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...
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
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
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
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
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.
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
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...
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.
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...
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
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)
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...
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.
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.
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Wintenberger, Olivier
2014-01-01
We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable...... limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition....
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
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.
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.
Directory of Open Access Journals (Sweden)
Shi Zhiyan
2009-01-01
Full Text Available We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.
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
Directory of Open Access Journals (Sweden)
Bao Wang
2014-01-01
Full Text Available We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.
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...
Directory of Open Access Journals (Sweden)
Huilin Huang
2014-01-01
Full Text Available We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.
Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees
Directory of Open Access Journals (Sweden)
Weicai Peng
2016-02-01
Full Text Available Abstract In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.
Weighted-indexed semi-Markov models for modeling financial returns
International Nuclear Information System (INIS)
D’Amico, Guglielmo; Petroni, Filippo
2012-01-01
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains for studying the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted-indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series such as the first-passage-time distributions and the persistence of volatility. The model is applied to data from the Italian and German stock markets from 1 January 2007 until the end of December 2010. (paper)
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
Reliability measures for indexed semi-Markov chains applied to wind energy production
International Nuclear Information System (INIS)
D'Amico, Guglielmo; Petroni, Filippo; Prattico, Flavio
2015-01-01
The computation of the dependability measures is a crucial point in many engineering problems as well as in the planning and development of a wind farm. In this paper we address the issue of energy production by wind turbines by using an indexed semi-Markov chain as a model of wind speed. We present the mathematical model, the data and technical characteristics of a commercial wind turbine (Aircon HAWT-10kW). We show how to compute some of the main dependability measures such as reliability, availability and maintainability functions. We compare the results of the model with real energy production obtained from data available in the Lastem station (Italy) and sampled every 10 min. - Highlights: • Semi-Markov models. • Time series generation of wind speed. • Computation of availability, reliability and maintainability.
Directory of Open Access Journals (Sweden)
Pradeepa Yahampath
2008-03-01
Full Text Available Speech coding techniques capable of generating encoded representations which are robust against channel losses play an important role in enabling reliable voice communication over packet networks and mobile wireless systems. In this paper, we investigate the use of multiple description index assignments (MDIAs for loss-tolerant transmission of line spectral frequency (LSF coefficients, typically generated by state-of-the-art speech coders. We propose a simulated annealing-based approach for optimizing MDIAs for Markov-model-based decoders which exploit inter- and intraframe correlations in LSF coefficients to reconstruct the quantized LSFs from coded bit streams corrupted by channel losses. Experimental results are presented which compare the performance of a number of novel LSF transmission schemes. These results clearly demonstrate that Markov-model-based decoders, when used in conjunction with optimized MDIA, can yield average spectral distortion much lower than that produced by methods such as interleaving/interpolation, commonly used to combat the packet losses.
Directory of Open Access Journals (Sweden)
Rondeau Paul
2008-01-01
Full Text Available Speech coding techniques capable of generating encoded representations which are robust against channel losses play an important role in enabling reliable voice communication over packet networks and mobile wireless systems. In this paper, we investigate the use of multiple description index assignments (MDIAs for loss-tolerant transmission of line spectral frequency (LSF coefficients, typically generated by state-of-the-art speech coders. We propose a simulated annealing-based approach for optimizing MDIAs for Markov-model-based decoders which exploit inter- and intraframe correlations in LSF coefficients to reconstruct the quantized LSFs from coded bit streams corrupted by channel losses. Experimental results are presented which compare the performance of a number of novel LSF transmission schemes. These results clearly demonstrate that Markov-model-based decoders, when used in conjunction with optimized MDIA, can yield average spectral distortion much lower than that produced by methods such as interleaving/interpolation, commonly used to combat the packet losses.
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.
Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain
Dai, Yonghui; Han, Dongmei; Dai, Weihui
2014-01-01
The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP) neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market. PMID:24782659
Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain
Directory of Open Access Journals (Sweden)
Yonghui Dai
2014-01-01
Full Text Available The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market.
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 ...
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.
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)
Imam Wahyudi
2014-08-01
Full Text Available Asia's inancial crisis in July 1997 affects currency, capital market, and real market throughout Asian countries. Countries in southeast region (ASEAN, including Indonesia, Malaysia, Philippines, Singapore, and Thailand, are some of the countries where the crisis hit the most. In these countries, where inancial sectors are far more developed than real sectors and the money market sectors, most of the economic activities are conducted in capital market. Movement in the capital market could be a proxy to describe the overall economic situation and therefore the prediction of it could be an early warning system of economic crises. This paper tries to investigate movement in ASEAN (Indonesia, Malaysia, Philippines, Singapore, and Thailand capital market to build an early warning system from inancial sectors perspective. This paper will be very beneicial for the government to anticipate the forthcoming crisis. The insight of this paper is from Hamilton (1990 model of regime switching process in which he divide the movement of currency into two regimes, describe the switching transition based on Markov process and creates different model for each regimes. Differ from Hamilton, our research focuses on index return instead of currency to model the regime switching. This research aimed to ind the probability of crisis in the future by combining the probability of switching and the probability distribution function of each regime. Probability of switching is estimated by categorizing the movement in index return into two regimes (negative return in regime 1 and positive return in regime 2 then measuring the proportion of switching to regime 1 in t given regime
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...
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.
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
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.
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...
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.
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.
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
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.
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.
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...
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.
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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.
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.
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
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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.
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.
Reflection Positive Stochastic Processes Indexed by Lie Groups
Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur
2016-06-01
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.
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
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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.
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)
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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
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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.
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
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.
Ciampi, Antonio; Dyachenko, Alina; Cole, Martin; McCusker, Jane
2011-12-01
The study of mental disorders in the elderly presents substantial challenges due to population heterogeneity, coexistence of different mental disorders, and diagnostic uncertainty. While reliable tools have been developed to collect relevant data, new approaches to study design and analysis are needed. We focus on a new analytic approach. Our framework is based on latent class analysis and hidden Markov chains. From repeated measurements of a multivariate disease index, we extract the notion of underlying state of a patient at a time point. The course of the disorder is then a sequence of transitions among states. States and transitions are not observable; however, the probability of being in a state at a time point, and the transition probabilities from one state to another over time can be estimated. Data from 444 patients with and without diagnosis of delirium and dementia were available from a previous study. The Delirium Index was measured at diagnosis, and at 2 and 6 months from diagnosis. Four latent classes were identified: fairly healthy, moderately ill, clearly sick, and very sick. Dementia and delirium could not be separated on the basis of these data alone. Indeed, as the probability of delirium increased, so did the probability of decline of mental functions. Eight most probable courses were identified, including good and poor stable courses, and courses exhibiting various patterns of improvement. Latent class analysis and hidden Markov chains offer a promising tool for studying mental disorders in the elderly. Its use may show its full potential as new data become available.
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
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.
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.
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
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...
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.
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...
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...
Radiographic rejection index using statistical process control
International Nuclear Information System (INIS)
Savi, M.B.M.B.; Camozzato, T.S.C.; Soares, F.A.P.; Nandi, D.M.
2015-01-01
The Repeat Analysis Index (IRR) is one of the items contained in the Quality Control Program dictated by brazilian law of radiological protection and should be performed frequently, at least every six months. In order to extract more and better information of IRR, this study presents the Statistical Quality Control applied to reject rate through Statistical Process Control (Control Chart for Attributes ρ - GC) and the Pareto Chart (GP). Data collection was performed for 9 months and the last four months of collection was given on a daily basis. The Limits of Control (LC) were established and Minitab 16 software used to create the charts. IRR obtained for the period was corresponding to 8.8% ± 2,3% and the generated charts analyzed. Relevant information such as orders for X-ray equipment and processors were crossed to identify the relationship between the points that exceeded the control limits and the state of equipment at the time. The GC demonstrated ability to predict equipment failures, as well as the GP showed clearly what causes are recurrent in IRR. (authors) [pt
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
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,
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
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
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...
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.
Similarity search processing. Paralelization and indexing technologies.
Directory of Open Access Journals (Sweden)
Eder Dos Santos
2015-08-01
The next Scientific-Technical Report addresses the similarity search and the implementation of metric structures on parallel environments. It also presents the state of the art related to similarity search on metric structures and parallelism technologies. Comparative analysis are also proposed, seeking to identify the behavior of a set of metric spaces and metric structures over processing platforms multicore-based and GPU-based.
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.
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.
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.
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.
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
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.
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...
Reliability analysis of Markov history-dependent repairable systems with neglected failures
International Nuclear Information System (INIS)
Du, Shijia; Zeng, Zhiguo; Cui, Lirong; Kang, Rui
2017-01-01
Markov history-dependent repairable systems refer to the Markov repairable systems in which some states are changeable and dependent on recent evolutional history of the system. In practice, many Markov history-dependent repairable systems are subjected to neglected failures, i.e., some failures do not affect system performances if they can be repaired promptly. In this paper, we develop a model based on the theory of aggregated stochastic processes to describe the history-dependent behavior and the effect of neglected failures on the Markov history-dependent repairable systems. Based on the developed model, instantaneous and steady-state availabilities are derived to characterize the reliability of the system. Four reliability-related time distributions, i.e., distribution for the k th working period, distribution for the k th failure period, distribution for the real working time in an effective working period, distribution for the neglected failure time in an effective working period, are also derived to provide a more comprehensive description of the system's reliability. Thanks to the power of the theory of aggregated stochastic processes, closed-form expressions are obtained for all the reliability indexes and time distributions. Finally, the developed indexes and analysis methods are demonstrated by a numerical example. - Highlights: • Markovian history-dependent repairable systems with neglected failures is modeled. • Aggregated stochastic processes are used to derive reliability indexes and time distributions. • Closed-form expressions are derived for the considered indexes and distributions.
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
A new approach to process control using Instability Index
Weintraub, Jeffrey; Warrick, Scott
2016-03-01
The merits of a robust Statistical Process Control (SPC) methodology have long been established. In response to the numerous SPC rule combinations, processes, and the high cost of containment, the Instability Index (ISTAB) is presented as a tool for managing these complexities. ISTAB focuses limited resources on key issues and provides a window into the stability of manufacturing operations. ISTAB takes advantage of the statistical nature of processes by comparing the observed average run length (OARL) to the expected run length (ARL), resulting in a gap value called the ISTAB index. The ISTAB index has three characteristic behaviors that are indicative of defects in an SPC instance. Case 1: The observed average run length is excessively long relative to expectation. ISTAB > 0 is indicating the possibility that the limits are too wide. Case 2: The observed average run length is consistent with expectation. ISTAB near zero is indicating that the process is stable. Case 3: The observed average run length is inordinately short relative to expectation. ISTAB system based on ISTAB as an enhancement to more traditional SPC approaches.
