depends on transition probabilities. The results show that the main determinants of FDI are GDP growth, macro instability, financial development, exchange rate, inflation and discount rate. This implies liberalization that stems inflation and enhance the value of domestic currency will attract more FDI into the country.
Markov chain modelling of pitting corrosion in underground pipelines
Energy Technology Data Exchange (ETDEWEB)
Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)
2009-09-15
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Markov chain modelling of pitting corrosion in underground pipelines
International Nuclear Information System (INIS)
Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.
2009-01-01
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
An Application of Graph Theory in Markov Chains Reliability Analysis
Directory of Open Access Journals (Sweden)
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
Rizvi, S.Z.; Mohammadpour, J.; Toth, R.; Meskin, N.
2015-01-01
This paper first describes the development of a nonparametric identification method for linear parameter-varying (LPV) state-space models and then applies it to a nonlinear process system. The proposed method uses kernel-based least-squares support vector machines (LS-SVM). While parametric
A semi-Markov model for the duration of stay in a non-homogenous ...
African Journals Online (AJOL)
The semi-Markov approach to a non-homogenous manpower system is considered. The mean duration of stay in a grade and the total duration of stay in the system are obtained. A renewal type equation is developed and used in deriving the limiting distribution of the semi – Markov process. Empirical estimators of the ...
Directory of Open Access Journals (Sweden)
Zhen Chen
2016-01-01
Full Text Available Accelerated degradation test (ADT has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.
Design and implementation of novel nonlinear processes in bulk and waveguide periodic structures
Kajal, Meenu
The telecommunication networks are facing increasing demand to implement all-optical network infrastructure for enabling the wide deployment of new triple play high-speed services (e.g. IPTV, Video On Demand, Voice over IP). One of the challenges with such video broadcasting applications is that these are much more distributed and multi-point in nature unlike the traditional point-to-point communication networks. Currently deployed high-speed electronic components in the optical networks are incapable of handling the unprecedented bandwidth demand for real-time multimedia based broadcasting. The solution essentially lies in increasing the transparency of networks i.e. by replacing high speed signal processing electronics with all-optical signal processors capable of performing signal manipulations such as wavelength switching, time and wavelength division multiplexing, optical pulse compression etc. all in optical domain. This thesis aims at providing an all-optical solution for broadband wavelength conversion and tunable broadcasting, a crucial optical network component, based on quasi-phase-matched wave mixing in nonlinear materials. The quasi phase matching (QPM) technique allows phase matching in long crystal lengths by employing domain-inverted gratings to periodically reverse the sign of nonlinearity, known as periodic poling. This results into new frequency components with high conversion efficiency and has been successfully implemented towards various processes such as second harmonic generation (SHG), sum- and difference- frequency generation (SFG and DFG). Conventionally, the optical networks has an operation window of ˜35 nm centered at 1.55 mum, known as C-band. The wavelength conversion of a signal channel in C-band to an output channel also in the C-band has been demonstrated in periodically poled lithium niobate (PPLN) waveguides via the process of difference frequency mixing, cascaded SHG/DFG and cascaded SFG/DFG. While a DFG process utilized a
ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
Directory of Open Access Journals (Sweden)
Mohammad Mirabi
2012-01-01
Full Text Available
ENGLISH ABSTRACT: In this research, a Markov analysis of acceptance sampling plans in a single stage and in two stages is proposed, based on the quality of the items inspected. In a stage of this policy, if the number of defective items in a sample of inspected items is more than the upper threshold, the batch is rejected. However, the batch is accepted if the number of defective items is less than the lower threshold. Nonetheless, when the number of defective items falls between the upper and lower thresholds, the decision-making process continues to inspect the items and collect further samples. The primary objective is to determine the optimal values of the upper and lower thresholds using a Markov process to minimise the total cost associated with a batch acceptance policy. A solution method is presented, along with a numerical demonstration of the application of the proposed methodology.
AFRIKAANSE OPSOMMING: In hierdie navorsing word ’n Markov-ontleding gedoen van aannamemonsternemingsplanne wat plaasvind in ’n enkele stap of in twee stappe na gelang van die kwaliteit van die items wat geïnspekteer word. Indien die eerste monster toon dat die aantal defektiewe items ’n boonste grens oorskry, word die lot afgekeur. Indien die eerste monster toon dat die aantal defektiewe items minder is as ’n onderste grens, word die lot aanvaar. Indien die eerste monster toon dat die aantal defektiewe items in die gebied tussen die boonste en onderste grense lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre doel is om die optimale waardes van die booonste en onderste grense te bepaal deur gebruik te maak van ’n Markov-proses sodat die totale koste verbonde aan die proses geminimiseer kan word. ’n Oplossing word daarna voorgehou tesame met ’n numeriese voorbeeld van die toepassing van die voorgestelde oplossing.
Benchmarking of a Markov multizone model of contaminant transport.
Jones, Rachael M; Nicas, Mark
2014-10-01
A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). © The Author 2014. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.