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
Protein Solubility as Quality Index for Processed Soybean
Directory of Open Access Journals (Sweden)
Rodica Căpriţă
2010-05-01
Full Text Available Protein quality of soybean meal (SBM is linked to both the reduction of antinutritional factors (ANFs, and the optimization of protein digestibility. Both insufficient- and over-heating result in poor quality SBM. Inadequate heating fails to completely destroy the ANFs, which may have a detrimental impact on animal performance, while excessive heating reduces the availability of lysine via the Maillard reaction and possibly, to a lesser extent, of other amino acids. The objective of our study was to compare some biochemical laboratory procedures for assessing quality of SBM: urease index (UI, protein dispersibility index (PDI, KOH protein solubility (PS, and nitrogen solubility index (NSI. The experimental data reveal that UI is not useful to determine excessive heat treatment since additional heating has no effect on the urease index. KOH protein solubility remains high, during initial heat treatment. In marked contrast, the PDI and NSI decreased incrementally from 78% to 20% and from 97% to 60%, respectively, when heating 0 to 30 minutes. Combing the PDI test with the urease test could be useful to monitor soybean quality. SBM containing low UI (0.3 or below and high PDI (40 to 45% may indicate that the sample is definitely high quality because it has been adequately heat processed, but not overprocessed.
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....
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.
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.
The Sustainable Process Index. A new dimension in ecological evaluation
International Nuclear Information System (INIS)
Krotscheck, Christian; Narodoslawsky, Michael
1996-01-01
The Sustainable Process Index (SPI) is a measure developed to evaluate the viability of processes under sustainable economic conditions. Its advantages are its universal applicability, its scientific basis, the possibility of adoption in process analyses and syntheses, the high sensitivity for sustainable qualities, and the capability of aggregation to one measure. It has proved to be useful in industrial strategic planning. The concept of the SPI is based on the assumption that in a truly sustainable society the basis of economy is the sustainable flow of solar exergy. The conversion of the solar exergy to services needs area. Thus, area becomes the limiting factor of a sustainable economy. The SPI evaluates the areas needed to provide the raw materials and energy demands and to accommodate by-product flows from a process in a sustainable way. It relates these areas to the area available to a citizen in a given geographical (from regional to global) context. The data necessary to calculate the SPI are usually known at an early stage in process development. The result of the computation is the ratio between the area needed to supply a citizen with a given service and the area needed to supply a citizen with all possible services. Thus, it is a measure of the expense of this service in an economy oriented towards sustainability
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+) .
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...
The impact of processing delay on the exposure index value
Butler, M. L.; Brennan, P. C.; Last, J.; Rainford, L.
2010-04-01
Digital radiography poses the risk of unnoticed increases in patient dose. Manufacturers responded to this by offering an exposure index (EI) value to clinicians. Use of the EI value in clinical practice is encouraged by the American College of Radiology and American Association of Physicists in Medicine. This study assesses the impact of processing delay on the EI value. An anthropormorphic phantom was used to simulate three radiographic examinations; skull, pelvis and chest. For each examination, the phantom was placed in the optimal position and exposures were chosen in accordance with international guidelines. A Carestream (previously Kodak) computed radiography system was used. The imaging plate was exposed, and processing was delayed in various increments from 30 seconds to 24 hours, representing common delays in clinical practice. The EI value was recorded for each exposure. The EI value decreased considerably with increasing processing delay. The EI value decreased by 100 within 25 minutes delay for the chest, and 20 minutes for the skull and pelvis. Within 1 hour, the EI value had fallen by 180, 160 and 100 for the chest, skull and pelvis respectively. After 24 hours, the value had decreased by 370, 350 and 340 for the chest, skull and pelvis respectively, representing to the clinician more then a halving of exposure to the detector in Carestream systems. The assessment of images using EI values should be approached with caution in clinical practice when delays in processing occur. The use of EI values as a feedback mechanism is questioned.
A Bayesian Markov geostatistical model for estimation of hydrogeological properties
International Nuclear Information System (INIS)
Rosen, L.; Gustafson, G.
1996-01-01
A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden
Random number generation as an index of controlled processing.
Jahanshahi, Marjan; Saleem, T; Ho, Aileen K; Dirnberger, Georg; Fuller, R
2006-07-01
Random number generation (RNG) is a functionally complex process that is highly controlled and therefore dependent on Baddeley's central executive. This study addresses this issue by investigating whether key predictions from this framework are compatible with empirical data. In Experiment 1, the effect of increasing task demands by increasing the rate of the paced generation was comprehensively examined. As expected, faster rates affected performance negatively because central resources were increasingly depleted. Next, the effects of participants' exposure were manipulated in Experiment 2 by providing increasing amounts of practice on the task. There was no improvement over 10 practice trials, suggesting that the high level of strategic control required by the task was constant and not amenable to any automatization gain with repeated exposure. Together, the results demonstrate that RNG performance is a highly controlled and demanding process sensitive to additional demands on central resources (Experiment 1) and is unaffected by repeated performance or practice (Experiment 2). These features render the easily administered RNG task an ideal and robust index of executive function that is highly suitable for repeated clinical use. ((c) 2006 APA, all rights reserved).
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.
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...
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)
Usefulness of surgical complexity classification index in cataract surgery process.
Salazar Méndez, R; Cuesta García, M; Llaneza Velasco, M E; Rodríguez Villa, S; Cubillas Martín, M; Alonso Álvarez, C M
2016-06-01
To evaluate the usefulness of surgical complexity classification index (SCCI) to predict the degree of surgical difficulty in cataract surgery. This retrospective study includes data collected between January 2013 and December 2014 from patients who underwent cataract extraction by phacoemulsification at our hospital. A sample size of 159 patients was obtained by simple random sampling (P=.5, 10% accuracy, 95% confidence). The main variables were: recording and value of SCCI in electronic medical record (EMR), presence of exfoliation syndrome (XFS), criteria for inclusion in surgical waiting list (SWL), and functional results. SCCI was classified into 7 categories (range: 1-4) according to predictors of technical difficulty, which was indirectly estimated in terms of surgical time (ST). All statistical analyses were performed using SPSS v15.0 statistical software. Prevalence of XFS was 18.2% (95%CI: 11.9-24.5). In terms of quality indicators in the cataract surgery process, 96.8% of patients met at least one of the criteria to be included in SWL, and 98.1% gained ≥2 Snellen lines. The SCCI was recorded in EMR of 98.1% patients, and it was grouped for study into 2 categories: High and low surgical complexity. Statistically significant differences in the distribution of ST were found depending on the assigned SCCI (Pde Oftalmología. Published by Elsevier España, S.L.U. All rights reserved.
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...
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
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.
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...
Hagy, Jessica
2008-01-01
Jessica Hagy is a different kind of thinker. She has an astonishing talent for visualizing relationships, capturing in pictures what is difficult for most of us to express in words. At indexed.blogspot.com, she posts charts, graphs, and Venn diagrams drawn on index cards that reveal in a simple and intuitive way the large and small truths of modern life. Praised throughout the blogosphere as “brilliant,” “incredibly creative,” and “comic genius,” Jessica turns her incisive, deadpan sense of humor on everything from office politics to relationships to religion. With new material along with some of Jessica’s greatest hits, this utterly unique book will thrill readers who demand humor that makes them both laugh and think.
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 ...
Massive-scale RDF Processing Using Compressed Bitmap Indexes
Energy Technology Data Exchange (ETDEWEB)
Madduri, Kamesh; Wu, Kesheng
2011-05-26
The Resource Description Framework (RDF) is a popular data model for representing linked data sets arising from the web, as well as large scienti c data repositories such as UniProt. RDF data intrinsically represents a labeled and directed multi-graph. SPARQL is a query language for RDF that expresses subgraph pattern- nding queries on this implicit multigraph in a SQL- like syntax. SPARQL queries generate complex intermediate join queries; to compute these joins e ciently, we propose a new strategy based on bitmap indexes. We store the RDF data in column-oriented structures as compressed bitmaps along with two dictionaries. This paper makes three new contributions. (i) We present an e cient parallel strategy for parsing the raw RDF data, building dictionaries of unique entities, and creating compressed bitmap indexes of the data. (ii) We utilize the constructed bitmap indexes to e ciently answer SPARQL queries, simplifying the join evaluations. (iii) To quantify the performance impact of using bitmap indexes, we compare our approach to the state-of-the-art triple-store RDF-3X. We nd that our bitmap index-based approach to answering queries is up to an order of magnitude faster for a variety of SPARQL queries, on gigascale RDF data sets.
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...
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
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...
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
Index change of chalcogenide materials from precision glass molding processes
Deegan, J.; Walsh, K.; Lindberg, G.; Benson, R.; Gibson, D.; Bayya, S.; Sanghera, J.; Stover, E.
2015-05-01
With the increase in demand for infrared optics for thermal applications and the use of glass molding of chalcogenide materials to support these higher volume optical designs, an investigation of changes to the optical properties of these materials is required. Typical precision glass molding requires specific thermal conditions for proper lens molding of any type of optical glass. With these conditions a change (reduction) of optical index occurs after molding of all oxide glass types and it is presumed that a similar behavior will happen with chalcogenide based materials. We will discuss the effects of a typical molding thermal cycle for use with commercially and newly developed chalcogenide materials and show results of index variation from nominally established material data.
Indexing business processes based on annotated finite state automata
Mahleko, B.; Wombacher, Andreas
The existing service discovery infrastructure with UDDI as the de facto standard, is limited in that it does not support more complex searching based on matching business processes. Two business processes match if they agree on their simple services, their processing order as well as any mandatory
FNet : An Index for Advanced Business Process Querying
Yan, Z.; Dijkman, R.M.; Grefen, P.W.P.J.; Barros, A.; Gal, A.; Kindler, E.
2012-01-01
Nowadays, more and more organizations describe their operations in terms of business processes. Consequently, it is common for organizations to have collections of hundreds or even thousands of business process models. This calls for techniques to quickly retrieve business process models that
FNet : an index for advanced business process querying
Yan, Z.; Dijkman, R.M.; Grefen, P.W.P.J.
2012-01-01
Nowadays, more and more organizations describe their operations in terms of business processes. Consequently, it is common for organizations to have collections of hundreds or even thousands of business process models. This calls for techniques to quickly retrieve business process models that
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 ...
De Jonckheere, J; Rommel, D; Nandrino, J L; Jeanne, M; Logier, R
2012-01-01
Autonomic Nervous System (ANS) variations are strongly influence by emotion regulation processes. Indeed, emotional stimuli are at the origin of an activation of the ANS and the way an individual pass from a state of alert in the case of emotional situation to a state of calm is closely coupled with the ANS flexibility. We have previously described and developed an Analgesia Nociception Index (ANI) for real time pain measurement during surgical procedure under general anesthesia. This index, based on heart rate variability analysis, constitutes a measure of parasympathetic tone and can be used in several other environments. In this paper, we hypothesized that such an index could be used as a tool to investigate the processes of emotional regulation of a human subject. To test this hypothesis, we analyzed ANI's response to a negative emotional stimulus. This analysis showed that the index decreases during the emotion induction phase and returns to its baseline after 2 minutes. This result confirms that ANI could be a good indicator of parasympathetic changes in emotional situation.
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...
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
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.
Tree-indexed processes: a high level crossing analysis
Directory of Open Access Journals (Sweden)
Mark Kelbert
2003-01-01
Full Text Available Consider a branching diffusion process on R1 starting at the origin. Take a high level u>0 and count the number R(u,n of branches reaching u by generation n. Let Fk,n(u be the probability P(R(u,n
Index Compression and Efficient Query Processing in Large Web Search Engines
Ding, Shuai
2013-01-01
The inverted index is the main data structure used by all the major search engines. Search engines build an inverted index on their collection to speed up query processing. As the size of the web grows, the length of the inverted list structures, which can easily grow to hundreds of MBs or even GBs for common terms (roughly linear in the size of…
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.
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.
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...
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
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)
Pratiwi, V. N.
2018-03-01
Rice is a staple food and regarded as a useful carbohydrate source. In general rice is high in glycaemic index (GI) and low colonic fermentation. People are aware of the alterations in blood glucose levels or glycaemic index after consuming rice. Resistant starch (RS) and amylose content play an important role in controlling GI. GI and RS content have been established as important indicators of starch digestibility. The aim of this study was to determine the precooked process with hydrothermal (boiling at 80°C, 10 minutes) and cooling process with low temperature (4°C, 1 h) to increase potential content of RS and decrease of glycaemic index of white rice. There were two stages of this research, 1) preparation of white rice with precooked process; 2) analysis of precooked white rice characteristics (resistant starch, amylose content, and estimated glycaemic index). The result of analysis on precooked white rice showed an increased RS content (1.11%) and white rice (0.99%), but the difference was not statistically significant. The amylose content increased significantly after precooked process in white rice (24.70%) compared with white rice (20.89%). Estimated glycaemic index (EGI) decreased after precooked proses (65.63%) but not significant as compared to white rice (66.47%). From the present study it was concluded that precooked process had no significant impact on increasing RS and decreasing EGI of white rice. This may be due to the relatively short cooling time (1hour) in 4°C.
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.
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
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...
Applying Markov Chains for NDVI Time Series Forecasting of Latvian Regions
Directory of Open Access Journals (Sweden)
Stepchenko Arthur
2015-12-01
Full Text Available Time series of earth observation based estimates of vegetation inform about variations in vegetation at the scale of Latvia. A vegetation index is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation. NDVI index is an important variable for vegetation forecasting and management of various problems, such as climate change monitoring, energy usage monitoring, managing the consumption of natural resources, agricultural productivity monitoring, drought monitoring and forest fire detection. In this paper, we make a one-step-ahead prediction of 7-daily time series of NDVI index using Markov chains. The choice of a Markov chain is due to the fact that a Markov chain is a sequence of random variables where each variable is located in some state. And a Markov chain contains probabilities of moving from one state to other.
Weak convergence of the function-indexed integrated periodogram for infinite variance processes
DEFF Research Database (Denmark)
Can, Umut; Mikosch, Thomas Valentin; Samorodnitsky, Gennady
2010-01-01
constitute α-stable processes which have representations as infinite Fourier series with i.i.d. α-stable coefficients. The cases α ∈ (0, 1) and α ∈ [1, 2) are dealt with by rather different methods and under different assumptions on the classes of functions. For example, in contrast to the case α ∈ (0, 1......In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric α-stable innovations. Under suitable summability conditions on the series of the Fourier coefficients of the index functions, we show that the weak limits...
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...
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
Hidden Markov Model for Stock Selection
Directory of Open Access Journals (Sweden)
Nguyet Nguyen
2015-10-01
Full Text Available The hidden Markov model (HMM is typically used to predict the hidden regimes of observation data. Therefore, this model finds applications in many different areas, such as speech recognition systems, computational molecular biology and financial market predictions. In this paper, we use HMM for stock selection. We first use HMM to make monthly regime predictions for the four macroeconomic variables: inflation (consumer price index (CPI, industrial production index (INDPRO, stock market index (S&P 500 and market volatility (VIX. At the end of each month, we calibrate HMM’s parameters for each of these economic variables and predict its regimes for the next month. We then look back into historical data to find the time periods for which the four variables had similar regimes with the forecasted regimes. Within those similar periods, we analyze all of the S&P 500 stocks to identify which stock characteristics have been well rewarded during the time periods and assign scores and corresponding weights for each of the stock characteristics. A composite score of each stock is calculated based on the scores and weights of its features. Based on this algorithm, we choose the 50 top ranking stocks to buy. We compare the performances of the portfolio with the benchmark index, S&P 500. With an initial investment of $100 in December 1999, over 15 years, in December 2014, our portfolio had an average gain per annum of 14.9% versus 2.3% for the S&P 500.
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...
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....
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.
Analysis of internationalization process of Bric countries with the Grubel and Lloyd index
Directory of Open Access Journals (Sweden)
Pedro Raffy Vartanian
2013-08-01
Full Text Available This research aims to show the internationalization of the BRIC (Brazil, Russia, India and China through the application of the Grubel and Lloyd index in the period 1994-2009. The hypothesis is that the BRIC countries have shown a growth in the internationalization process, as reflected by increased levels of productive investment in other countries. The research is the application method of the Grubel and Lloyd index in the flows of foreign direct investment and foreign investment by residents abroad in the period 1994-2009, in the BRIC countries. The results showed an increase in the Grubel and Lloyd index related to foreign investment flows, which suggests that companies from the BRIC countries have been increasing productive investment in other countries by the same way that the companies from the advanced economies in order to maximize profits through internationalization.
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 ...
Mukawa, Yoshiki; Kondo, Atsushi; Koike, Yasuhiro
2012-04-01
Graded-index polymer optical fiber (GI-POF) is a promising high-speed communication medium for very-short-reach networks, such as home or office networks. The refractive-index distribution of GI-POF needs to be accurately controlled to maximize the bandwidth. We attempted to control the refractive-index distribution by developing a simulation for dopant diffusion. In the rod-in-tube method, GI-POF with an optimal refractive-index distribution was obtained by adjusting the diffusion temperature and the diffusion time, whereas in the coextrusion process, GI-POF with an optimal refractive-index distribution was fabricated by controlling the length of the diffusion tube and the rate of discharge of polymer.
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.
Salazar-Miranda, D.; Castillón, F. F.; Sánchez-Sánchez, J. J.; Angel-Valenzuela, J. L.; Márquez, H.
2010-01-01
This paper describes the fabrication and characterization of multimode polymer optical waveguides obtained using a SU-8-2005 polymer by means of photolithographic process. Critical information about refractive index modulation of polymer waveguides as function of fabrication parameters as pre-baked and ultraviolet exposure times is presented. Physical properties of the waveguides were determined by means prism-coupling technique, optical and SEM microscopy. Este trabajo describe la fabrica...
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)
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
Delta, theta, beta, and gamma brain oscillations index levels of auditory sentence processing.
Mai, Guangting; Minett, James W; Wang, William S-Y
2016-06-01
A growing number of studies indicate that multiple ranges of brain oscillations, especially the delta (δ, processing. It is not clear, however, how these oscillations relate to functional processing at different linguistic hierarchical levels. Using scalp electroencephalography (EEG), the current study tested the hypothesis that phonological and the higher-level linguistic (semantic/syntactic) organizations during auditory sentence processing are indexed by distinct EEG signatures derived from the δ, θ, β, and γ oscillations. We analyzed specific EEG signatures while subjects listened to Mandarin speech stimuli in three different conditions in order to dissociate phonological and semantic/syntactic processing: (1) sentences comprising valid disyllabic words assembled in a valid syntactic structure (real-word condition); (2) utterances with morphologically valid syllables, but not constituting valid disyllabic words (pseudo-word condition); and (3) backward versions of the real-word and pseudo-word conditions. We tested four signatures: band power, EEG-acoustic entrainment (EAE), cross-frequency coupling (CFC), and inter-electrode renormalized partial directed coherence (rPDC). The results show significant effects of band power and EAE of δ and θ oscillations for phonological, rather than semantic/syntactic processing, indicating the importance of tracking δ- and θ-rate phonetic patterns during phonological analysis. We also found significant β-related effects, suggesting tracking of EEG to the acoustic stimulus (high-β EAE), memory processing (θ-low-β CFC), and auditory-motor interactions (20-Hz rPDC) during phonological analysis. For semantic/syntactic processing, we obtained a significant effect of γ power, suggesting lexical memory retrieval or processing grammatical word categories. Based on these findings, we confirm that scalp EEG signatures relevant to δ, θ, β, and γ oscillations can index phonological and semantic/syntactic organizations
Synthesis of the Markov model of the thermochemical degradation of a polymer in solution
Directory of Open Access Journals (Sweden)
V. K. Bityukov
2017-01-01
Full Text Available The paper deals with the problem of mathematical modeling of thermochemical destruction process. The apparatus of Markov's chains is used to synthesize a mathematical model. The authors of the study suggest to consider the destruction process as a random one, where the system state changes, which is characterized by the proportion of macromolecules in each fraction of the molecular- and weight distribution. The intensities of transitions from one state to another characterize the corresponding rates of destruction processes for each fraction of the molecular- and weight distribution. The processes of crosslinking and polymerization in this work were neglected, and it was accepted that there is a probability of transition from any state with a lower order index (corresponding to fractions with higher molecular weights to any state with a higher index (corresponding to fractions with lower molecular weights. Markov's chain with discrete states and continuous time was taken as the mathematical model basis. Interactive graphical simulation environment MathWorksSimulink was used as a simulation environment. Experimental studies of polybutadiene destruction in solution were carried out to evaluate the mathematical model parameters. The GPC (gel-penetration chromatography data of the polybutadiene solution were used as the initial (starting data for estimating the polymer WMD (molecular weight distribution. Mean-square deviation of the calculated data from the experimental data for each fraction and at specified times was minimized for the numerical search of parameter values. The results of comparison of experimental and calculated on mathematical model data showed an error of calculations on the average about 5%, which indicates an acceptable error in estimating of polymer fractions proportions change during the process of destruction for the process under consideration and conditions.
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
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.
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan
2014-02-27
A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.
New Path Based Index Structure for Processing CAS Queries over XML Database
Directory of Open Access Journals (Sweden)
Krishna Asawa
2017-01-01
Full Text Available Querying nested data has become one of the most challenging issues for retrieving desired information from the Web. Today diverse applications generate a tremendous amount of data in different formats. These data and information exchanged on the Web are commonly expressed as nested representation such as XML, JSON, etc. Unlike the traditional database system, they don't have a rigid schema. In general, the nested data is managed by storing data and its structures separately which significantly reduces the performance of data retrieving. Ensuring efficiency of processing queries which locates the exact positions of the elements has become a big challenging issue. There are different indexing structures which have been proposed in the literature to improve the performance of the query processing on the nested structure. Most of the past researches on nested structure concentrate on the structure alone. This paper proposes new index structure which combines siblings of the terminal nodes as one path which efficiently processes twig queries with less number of lookups and joins. The proposed approach is compared with some of the existing approaches. The results also show that they are processed with better performance compared to the existing ones.
Monte Carlo methods for the reliability analysis of Markov systems
International Nuclear Information System (INIS)
Buslik, A.J.
1985-01-01
This paper presents Monte Carlo methods for the reliability analysis of Markov systems. Markov models are useful in treating dependencies between components. The present paper shows how the adjoint Monte Carlo method for the continuous time Markov process can be derived from the method for the discrete-time Markov process by a limiting process. The straightforward extensions to the treatment of mean unavailability (over a time interval) are given. System unavailabilities can also be estimated; this is done by making the system failed states absorbing, and not permitting repair from them. A forward Monte Carlo method is presented in which the weighting functions are related to the adjoint function. In particular, if the exact adjoint function is known then weighting factors can be constructed such that the exact answer can be obtained with a single Monte Carlo trial. Of course, if the exact adjoint function is known, there is no need to perform the Monte Carlo calculation. However, the formulation is useful since it gives insight into choices of the weight factors which will reduce the variance of the estimator
Operations and support cost modeling using Markov chains
Unal, Resit
1989-01-01
Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.