DEFF Research Database (Denmark)
Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben
2017-01-01
The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo......-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations...
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk
2015-01-01
Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics
Nonlinear processes in laser-produced dense plasma (observation of the fractional harmonics)
International Nuclear Information System (INIS)
Lyu, K.S.
1988-01-01
One of the main issues of laser plasma physics interactions is harmonic generation. The harmonic emission spectrum provides clues as to which non-linear processes take place in the plasma. Several effects contribute to a given line as judged from the complexity of the actual spectra. Unfolding of them has not been done satisfactorily yet. Harmonic lines with half integer or integer orders have been observed, but the physics are far from complete. In this dissertation research, we observed the usual second harmonic generation and a set of fractional harmonics which we believe have been observed for the first time in plasma physics. The plasma was produced by a high power laser and we have characterized its properties from the analysis of the radiation spectra, including the harmonic lines, as measured using the methods of transient spectroscopy. We produced the plasma with a Nd:glass laser which had a 65 nsec pulse width (FWHM) with a total energy of up to 6 Joules. The targets were steel alloys, copper, and aluminum. The harmonic generation from the plasma with a planar metal target was not strong. But, it became stronger when we made a dead hole (cavity) at the laser spot on the target surface. The second harmonic line appears first before the time of the peak of laser pulse. The fractional harmonics, which are related to the laser wavelength by rational number other than integers or half integers, appear near or after the time of the laser peak and weaker in UV wavelength range but stronger if some atomic emission line are near by. To understand the plasma evolution better, we developed computer simulation codes. The codes contain all relevant processes necessary to compute the plasma evolution
Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing
Directory of Open Access Journals (Sweden)
Ming Ma
2016-11-01
Full Text Available All-optical signal processing based on nonlinear optical effects allows for the realization of important functions in telecommunications including wavelength conversion, optical multiplexing/demultiplexing, Fourier transformation, and regeneration, amongst others, on ultrafast time scales to support high data rate transmission. In integrated photonic subsystems, the majority of all-optical signal processing systems demonstrated to date typically process only a single channel at a time or perform a single processing function, which imposes a serious limitation on the functionality of integrated solutions. Here, we demonstrate how nonlinear optical effects can be harnessed in a mode-selective manner to perform simultaneous multi-channel (two and multi-functional optical signal processing (i.e., regenerative wavelength conversion in an integrated silicon photonic device. This approach, which can be scaled to a higher number of channels, opens up a new degree of freedom for performing a broad range of multi-channel nonlinear optical signal processing functions using a single integrated photonic device.
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
Influence of credit scoring on the dynamics of Markov chain
Galina, Timofeeva
2015-11-01
Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
Prediction of pipeline corrosion rate based on grey Markov models
International Nuclear Information System (INIS)
Chen Yonghong; Zhang Dafa; Peng Guichu; Wang Yuemin
2009-01-01
Based on the model that combined by grey model and Markov model, the prediction of corrosion rate of nuclear power pipeline was studied. Works were done to improve the grey model, and the optimization unbiased grey model was obtained. This new model was used to predict the tendency of corrosion rate, and the Markov model was used to predict the residual errors. In order to improve the prediction precision, rolling operation method was used in these prediction processes. The results indicate that the improvement to the grey model is effective and the prediction precision of the new model combined by the optimization unbiased grey model and Markov model is better, and the use of rolling operation method may improve the prediction precision further. (authors)
Triangular M/G/1-type and tree-like QBD Markov chains
Van Houdt, B.; Leeuwaarden, van J.S.H.
2009-01-01
In applying matrix-analytic methods to M/G/1-type and tree-like QBD Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1-type and tree-like QBD
Markov chain Monte Carlo methods for statistical analysis of RF photonic devices
DEFF Research Database (Denmark)
Piels, Molly; Zibar, Darko
2016-01-01
uncertainty is shown to give unsatisfactory and incorrect results due to the nonlinear relationship between the circuit parameters and the measured data. Markov chain Monte Carlo methods are shown to provide superior results, both for individual devices and for assessing within-die variation...
Application of Hidden Markov Models in Biomolecular Simulations.
Shukla, Saurabh; Shamsi, Zahra; Moffett, Alexander S; Selvam, Balaji; Shukla, Diwakar
2017-01-01
Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
Hennecke, M.
1997-01-01
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation
Czech Academy of Sciences Publication Activity Database
Scarpa, G.; Gaetano, R.; Haindl, Michal; Zerubia, J.
2009-01-01
Roč. 18, č. 8 (2009), s. 1830-1843 ISSN 1057-7149 R&D Projects: GA ČR GA102/08/0593 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : Classification * texture analysis * segmentation * hierarchical image models * Markov process Subject RIV: BD - Theory of Information Impact factor: 2.848, year: 2009 http://library.utia.cas.cz/separaty/2009/RO/haindl-hierarchical multiple markov chain model for unsupervised texture segmentation.pdf
Detecting Faults By Use Of Hidden Markov Models
Smyth, Padhraic J.