Johnson, Jeffrey C.; Luczkovich, Joseph J.; Borgatti, Stephen P.; Snijders, Tom A. B.; Luczkovich, S.P.
2009-01-01
Ecosystem components interact in complex ways and change over time due to a variety of both internal and external influences (climate change, season cycles, human impacts). Such processes need to be modeled dynamically using appropriate statistical methods for assessing change in network structure.
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
Abler, Daniel; Davies, Jim; Dosanjh, Manjit; Jena, Raj; Kirkby, Norman; Peach, Ken
2013-01-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of ‘general Markov models’, providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy ...
Ecological assessment of integrated bioenergy systems using the Sustainable Process Index
International Nuclear Information System (INIS)
Krotscheck, C.; Konig, F.; Obernberger, I.
2000-01-01
Biomass utilisation for energy production presently faces an uphill battle against fossil fuels. The use of biomass must offer additional benefits to compensate for higher prices: on the basis of a life cycle assessment (using BEAM to evaluate a variety of integrated bioenergy systems in connection with the Sustainable Process Index as a highly aggregated environmental pressure index) it is shown that integrated bioenergy systems are superior to fossil fuel systems in terms of environmental compatibility. The implementation of sustainability measures provides additional valuable information that might help in constructing and optimising integrated bioenergy systems. For a set of reference processes, among them fast pyrolysis, atmospheric gasification, integrated gasification combined cycle (IGCC), combustion and steam cycle (CS) and conventional hydrolysis, a detailed impact assessment is shown. Sensitivity analyses of the most important ecological parameters are calculated, giving an overview of the impacts of various stages in the total life cycle and showing 'what really matters'. Much of the ecological impact of integrated bioenergy systems is induced by feedstock production. It is mainly the use of fossil fuels in cultivation, harvesting and transportation as well as the use of fertilisers in short-rotation coppice production that impose considerable ecological pressure. Concerning electricity generation the most problematic pressures are due to gaseous emissions, most notably the release of NO x . Moreover, a rather complicated process (high amount of grey energy) and the use of fossil pilot fuel (co-combustion) leads to a rather weak ecological performance in contrast to other 100% biomass-based systems. (author)
Verification of Open Interactive Markov Chains
Brazdil, Tomas; Hermanns, Holger; Krcal, Jan; Kretinsky, Jan; Rehak, Vojtech
2012-01-01
Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation....
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
2012-01-01
If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both
Criterion of Semi-Markov Dependent Risk Model
Institute of Scientific and Technical Information of China (English)
Xiao Yun MO; Xiang Qun YANG
2014-01-01
A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi-Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.
Markov chain aggregation for agent-based models
Banisch, Sven
2016-01-01
This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the upd...
Directory of Open Access Journals (Sweden)
Jean B. Lasserre
2000-01-01
Full Text Available We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.
Rallapalli, Arjun
A RET network consists of a network of photo-active molecules called chromophores that can participate in inter-molecular energy transfer called resonance energy transfer (RET). RET networks are used in a variety of applications including cryptographic devices, storage systems, light harvesting complexes, biological sensors, and molecular rulers. In this dissertation, we focus on creating a RET device called closed-diffusive exciton valve (C-DEV) in which the input to output transfer function is controlled by an external energy source, similar to a semiconductor transistor like the MOSFET. Due to their biocompatibility, molecular devices like the C-DEVs can be used to introduce computing power in biological, organic, and aqueous environments such as living cells. Furthermore, the underlying physics in RET devices are stochastic in nature, making them suitable for stochastic computing in which true random distribution generation is critical. In order to determine a valid configuration of chromophores for the C-DEV, we developed a systematic process based on user-guided design space pruning techniques and built-in simulation tools. We show that our C-DEV is 15x better than C-DEVs designed using ad hoc methods that rely on limited data from prior experiments. We also show ways in which the C-DEV can be improved further and how different varieties of C-DEVs can be combined to form more complex logic circuits. Moreover, the systematic design process can be used to search for valid chromophore network configurations for a variety of RET applications. We also describe a feasibility study for a technique used to control the orientation of chromophores attached to DNA. Being able to control the orientation can expand the design space for RET networks because it provides another parameter to tune their collective behavior. While results showed limited control over orientation, the analysis required the development of a mathematical model that can be used to determine the
A Moving-Object Index for Efficient Query Processing with PeerWise Location Privacy
DEFF Research Database (Denmark)
Lin, Dan; Jensen, Christian S.; Zhang, Rui
2011-01-01
attention has been paid to enabling so-called peer-wise privacy—the protection of a user’s location from unauthorized peer users. This paper identifies an important efficiency problem in existing peer-privacy approaches that simply apply a filtering step to identify users that are located in a query range......, but that do not want to disclose their location to the querying peer. To solve this problem, we propose a novel, privacy-policy enabled index called the PEB-tree that seamlessly integrates location proximity and policy compatibility. We propose efficient algorithms that use the PEB-tree for processing privacy......-aware range and kNN queries. Extensive experiments suggest that the PEB-tree enables efficient query processing....
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.
Learning Markov models for stationary system behaviors
DEFF Research Database (Denmark)
Chen, Yingke; Mao, Hua; Jaeger, Manfred
2012-01-01
to a single long observation sequence, and in these situations existing automatic learning methods cannot be applied. In this paper, we adapt algorithms for learning variable order Markov chains from a single observation sequence of a target system, so that stationary system properties can be verified using......Establishing an accurate model for formal verification of an existing hardware or software system is often a manual process that is both time consuming and resource demanding. In order to ease the model construction phase, methods have recently been proposed for automatically learning accurate...... the learned model. Experiments demonstrate that system properties (formulated as stationary probabilities of LTL formulas) can be reliably identified using the learned model....
Estimation and uncertainty of reversible Markov models.
Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank
2015-11-07
Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software--http://pyemma.org--as of version 2.0.
Monte Carlo simulation of Markov unreliability models
International Nuclear Information System (INIS)
Lewis, E.E.; Boehm, F.
1984-01-01
A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependences between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented. (orig.)
Markov state models of protein misfolding
Sirur, Anshul; De Sancho, David; Best, Robert B.
2016-02-01
Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.
Numerical research of the optimal control problem in the semi-Markov inventory model
Energy Technology Data Exchange (ETDEWEB)
Gorshenin, Andrey K. [Institute of Informatics Problems, Russian Academy of Sciences, Vavilova str., 44/2, Moscow, Russia MIREA, Faculty of Information Technology (Russian Federation); Belousov, Vasily V. [Institute of Informatics Problems, Russian Academy of Sciences, Vavilova str., 44/2, Moscow (Russian Federation); Shnourkoff, Peter V.; Ivanov, Alexey V. [National research university Higher school of economics, Moscow (Russian Federation)
2015-03-10
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.
Numerical research of the optimal control problem in the semi-Markov inventory model
International Nuclear Information System (INIS)
Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.; Ivanov, Alexey V.
2015-01-01
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented
High index glass thin film processing for photonics and photovoltaic (PV) applications
Ogbuu, Okechukwu Anthony
To favorably compete with fossil-fuel technology, the greatest challenge for thin film solar-cells is to improve efficiency and reduce material cost. Thickness scaling to thin film reduces material cost but affects the light absorption in the cells; therefore a concept that traps incident photons and increases its optical path length is needed to boost absorption in thin film solar cells. One approach is the integration of low symmetric gratings (LSG), using high index material, on either the front-side or backside of 30 um thin c-Si cells. In this study, Multicomponent TeO2--Bi2O 3--ZnO (TBZ) glass thin films were prepared using RF magnetron sputtering under different oxygen flow rates. The influences of oxygen flow rate on the structural and optical properties of the resulting thin films were investigated. The structural origin of the optical property variation was studied using X-ray diffraction, X-ray photoelectron spectroscopy, Raman Spectroscopy, and transmission electron microscopy. The results indicate that TBZ glass thin film is a suitable material for front side LSG material photovoltaic and photonics applications due to their amorphous nature, high refractive index (n > 2), broad band optical transparency window, low processing temperature. We developed a simple maskless method to pattern sputtered tellurite based glass thin films using unconventional agarose hydrogel mediated wet etching. Conventional wet etching process, while claiming low cost and high throughput, suffers from reproducibility and pattern fidelity issues due to the isotropic nature of wet chemical etching when applied to glasses and polymers. This method overcomes these challenges by using an agarose hydrogel stamp to mediate a conformal etching process. In our maskless method, agarose hydrogel stamps are patterned following a standard soft lithography and replica molding process from micropatterned masters and soaked in a chemical etchant. The micro-scale features on the stamp are
Energy Technology Data Exchange (ETDEWEB)
Cassibba, M.; Bertani, M. [SNAM, (Italy)
2000-07-01
Natural gas supplied to industry for process utilizations originates from different sources and that can cause fluctuations in gas composition. Changing gas composition may lead to production problems in industry with sensitive thermal processes (particularly glass industry and thermal metal treatments), such as efficiency and product quality. An equipment suitable to control and adjust such variations has been developed. Experimental tests in laboratory were carried out in order to investigate the control system accuracy and reliability. In particular five different settings were tested: at a preset thermal input by adjusting the natural gas flow rate in respect to Wobbe Index variations; at a set furnace temperature and stack oxygen level with variable thermal input by monitoring the Wobbe Index value; at constant Wobbe Index value by adding air to natural gas; at constant thermal input and prefixed Wobbe Index value by adding air to natural gas and varying the air and gas mixture flow rate; gross calorific value control by adding air or LPG to natural gas. All the tested settings gave good results. This report illustrates these results and the main features of the control system. The control and regulation system was installed in two glass factories for field tests. (authors)
Probabilistic Reachability for Parametric Markov Models
DEFF Research Database (Denmark)
Hahn, Ernst Moritz; Hermanns, Holger; Zhang, Lijun
2011-01-01
Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression...
Markov-modulated and feedback fluid queues
Scheinhardt, Willem R.W.
1998-01-01
In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short
INDEX - a solution to the high cost of processing transient workers
International Nuclear Information System (INIS)
Stroupe, E.P.
1987-01-01
In 1985 twelve midwestern utilities formed the Nuclear Employee Data System for the US Nuclear Regulatory Commission's (NRC's) Region III (NEDS III) group. These utilities are Cleveland Electric Illuminating Company, Commonwealth Edison Company, Consumers Power Company, Detroit Edison Company, Illinois Power Company, Indiana and Michigan Electric Company, Iowa Electric Light and Power Company, Northern States Power Company, Toledo Edison Company, Union Electric Company, and Wisconsin Public Service Corporation. Early in 1986, Kansas Gas and Electric of NRC's Region IV joined the group and a cost-benefit study of a nuclear employee data system was initiated. The purpose of this system is to reduce the cost of processing workers requiring unescorted access to nuclear power plants. The involved utilities continued this project as the Integrated Nuclear Data Exchange (INDEX). In 1987 the following additional utilities joined INDEX: Houston Lighting and Power, Pacific Gas and Electric, Texas Utilities Electric Company, Arkansas Power and Light, Louisiana Power and Light, Systems Energy Resources Inc., and Southern California Edison. This paper summarizes the results of the study and discusses the current status of the program
Classification Using Markov Blanket for Feature Selection
DEFF Research Database (Denmark)
Zeng, Yifeng; Luo, Jian
2009-01-01
Selecting relevant features is in demand when a large data set is of interest in a classification task. It produces a tractable number of features that are sufficient and possibly improve the classification performance. This paper studies a statistical method of Markov blanket induction algorithm...... for filtering features and then applies a classifier using the Markov blanket predictors. The Markov blanket contains a minimal subset of relevant features that yields optimal classification performance. We experimentally demonstrate the improved performance of several classifiers using a Markov blanket...... induction as a feature selection method. In addition, we point out an important assumption behind the Markov blanket induction algorithm and show its effect on the classification performance....
[Succession caused by beaver (Castor fiber L.) life activity: II. A refined Markov model].
Logofet; Evstigneev, O I; Aleinikov, A A; Morozova, A O
2015-01-01
The refined Markov model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity represents a discrete chain of the following six states: flooded forest, swamped forest, pond, grassy swamp, shrubby swamp, and wet forest, which correspond to certain stages of succession. Those stages are defined, and a conceptual scheme of probable transitions between them for one time step is constructed from the knowledge of beaver behaviour in small river floodplains of "Bryanskii Les" Reserve. We calibrated the corresponding matrix of transition probabilities according to the optimization principle: minimizing differences between the model outcome and reality; the model generates a distribution of relative areas corresponding to the stages of succession, that has to be compared to those gained from case studies in the Reserve during 2002-2006. The time step is chosen to equal 2 years, and the first-step data in the sum of differences are given various weights, w (between 0 and 1). The value of w = 0.2 is selected due to its optimality and for some additional reasons. By the formulae of finite homogeneous Markov chain theory, we obtained the main results of the calibrated model, namely, a steady-state distribution of stage areas, indexes of cyclicity, and the mean durations (M(j)) of succession stages. The results of calibration give an objective quantitative nature to the expert knowledge of the course of succession and get a proper interpretation. The 2010 data, which are not involved in the calibration procedure, enabled assessing the quality of prediction by the homogeneous model in short-term (from the 2006 situation): the error of model area distribution relative to the distribution observed in 2010 falls into the range of 9-17%, the best prognosis being given by the least optimal matrices (rejected values of w). This indicates a formally heterogeneous nature of succession processes in time. Thus, the refined version of the homogeneous Markov chain
Long time behavior of Markov processes
Directory of Open Access Journals (Sweden)
Cattiaux Patrick
2014-01-01
Full Text Available These notes correspond to a three hours lecture given during the workshop “Metastability and Stochastic Processes”held in Marne-la-Vallée in September 21st-23rd 2011. I would like to warmly thank the organizers Tony Lelièvre and Arnaud Guillin for a very nice organization and for obliging me first to give the lecture, second to write these notes. I also want to acknowledge all the people who attended the lecture.
Markov Decision Processes Discrete Stochastic Dynamic Programming
Puterman, Martin L
2005-01-01
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. "This text is unique in bringing together so many results hitherto found only in part in other texts and papers. . . . The text is fairly self-contained, inclusive of some basic mathematical results needed, and provides a rich diet
A Markov Decision Process * EZUGWU, VO
African Journals Online (AJOL)
ADOWIE PERE
strategy of traders who, in the presence of cost transaction, invest on this risky ... designing autonomous intelligent agent for forest fire fighting. ... minimizing energy consumption and maximizing sensing .... The actions allow us to modify the ...
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....
Lin, Po-Chuan; Chen, Bo-Wei; Chang, Hangbae
2016-07-01
This study presents a human-centric technique for social video expansion based on semantic processing and graph analysis. The objective is to increase metadata of an online video and to explore related information, thereby facilitating user browsing activities. To analyze the semantic meaning of a video, shots and scenes are firstly extracted from the video on the server side. Subsequently, this study uses annotations along with ConceptNet to establish the underlying framework. Detailed metadata, including visual objects and audio events among the predefined categories, are indexed by using the proposed method. Furthermore, relevant online media associated with each category are also analyzed to enrich the existing content. With the above-mentioned information, users can easily browse and search the content according to the link analysis and its complementary knowledge. Experiments on a video dataset are conducted for evaluation. The results show that our system can achieve satisfactory performance, thereby demonstrating the feasibility of the proposed idea.
Indexing, Query Processing, and Clustering of Spatio-Temporal Text Objects
DEFF Research Database (Denmark)
Skovsgaard, Anders
With the increasing mobile use of the web from geo-positioned devices, the Internet is increasingly acquiring a spatial aspect, with still more types of content being geo-tagged. As a result of this development, a wide range of location-aware queries and applications have emerged. The large amounts...... of data available coupled with the increasing number of location-aware queries calls for efficient indexing and query processing techniques. This dissertation investigates how to manage geo-tagged text content to support these workloads in three specific areas: (i) grouping of spatio-textual objects, (ii......, the grouping of spatio-textual objects is done without considering query locations, and a clustering approach is proposed that takes into account both the spatial and textual attributes of the objects. The technique expands clusters based on a proposed quality function that enables clusters of arbitrary shape...
International Nuclear Information System (INIS)
Gomez-Navarro, Tomas; Garcia-Melon, Monica; Acuna-Dutra, Silvia; Diaz-Martin, Diego
2009-01-01
This paper introduces a new approach to prioritize urban planning projects according to their environmental pressure in an efficient and reliable way. It is based on the combination of three procedures: (i) the use of environmental pressure indicators, (ii) the aggregation of the indicators in an Environmental Pressure Index by means of the Analytic Network Process method (ANP) and (iii) the interpretation of the information obtained from the experts during the decision-making process. The method has been applied to a proposal for urban development of La Carlota airport in Caracas (Venezuela). There are three options which are currently under evaluation. They include a Health Club, a Residential Area and a Theme Park. After a selection process the experts chose the following environmental pressure indicators as ANP criteria for the project life cycle: used land area, population density, energy consumption, water consumption and waste generation. By using goal-oriented questionnaires designed by the authors, the experts determined the importance of the criteria, the relationships among criteria, and the relationships between the criteria and the urban development alternatives. The resulting data showed that water consumption is the most important environmental pressure factor, and the Theme Park project is by far the urban development alternative which exerts the least environmental pressure on the area. The participating experts coincided in appreciating the technique proposed in this paper is useful and, for ranking ordering these alternatives, an improvement from traditional techniques such as environmental impact studies, life-cycle analysis, etc.
Directory of Open Access Journals (Sweden)
Z. Lari
2012-07-01
Full Text Available Over the past few years, LiDAR systems have been established as a leading technology for the acquisition of high density point clouds over physical surfaces. These point clouds will be processed for the extraction of geo-spatial information. Local point density is one of the most important properties of the point cloud that highly affects the performance of data processing techniques and the quality of extracted information from these data. Therefore, it is necessary to define a standard methodology for the estimation of local point density indices to be considered for the precise processing of LiDAR data. Current definitions of local point density indices, which only consider the 2D neighbourhood of individual points, are not appropriate for 3D LiDAR data and cannot be applied for laser scans from different platforms. In order to resolve the drawbacks of these methods, this paper proposes several approaches for the estimation of the local point density index which take the 3D relationship among the points and the physical properties of the surfaces they belong to into account. In the simplest approach, an approximate value of the local point density for each point is defined while considering the 3D relationship among the points. In the other approaches, the local point density is estimated by considering the 3D neighbourhood of the point in question and the physical properties of the surface which encloses this point. The physical properties of the surfaces enclosing the LiDAR points are assessed through eigen-value analysis of the 3D neighbourhood of individual points and adaptive cylinder methods. This paper will discuss these approaches and highlight their impact on various LiDAR data processing activities (i.e., neighbourhood definition, region growing, segmentation, boundary detection, and classification. Experimental results from airborne and terrestrial LiDAR data verify the efficacy of considering local point density variation for
Schmidt games and Markov partitions
International Nuclear Information System (INIS)
Tseng, Jimmy
2009-01-01
Let T be a C 2 -expanding self-map of a compact, connected, C ∞ , Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x 0 in M, the set of points whose forward orbit closures miss x 0 is a winning set. Finally, our key lemma, the no matching lemma, may be of independent interest in the theory of symbolic dynamics or the theory of Markov partitions
Alpha and theta brain oscillations index dissociable processes in spoken word recognition.
Strauß, Antje; Kotz, Sonja A; Scharinger, Mathias; Obleser, Jonas
2014-08-15
Slow neural oscillations (~1-15 Hz) are thought to orchestrate the neural processes of spoken language comprehension. However, functional subdivisions within this broad range of frequencies are disputed, with most studies hypothesizing only about single frequency bands. The present study utilizes an established paradigm of spoken word recognition (lexical decision) to test the hypothesis that within the slow neural oscillatory frequency range, distinct functional signatures and cortical networks can be identified at least for theta- (~3-7 Hz) and alpha-frequencies (~8-12 Hz). Listeners performed an auditory lexical decision task on a set of items that formed a word-pseudoword continuum: ranging from (1) real words over (2) ambiguous pseudowords (deviating from real words only in one vowel; comparable to natural mispronunciations in speech) to (3) pseudowords (clearly deviating from real words by randomized syllables). By means of time-frequency analysis and spatial filtering, we observed a dissociation into distinct but simultaneous patterns of alpha power suppression and theta power enhancement. Alpha exhibited a parametric suppression as items increasingly matched real words, in line with lowered functional inhibition in a left-dominant lexical processing network for more word-like input. Simultaneously, theta power in a bilateral fronto-temporal network was selectively enhanced for ambiguous pseudowords only. Thus, enhanced alpha power can neurally 'gate' lexical integration, while enhanced theta power might index functionally more specific ambiguity-resolution processes. To this end, a joint analysis of both frequency bands provides neural evidence for parallel processes in achieving spoken word recognition. Copyright © 2014 Elsevier Inc. All rights reserved.
Ravasio, Andrea; Vaishnavi, Sree; Ladoux, Benoit; Viasnoff, Virgile
2015-03-01
Understanding and controlling how cells interact with the microenvironment has emerged as a prominent field in bioengineering, stem cell research and in the development of the next generation of in vitro assays as well as organs on a chip. Changing the local rheology or the nanotextured surface of substrates has proved an efficient approach to improve cell lineage differentiation, to control cell migration properties and to understand environmental sensing processes. However, introducing substrate surface textures often alters the ability to image cells with high precision, compromising our understanding of molecular mechanisms at stake in environmental sensing. In this paper, we demonstrate how nano/microstructured surfaces can be molded from an elastomeric material with a refractive index matched to the cell culture medium. Once made biocompatible, contrast imaging (differential interference contrast, phase contrast) and high-resolution fluorescence imaging of subcellular structures can be implemented through the textured surface using an inverted microscope. Simultaneous traction force measurements by micropost deflection were also performed, demonstrating the potential of our approach to study cell-environment interactions, sensing processes and cellular force generation with unprecedented resolution. Copyright © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
MARKOV CHAIN MODELING OF PERFORMANCE DEGRADATION OF PHOTOVOLTAIC SYSTEM
E. Suresh Kumar; Asis Sarkar; Dhiren kumar Behera
2012-01-01
Modern probability theory studies chance processes for which theknowledge of previous outcomes influence predictions for future experiments. In principle, when a sequence of chance experiments, all of the past outcomes could influence the predictions for the next experiment. In Markov chain type of chance, the outcome of a given experiment can affect the outcome of the next experiment. The system state changes with time and the state X and time t are two random variables. Each of these variab...