1995-01-01
Frequency of false alarms reduced. Faults in complicated dynamic system (e.g., antenna-aiming system, telecommunication network, or human heart) detected automatically by method of automated, continuous monitoring. Obtains time-series data by sampling multiple sensor outputs at discrete intervals of t and processes data via algorithm determining whether system in normal or faulty state. Algorithm implements, among other things, hidden first-order temporal Markov model of states of system. Mathematical model of dynamics of system not needed. Present method is "prior" method mentioned in "Improved Hidden-Markov-Model Method of Detecting Faults" (NPO-18982).
Honest Importance Sampling with Multiple Markov Chains.
Tan, Aixin; Doss, Hani; Hobert, James P
2015-01-01
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable
Zhao, Ning-bo; Yang, Jia-long; Li, Shu-ying; Sun, Yue-wu
2014-01-01
Performance degradation forecast technology for quantitatively assessing degradation states of aeroengine using exhaust gas temperature is an important technology in the aeroengine health management. In this paper, a GM (1, 1) Markov chain-based approach is introduced to forecast exhaust gas temperature by taking the advantages of GM (1, 1) model in time series and the advantages of Markov chain model in dealing with highly nonlinear and stochastic data caused by uncertain factors. In this ap...
Markov Chain Ontology Analysis (MCOA).
Frost, H Robert; McCray, Alexa T
2012-02-03
Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.
Neuroevolution Mechanism for Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-12-01
Full Text Available Hidden Markov Model (HMM is a statistical model based on probabilities. HMM is becoming one of the major models involved in many applications such as natural language
processing, handwritten recognition, image processing, prediction systems and many more. In this research we are concerned with finding out the best HMM for a certain application domain. We propose a neuroevolution process that is based first on converting the HMM to a neural network, then generating many neural networks at random where each represents a HMM. We proceed by
applying genetic operators to obtain new set of neural networks where each represents HMMs, and updating the population. Finally select the best neural network based on a fitness function.
A Markov Chain Model for Contagion
Directory of Open Access Journals (Sweden)
Angelos Dassios
2014-11-01
Full Text Available We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011.
Estimation of the workload correlation in a Markov fluid queue
Kaynar, B.; Mandjes, M.R.H.
2013-01-01
This paper considers a Markov fluid queue, focusing on the correlation function of the stationary workload process. A simulation-based computation technique is proposed, which relies on a coupling idea. Then an upper bound on the variance of the resulting estimator is given, which reveals how the
Efficient Approximation of Optimal Control for Markov Games
DEFF Research Database (Denmark)
Fearnley, John; Rabe, Markus; Schewe, Sven
2011-01-01
We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately...
The Candy model revisited: Markov properties and inference
M.N.M. van Lieshout (Marie-Colette); R.S. Stoica
2001-01-01
textabstractThis paper studies the Candy model, a marked point process introduced by Stoica et al. (2000). We prove Ruelle and local stability, investigate its Markov properties, and discuss how the model may be sampled. Finally, we consider estimation of the model parameters and present some
Efficient Modelling and Generation of Markov Automata (extended version)
Timmer, Mark; Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
2012-01-01
This paper introduces a framework for the efficient modelling and generation of Markov automata. It consists of (1) the data-rich process-algebraic language MAPA, allowing concise modelling of systems with nondeterminism, probability and Markovian timing; (2) a restricted form of the language, the
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1985-01-01
A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds as t/sup -4.05/
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1984-10-01
A continuous time Markov chain is used to model motion in the neighborhood of a critical noble invariant circle in an area-preserving map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. The nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to Hamiltonian systems the decay proceeds as t -4 05
Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process. Initially it is shown how the indicated systems can be converted to an equivalent Poisson driven system at the expense of introducing...... additional discrete-valued state variables for which the stochastic equations are also formulated....
Epitope discovery with phylogenetic hidden Markov models.
LENUS (Irish Health Repository)
Lacerda, Miguel
2010-05-01
Existing methods for the prediction of immunologically active T-cell epitopes are based on the amino acid sequence or structure of pathogen proteins. Additional information regarding the locations of epitopes may be acquired by considering the evolution of viruses in hosts with different immune backgrounds. In particular, immune-dependent evolutionary patterns at sites within or near T-cell epitopes can be used to enhance epitope identification. We have developed a mutation-selection model of T-cell epitope evolution that allows the human leukocyte antigen (HLA) genotype of the host to influence the evolutionary process. This is one of the first examples of the incorporation of environmental parameters into a phylogenetic model and has many other potential applications where the selection pressures exerted on an organism can be related directly to environmental factors. We combine this novel evolutionary model with a hidden Markov model to identify contiguous amino acid positions that appear to evolve under immune pressure in the presence of specific host immune alleles and that therefore represent potential epitopes. This phylogenetic hidden Markov model provides a rigorous probabilistic framework that can be combined with sequence or structural information to improve epitope prediction. As a demonstration, we apply the model to a data set of HIV-1 protein-coding sequences and host HLA genotypes.