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Markov chains analytic and Monte Carlo computations
Graham, Carl
2014-01-01
Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix presenting probabilistic notions that are nec
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.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain $(C_n)$ on a discrete state space ${\\cal S}$, a Markov chain $(C_n,M_n)$ on the product space ${\\cal S}^2$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain
APPLICATION OF HIDDEN MARKOV CHAINS IN QUALITY CONTROL
Directory of Open Access Journals (Sweden)
Hanife DEMIRALP
2013-01-01
Full Text Available The ever growing technological innovations and sophistication in industrial processes require adequate checks on quality. Thus, there is an increasing demand for simple and efficient quality control methods. In this regard the control charts stand out in simplicity and efficiency. In this paper, we propose a method of controlling quality based on the theory of hidden Markov chains. Based on samples drawn at different times from the production process, the method obtains the state of the process probabilistically. The main advantage of the method is that it requires no assumption on the normality of the process output.
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.
Multivariate longitudinal data analysis with mixed effects hidden Markov models.
Raffa, Jesse D; Dubin, Joel A
2015-09-01
Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. © 2015, The International Biometric Society.
A Bayesian model for binary Markov chains
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Belkheir Essebbar
2004-02-01
Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.
Subharmonic projections for a quantum Markov semigroup
International Nuclear Information System (INIS)
Fagnola, Franco; Rebolledo, Rolando
2002-01-01
This article introduces a concept of subharmonic projections for a quantum Markov semigroup, in view of characterizing the support projection of a stationary state in terms of the semigroup generator. These results, together with those of our previous article [J. Math. Phys. 42, 1296 (2001)], lead to a method for proving the existence of faithful stationary states. This is often crucial in the analysis of ergodic properties of quantum Markov semigroups. The method is illustrated by applications to physical models
Transition Effect Matrices and Quantum Markov Chains
Gudder, Stan
2009-06-01
A transition effect matrix (TEM) is a quantum generalization of a classical stochastic matrix. By employing a TEM we obtain a quantum generalization of a classical Markov chain. We first discuss state and operator dynamics for a quantum Markov chain. We then consider various types of TEMs and vector states. In particular, we study invariant, equilibrium and singular vector states and investigate projective, bistochastic, invertible and unitary TEMs.
Robust Dynamics and Control of a Partially Observed Markov Chain
International Nuclear Information System (INIS)
Elliott, R. J.; Malcolm, W. P.; Moore, J. P.
2007-01-01
In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established
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.
Fitting Hidden Markov Models to Psychological Data
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Ingmar Visser
2002-01-01
Full Text Available Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.
Robust filtering and prediction for systems with embedded finite-state Markov-Chain dynamics
International Nuclear Information System (INIS)
Pate, E.B.
1986-01-01
This research developed new methodologies for the design of robust near-optimal filters/predictors for a class of system models that exhibit embedded finite-state Markov-chain dynamics. These methodologies are developed through the concepts and methods of stochastic model building (including time-series analysis), game theory, decision theory, and filtering/prediction for linear dynamic systems. The methodology is based on the relationship between the robustness of a class of time-series models and quantization which is applied to the time series as part of the model identification process. This relationship is exploited by utilizing the concept of an equivalence, through invariance of spectra, between the class of Markov-chain models and the class of autoregressive moving average (ARMA) models. This spectral equivalence permits a straightforward implementation of the desirable robust properties of the Markov-chain approximation in a class of models which may be applied in linear-recursive form in a linear Kalman filter/predictor structure. The linear filter/predictor structure is shown to provide asymptotically optimal estimates of states which represent one or more integrations of the Markov-chain state. The development of a new saddle-point theorem for a game based on the Markov-chain model structure gives rise to a technique for determining a worst case Markov-chain process, upon which a robust filter/predictor design if based
Li, Zhenlong; Hu, Fei; Schnase, John L.; Duffy, Daniel Q.; Lee, Tsengdar; Bowen, Michael K.; Yang, Chaowei
2016-01-01
Climate observations and model simulations are producing vast amounts of array-based spatiotemporal data. Efficient processing of these data is essential for assessing global challenges such as climate change, natural disasters, and diseases. This is challenging not only because of the large data volume, but also because of the intrinsic high-dimensional nature of geoscience data. To tackle this challenge, we propose a spatiotemporal indexing approach to efficiently manage and process big climate data with MapReduce in a highly scalable environment. Using this approach, big climate data are directly stored in a Hadoop Distributed File System in its original, native file format. A spatiotemporal index is built to bridge the logical array-based data model and the physical data layout, which enables fast data retrieval when performing spatiotemporal queries. Based on the index, a data-partitioning algorithm is applied to enable MapReduce to achieve high data locality, as well as balancing the workload. The proposed indexing approach is evaluated using the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective Analysis for Research and Applications (MERRA) climate reanalysis dataset. The experimental results show that the index can significantly accelerate querying and processing (10 speedup compared to the baseline test using the same computing cluster), while keeping the index-to-data ratio small (0.0328). The applicability of the indexing approach is demonstrated by a climate anomaly detection deployed on a NASA Hadoop cluster. This approach is also able to support efficient processing of general array-based spatiotemporal data in various geoscience domains without special configuration on a Hadoop cluster.
Ye, Jing; Dang, Yaoguo; Li, Bingjun
2018-01-01
Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.
Finding metastabilities in reversible Markov chains based on incomplete sampling
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Fackeldey Konstantin
2017-01-01
Full Text Available In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy, which provides a partial sampling of only a subset of the rows of such a matrix P. Our proposed approach fits very well to stochastic processes stemming from simulation of molecular systems or random walks on graphs and it is different from the matrix completion approaches which try to approximate the transition matrix by using a low-rank-assumption. It will be shown how Markov chains can be analyzed on the basis of a partial sampling. More precisely. First, we will estimate the stationary distribution from a partially given matrix P. Second, we will estimate the infinitesimal generator Q of P on the basis of this stationary distribution. Third, from the generator we will compute the leading invariant subspace, which should be identical to the leading invariant subspace of P. Forth, we will apply Robust Perron Cluster Analysis (PCCA+ in order to identify metastabilities using this subspace.
Hidden Markov models: the best models for forager movements?
Joo, Rocio; Bertrand, Sophie; Tam, Jorge; Fablet, Ronan
2013-01-01
One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs). We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs). They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour), while their behavioural modes (fishing, searching and cruising) were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines) for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%), significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.
Hidden Markov models: the best models for forager movements?
Directory of Open Access Journals (Sweden)
Rocio Joo
Full Text Available One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs. We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs. They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour, while their behavioural modes (fishing, searching and cruising were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%, significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.
Hidden Markov models in automatic speech recognition
Wrzoskowicz, Adam
1993-11-01
This article describes a method for constructing an automatic speech recognition system based on hidden Markov models (HMMs). The author discusses the basic concepts of HMM theory and the application of these models to the analysis and recognition of speech signals. The author provides algorithms which make it possible to train the ASR system and recognize signals on the basis of distinct stochastic models of selected speech sound classes. The author describes the specific components of the system and the procedures used to model and recognize speech. The author discusses problems associated with the choice of optimal signal detection and parameterization characteristics and their effect on the performance of the system. The author presents different options for the choice of speech signal segments and their consequences for the ASR process. The author gives special attention to the use of lexical, syntactic, and semantic information for the purpose of improving the quality and efficiency of the system. The author also describes an ASR system developed by the Speech Acoustics Laboratory of the IBPT PAS. The author discusses the results of experiments on the effect of noise on the performance of the ASR system and describes methods of constructing HMM's designed to operate in a noisy environment. The author also describes a language for human-robot communications which was defined as a complex multilevel network from an HMM model of speech sounds geared towards Polish inflections. The author also added mandatory lexical and syntactic rules to the system for its communications vocabulary.
Tornadoes and related damage costs: statistical modelling with a semi-Markov approach
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Guglielmo D’Amico
2016-09-01
Full Text Available We propose a statistical approach to modelling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modelling the tornado intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornado intensity into six states, it is possible to model the tornado intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornado occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application, we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. The paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
Abler, Daniel; Kanellopoulos, Vassiliki; Davies, Jim; Dosanjh, Manjit; Jena, Raj; Kirkby, Norman; Peach, Ken
2013-01-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of ‘general Markov models’, providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. PMID:23824126
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
International Nuclear Information System (INIS)
Abler, Daniel; Kanellopoulos, Vassiliki; Dosanjh, Manjit; Davies, Jim; Peach, Ken; Jena, Raj; Kirkby, Norman
2013-01-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of 'general Markov models', providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. (author)
MARKOV Model Application to Proliferation Risk Reduction of an Advanced Nuclear System
International Nuclear Information System (INIS)
Bari, R.A.
2008-01-01
The Generation IV International Forum (GIF) emphasizes proliferation resistance and physical protection (PR and PP) as a main goal for future nuclear energy systems. The GIF PR and PP Working Group has developed a methodology for the evaluation of these systems. As an application of the methodology, Markov model has been developed for the evaluation of proliferation resistance and is demonstrated for a hypothetical Example Sodium Fast Reactor (ESFR) system. This paper presents the case of diversion by the facility owner/operator to obtain material that could be used in a nuclear weapon. The Markov model is applied to evaluate material diversion strategies. The following features of the Markov model are presented here: (1) An effective detection rate has been introduced to account for the implementation of multiple safeguards approaches at a given strategic point; (2) Technical failure to divert material is modeled as intrinsic barriers related to the design of the facility or the properties of the material in the facility; and (3) Concealment to defeat or degrade the performance of safeguards is recognized in the Markov model. Three proliferation risk measures are calculated directly by the Markov model: the detection probability, technical failure probability, and proliferation time. The material type is indicated by an index that is based on the quality of material diverted. Sensitivity cases have been done to demonstrate the effects of different modeling features on the measures of proliferation resistance
Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe
2016-01-01
Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.
International Nuclear Information System (INIS)
Potts, J.E.
1976-01-01
Application of ionizing radiation in a dose between 0.5 and 1.5 megareps to copolymers of ethylene and vinyl acetate lowers the melt index and increases the toughness and flexibility of the copolymers without substantially decreasing solubility or thermoplasticity. The increased toughness and flexibility carries over into blends with wax or polyethylene. (author)
Maximally reliable Markov chains under energy constraints.
Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam
2009-07-01
Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.
SDI and Markov Chains for Regional Drought Characteristics
Directory of Open Access Journals (Sweden)
Chen-Feng Yeh
2015-08-01
Full Text Available In recent years, global climate change has altered precipitation patterns, causing uneven spatial and temporal distribution of precipitation that gradually induces precipitation polarization phenomena. Taiwan is located in the subtropical climate zone, with distinct wet and dry seasons, which makes the polarization phenomenon more obvious; this has also led to a large difference between river flows during the wet and dry seasons, which is significantly influenced by precipitation, resulting in hydrological drought. Therefore, to effectively address the growing issue of water shortages, it is necessary to explore and assess the drought characteristics of river systems. In this study, the drought characteristics of northern Taiwan were studied using the streamflow drought index (SDI and Markov chains. Analysis results showed that the year 2002 was a turning point for drought severity in both the Lanyang River and Yilan River basins; the severity of rain events in the Lanyang River basin increased after 2002, and the severity of drought events in the Yilan River basin exhibited a gradual upward trend. In the study of drought severity, analysis results from periods of three months (November to January and six months (November to April have shown significant drought characteristics. In addition, analysis of drought occurrence probabilities using the method of Markov chains has shown that the occurrence probabilities of drought events are higher in the Lanyang River basin than in the Yilan River basin; particularly for extreme events, the occurrence probability of an extreme drought event is 20.6% during the dry season (November to April in the Lanyang River basin, and 3.4% in the Yilan River basin. This study shows that for analysis of drought/wet occurrence probabilities, the results obtained for the drought frequency and occurrence probability using short-term data with the method of Markov chains can be used to predict the long-term occurrence
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Zipf exponent of trajectory distribution in the hidden Markov model
International Nuclear Information System (INIS)
Bochkarev, V V; Lerner, E Yu
2014-01-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
Turner, Sean; Galelli, Stefano; Wilcox, Karen
2015-04-01
Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating
Radioactive waste processing and disposal: a bibliography. Part 1. Abstracts; Part 2. Indexes
International Nuclear Information System (INIS)
McLaren, L.H.
1985-03-01
This compilation contains 4567 citations to foreign and domestic research reports, journal articles, patents, conference proceedings, and books dealing with radioactive waste management. These citations were added to the DOE Energy Data Base from January 1983 through December 1983. Five indexes are included: Corporate Author, Personal Author, Subject, Contract Number, and Report Number
Franchise Index/Profile: A Franchise Evaluation Process. Small Business Management Series No. 35.
Stigelman, C. R.
The book is presented as an aid to those who have decided to invest in, or who are seriously interested in investigating, a franchise opportunity. The material presented is an index of basic information a person should have about a particular franchise to enable him to make a valid determination as to whether or not a specific franchise is the…
Coding with partially hidden Markov models
DEFF Research Database (Denmark)
Forchhammer, Søren; Rissanen, J.
1995-01-01
Partially hidden Markov models (PHMM) are introduced. They are a variation of the hidden Markov models (HMM) combining the power of explicit conditioning on past observations and the power of using hidden states. (P)HMM may be combined with arithmetic coding for lossless data compression. A general...... 2-part coding scheme for given model order but unknown parameters based on PHMM is presented. A forward-backward reestimation of parameters with a redefined backward variable is given for these models and used for estimating the unknown parameters. Proof of convergence of this reestimation is given....... The PHMM structure and the conditions of the convergence proof allows for application of the PHMM to image coding. Relations between the PHMM and hidden Markov models (HMM) are treated. Results of coding bi-level images with the PHMM coding scheme is given. The results indicate that the PHMM can adapt...
Inhomogeneous Markov Models for Describing Driving Patterns
DEFF Research Database (Denmark)
Iversen, Emil Banning; Møller, Jan K.; Morales, Juan Miguel
2017-01-01
. Specifically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is defined by the time-varying probabilities of starting and ending a trip, and is justified due to the uncertainty associated with the use of the vehicle. The model is fitted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....
Inhomogeneous Markov Models for Describing Driving Patterns
DEFF Research Database (Denmark)
Iversen, Jan Emil Banning; Møller, Jan Kloppenborg; Morales González, Juan Miguel
. Specically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is dened by the time-varying probabilities of starting and ending a trip and is justied due to the uncertainty associated with the use of the vehicle. The model is tted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....
Detecting Structural Breaks using Hidden Markov Models
DEFF Research Database (Denmark)
Ntantamis, Christos
Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another....... The estimation of the HMM is conducted using a variant of the Iterative Conditional Expectation-Generalized Mixture (ICE-GEMI) algorithm proposed by Delignon et al. (1997), that permits analysis of the conditional distributions of economic data and allows for different functional forms across regimes...
Predicting Protein Secondary Structure with Markov Models
DEFF Research Database (Denmark)
Fischer, Paul; Larsen, Simon; Thomsen, Claus
2004-01-01
we are considering here, is to predict the secondary structure from the primary one. To this end we train a Markov model on training data and then use it to classify parts of unknown protein sequences as sheets, helices or coils. We show how to exploit the directional information contained...... in the Markov model for this task. Classifications that are purely based on statistical models might not always be biologically meaningful. We present combinatorial methods to incorporate biological background knowledge to enhance the prediction performance....
Estimation with Right-Censored Observations Under A Semi-Markov Model.
Zhao, Lihui; Hu, X Joan
2013-06-01
The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition probability of the semi-Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi-Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study.
Directory of Open Access Journals (Sweden)
S. Varmazyar
2008-04-01
Full Text Available Background and aims Fire and explosion hazards are the first and second of major hazards in process industries, respectively. This study has been done to determine fire and explosion risk severity,radius of exposure and estimating of most probable loss. Methods In this quantitative study process unit has been selected with affecting parameters on fire and explosion risk. Then, it was analyzed by DOW's fire and explosion index (F&EI. Technical data were obtained from process documents and reports, fire and explosion guideline.After calculating of DOW's index, radius of exposure determined and finally most probable loss was estimated. Results The results showed an F&EI value of 226 for this process unit.The F&EI was extremely high and unacceptable.Risk severity was categorized in sever class.Radius of exposure and damage factor were calculated 57 meters and 83%,respectively. As well as most probable loss was estimated about 6.7 million dollars. Conclusion F&EI is a proper technique for risk assessment and loss estimation of fire and explosion in process industries.Also,It is an important index for detecting high risk and low risk areas in an industry. At this technique, all of factors affecting on fire and explosion risk was showed as index that is a base for judgement risk class. Finally, estimated losses could be used as a base of fire and explosion insurance.
Prediction of Annual Rainfall Pattern Using Hidden Markov Model ...
African Journals Online (AJOL)
ADOWIE PERE
Hidden Markov model is very influential in stochastic world because of its ... the earth from the clouds. The usual ... Rainfall modelling and ... Markov Models have become popular tools ... environment sciences, University of Jos, plateau state,.
Extending Markov Automata with State and Action Rewards
Guck, Dennis; Timmer, Mark; Blom, Stefan; Bertrand, N.; Bortolussi, L.
This presentation introduces the Markov Reward Automaton (MRA), an extension of the Markov automaton that allows the modelling of systems incorporating rewards in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Our models support both rewards that are
Assessing type I error and power of multistate Markov models for panel data-A simulation study.
Cassarly, Christy; Martin, Renee' H; Chimowitz, Marc; Peña, Edsel A; Ramakrishnan, Viswanathan; Palesch, Yuko Y
2017-01-01
Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.
The Walkability Index dataset characterizes every Census 2010 block group in the U.S. based on its relative walkability. Walkability depends upon characteristics of the built environment that influence the likelihood of walking being used as a mode of travel. The Walkability Index is based on the EPA's previous data product, the Smart Location Database (SLD). Block group data from the SLD was the only input into the Walkability Index, and consisted of four variables from the SLD weighted in a formula to create the new Walkability Index. This dataset shares the SLD's block group boundary definitions from Census 2010. The methodology describing the process of creating the Walkability Index can be found in the documents located at ftp://newftp.epa.gov/EPADataCommons/OP/WalkabilityIndex.zip. You can also learn more about the Smart Location Database at https://edg.epa.gov/data/Public/OP/Smart_Location_DB_v02b.zip.
Hidden-Markov-Model Analysis Of Telemanipulator Data
Hannaford, Blake; Lee, Paul
1991-01-01
Mathematical model and procedure based on hidden-Markov-model concept undergoing development for use in analysis and prediction of outputs of force and torque sensors of telerobotic manipulators. In model, overall task broken down into subgoals, and transition probabilities encode ease with which operator completes each subgoal. Process portion of model encodes task-sequence/subgoal structure, and probability-density functions for forces and torques associated with each state of manipulation encode sensor signals that one expects to observe at subgoal. Parameters of model constructed from engineering knowledge of task.
Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel; Schweizer, Nikolaus
2017-01-01
Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains
Directory of Open Access Journals (Sweden)
Yuxian Zhang
2015-01-01
Full Text Available The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.
Quantum Enhanced Inference in Markov Logic Networks.
Wittek, Peter; Gogolin, Christian
2017-04-19
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Evaluation of Usability Utilizing Markov Models
Penedo, Janaina Rodrigues; Diniz, Morganna; Ferreira, Simone Bacellar Leal; Silveira, Denis S.; Capra, Eliane
2012-01-01
Purpose: The purpose of this paper is to analyze the usability of a remote learning system in its initial development phase, using a quantitative usability evaluation method through Markov models. Design/methodology/approach: The paper opted for an exploratory study. The data of interest of the research correspond to the possible accesses of users…
Bayesian analysis for reversible Markov chains
Diaconis, P.; Rolles, S.W.W.
2006-01-01
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple
Discounted Markov games : generalized policy iteration method
Wal, van der J.
1978-01-01
In this paper, we consider two-person zero-sum discounted Markov games with finite state and action spaces. We show that the Newton-Raphson or policy iteration method as presented by Pollats-chek and Avi-Itzhak does not necessarily converge, contradicting a proof of Rao, Chandrasekaran, and Nair.
Hidden Markov Models for Human Genes
DEFF Research Database (Denmark)
Baldi, Pierre; Brunak, Søren; Chauvin, Yves
1997-01-01
We analyse the sequential structure of human genomic DNA by hidden Markov models. We apply models of widely different design: conventional left-right constructs and models with a built-in periodic architecture. The models are trained on segments of DNA sequences extracted such that they cover com...
Markov Trends in Macroeconomic Time Series
R. Paap (Richard)
1997-01-01
textabstractMany macroeconomic time series are characterised by long periods of positive growth, expansion periods, and short periods of negative growth, recessions. A popular model to describe this phenomenon is the Markov trend, which is a stochastic segmented trend where the slope depends on the
Optimal dividend distribution under Markov regime switching
Jiang, Z.; Pistorius, M.
2012-01-01
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness...
Multi-dimensional quasitoeplitz Markov chains
Directory of Open Access Journals (Sweden)
Alexander N. Dudin
1999-01-01
Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.
Markov chains with quasitoeplitz transition matrix
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Model Checking Infinite-State Markov Chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.
2004-01-01
In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state
Model Checking Markov Chains: Techniques and Tools
Zapreev, I.S.
2008-01-01
This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking
Quantum Enhanced Inference in Markov Logic Networks
Wittek, Peter; Gogolin, Christian
2017-04-01
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Model Checking Structured Infinite Markov Chains
Remke, Anne Katharina Ingrid
2008-01-01
In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special
Hidden Markov models for labeled sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
1994-01-01
A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI...
Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.
Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu
2013-01-01
Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.
Stochastic modeling of pitting corrosion in underground pipelines using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Velazquez, J.C.; Caleyo, F.; Hallen, J.M.; Araujo, J.E. [Instituto Politecnico Nacional (IPN), Mexico D.F. (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE); Valor, A. [Universidad de La Habana, La Habana (Cuba)
2009-07-01
A non-homogenous, linear growth (pure birth) Markov process, with discrete states in continuous time, has been used to model external pitting corrosion in underground pipelines. The transition probability function for the pit depth is obtained from the analytical solution of the forward Kolmogorov equations for this process. The parameters of the transition probability function between depth states can be identified from the observed time evolution of the mean of the pit depth distribution. Monte Carlo simulations were used to predict the time evolution of the mean value of the pit depth distribution in soils with different physicochemical characteristics. The simulated distributions have been used to create an empirical Markov-chain-based stochastic model for predicting the evolution of pitting corrosion from the observed properties of the soil in contact with the pipeline. Real- life case studies, involving simulated and measured pit depth distributions are presented to illustrate the application of the proposed Markov chains model. (author)
Nickelsen, Daniel
2017-07-01
The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.
INDEXABILITY AND OPTIMAL INDEX POLICIES FOR A CLASS OF REINITIALISING RESTLESS BANDITS.
Villar, Sofía S
2016-01-01
Motivated by a class of Partially Observable Markov Decision Processes with application in surveillance systems in which a set of imperfectly observed state processes is to be inferred from a subset of available observations through a Bayesian approach, we formulate and analyze a special family of multi-armed restless bandit problems. We consider the problem of finding an optimal policy for observing the processes that maximizes the total expected net rewards over an infinite time horizon subject to the resource availability. From the Lagrangian relaxation of the original problem, an index policy can be derived, as long as the existence of the Whittle index is ensured. We demonstrate that such a class of reinitializing bandits in which the projects' state deteriorates while active and resets to its initial state when passive until its completion possesses the structural property of indexability and we further show how to compute the index in closed form. In general, the Whittle index rule for restless bandit problems does not achieve optimality. However, we show that the proposed Whittle index rule is optimal for the problem under study in the case of stochastically heterogenous arms under the expected total criterion, and it is further recovered by a simple tractable rule referred to as the 1-limited Round Robin rule. Moreover, we illustrate the significant suboptimality of other widely used heuristic: the Myopic index rule, by computing in closed form its suboptimality gap. We present numerical studies which illustrate for the more general instances the performance advantages of the Whittle index rule over other simple heuristics.
Markov-switching model for nonstationary runoff conditioned on El Nino information
DEFF Research Database (Denmark)
Gelati, Emiliano; Madsen, H.; Rosbjerg, Dan
2010-01-01
We define a Markov-modulated autoregressive model with exogenous input (MARX) to generate runoff scenarios using climatic information. Runoff parameterization is assumed to be conditioned on a hidden climate state following a Markov chain, where state transition probabilities are functions...... of the climatic input. MARX allows stochastic modeling of nonstationary runoff, as runoff anomalies are described by a mixture of autoregressive models with exogenous input, each one corresponding to a climate state. We apply MARX to inflow time series of the Daule Peripa reservoir (Ecuador). El Nino Southern...... Oscillation (ENSO) information is used to condition runoff parameterization. Among the investigated ENSO indexes, the NINO 1+2 sea surface temperature anomalies and the trans-Nino index perform best as predictors. In the perspective of reservoir optimization at various time scales, MARX produces realistic...
Energy Technology Data Exchange (ETDEWEB)
Adaro, Jorge; Cesari, Daniela; Lema, Alba; Galimberti, Pablo [Universidad Nacional de Rio Cuarto (Argentina). Facultad de Ingenieria]. E-mail: aadaro@ing.unrc.edu.ar
2000-07-01
The objective of the present work is to adopt a methodology that allows to generate sequences of values of global solar radiation. It is carried out a preliminary study on the generation of radiation sequence a concept of Chains of Markov. For it is analyzed it the readiness of data and it is investigated about the possibility of using such a methodology calculating values of indexes of clarity previously. With data of available radiation and provided the National Meteorological Service for Rio Cuarto, the preliminary study is carried out the preliminary study looking for to validated the pattern to the effects of being able to transfer the use of the methodology in other regions. (author)
Markov analysis of different standby computer based systems
International Nuclear Information System (INIS)
Srinivas, G.; Guptan, Rajee; Mohan, Nalini; Ghadge, S.G.; Bajaj, S.S.
2006-01-01
As against the conventional triplicated systems of hardware and the generation of control signals for the actuator elements by means of redundant hardwired median circuits, employed in the early Indian PHWR's, a new approach of generating control signals based on software by a redundant system of computers is introduced in the advanced/current generation of Indian PHWR's. Reliability is increased by fault diagnostics and automatic switch over of all the loads to one computer in case of total failure of the other computer. Independent processing by a redundant CPU in each system enables inter-comparison to quickly identify system failure, in addition to the other self-diagnostic features provided. Combinatorial models such as reliability block diagrams and fault trees are frequently used to predict the reliability, maintainability and safety of complex systems. Unfortunately, these methods cannot accurately model dynamic system behavior; Because of its unique ability to handle dynamic cases, Markov analysis can be a powerful tool in the reliability maintainability and safety (RMS) analyses of dynamic systems. A Markov model breaks the system configuration into a number of states. Each of these states is connected to all other states by transition rates. It then utilizes transition matrices to evaluate the reliability and safety of the systems, either through matrix manipulation or other analytical solution methods, such as Laplace transforms. Thus, Markov analysis is a powerful reliability, maintainability and safety analysis tool. It allows the analyst to model complex, dynamic, highly distributed, fault tolerant systems that would otherwise be very difficult to model using classical techniques like the Fault tree method. The Dual Processor Hot Standby Process Control System (DPHS-PCS) and the Computerized Channel Temperature Monitoring System (CCTM) are typical examples of hot standby systems in the Indian PHWR's. While such systems currently in use in Indian PHWR
Memory Indexing: A Novel Method for Tracing Memory Processes in Complex Cognitive Tasks
Renkewitz, Frank; Jahn, Georg
2012-01-01
We validate an eye-tracking method applicable for studying memory processes in complex cognitive tasks. The method is tested with a task on probabilistic inferences from memory. It provides valuable data on the time course of processing, thus clarifying previous results on heuristic probabilistic inference. Participants learned cue values of…
Comparison of Langevin and Markov channel noise models for neuronal signal generation.
Sengupta, B; Laughlin, S B; Niven, J E
2010-01-01
The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either Na+ and K+, or only K+ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas, and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and nonspiking membranes. Even with increasing numbers of channels, the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.
Directory of Open Access Journals (Sweden)
Melike Bildirici
2014-01-01
Full Text Available The study has two aims. The first aim is to propose a family of nonlinear GARCH models that incorporate fractional integration and asymmetric power properties to MS-GARCH processes. The second purpose of the study is to augment the MS-GARCH type models with artificial neural networks to benefit from the universal approximation properties to achieve improved forecasting accuracy. Therefore, the proposed Markov-switching MS-ARMA-FIGARCH, APGARCH, and FIAPGARCH processes are further augmented with MLP, Recurrent NN, and Hybrid NN type neural networks. The MS-ARMA-GARCH family and MS-ARMA-GARCH-NN family are utilized for modeling the daily stock returns in an emerging market, the Istanbul Stock Index (ISE100. Forecast accuracy is evaluated in terms of MAE, MSE, and RMSE error criteria and Diebold-Mariano equal forecast accuracy tests. The results suggest that the fractionally integrated and asymmetric power counterparts of Gray’s MS-GARCH model provided promising results, while the best results are obtained for their neural network based counterparts. Further, among the models analyzed, the models based on the Hybrid-MLP and Recurrent-NN, the MS-ARMA-FIAPGARCH-HybridMLP, and MS-ARMA-FIAPGARCH-RNN provided the best forecast performances over the baseline single regime GARCH models and further, over the Gray’s MS-GARCH model. Therefore, the models are promising for various economic applications.
Assessing type I error and power of multistate Markov models for panel data-A simulation study
Cassarly, Christy; Martin, Renee’ H.; Chimowitz, Marc; Peña, Edsel A.; Ramakrishnan, Viswanathan; Palesch, Yuko Y.
2016-01-01
Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that ...
Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis
Directory of Open Access Journals (Sweden)
Gertsbakh Ilya B.
2015-09-01
Full Text Available We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s. We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD. The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn]/E[Yn]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.
Nonequilibrium thermodynamic potentials for continuous-time Markov chains.
Verley, Gatien
2016-01-01
We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.
Characterizing Fiber Bragg Grating Index Profiles to Improve the Writing Process
DEFF Research Database (Denmark)
Espejo, M.J.; Svalgaard, Mikael; Dyer, S.D.
2006-01-01
We demonstrate an accurate method for identifying both systematic and random errors in a fiber Bragg grating (FBG) writing system and show its application to calibration of the writing process. We first measure the FBG impulse response using low-coherence interferometry, and then we calculate......-beam dithered phase mask FBG writing system. We demonstrate the ability to identify errors in the writing process that would not likely be found from a measurement of the FBG reflection spectrum alone....
[Compared Markov with fractal models by using single-channel experimental and simulation data].
Lan, Tonghan; Wu, Hongxiu; Lin, Jiarui
2006-10-01
The gating mechanical kinetical of ion channels has been modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant, the transition rate constants among the states is independent both of time and of the previous channel activity. It is assumed in Liebovitch's fractal model that the channel exists in an infinite number of energy states, consequently, transitions from one conductance state to another would be governed by a continuum of rate constants. In this paper, a statistical comparison is presented of Markov and fractal models of ion channel gating, the analysis is based on single-channel data from ion channel voltage-dependence K+ single channel of neuron cell and simulation data from three-states Markov model.
Un calcul de Viterbi pour un Modèle de Markov Caché Contraint
DEFF Research Database (Denmark)
Petit, Matthieu; Christiansen, Henning
2009-01-01
A hidden Markov model (HMM) is a statistical model in which the system being modeled is assumed to be a Markov process with hidden states. This model has been widely used in speech recognition and biological sequence analysis. Viterbi algorithm has been proposed to compute the most probable value....... Several constraint techniques are used to reduce the search of the most probable value of hidden states of a constrained HMM. An implementation based on PRISM, a logic programming language for statistical modeling, is presented....
Discrete-time semi-Markov modeling of human papillomavirus persistence
Mitchell, C. E.; Hudgens, M. G.; King, C. C.; Cu-Uvin, S.; Lo, Y.; Rompalo, A.; Sobel, J.; Smith, J. S.
2011-01-01
Multi-state modeling is often employed to describe the progression of a disease process. In epidemiological studies of certain diseases, the disease state is typically only observed at periodic clinical visits, producing incomplete longitudinal data. In this paper we consider fitting semi-Markov models to estimate the persistence of human papillomavirus (HPV) type-specific infection in studies where the status of HPV type(s) is assessed periodically. Simulation study results are presented indicating the semi-Markov estimator is more accurate than an estimator currently used in the HPV literature. The methods are illustrated using data from the HIV Epidemiology Research Study (HERS). PMID:21538985
The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...
Determination of laser cutting process conditions using the preference selection index method
Madić, Miloš; Antucheviciene, Jurgita; Radovanović, Miroslav; Petković, Dušan
2017-03-01
Determination of adequate parameter settings for improvement of multiple quality and productivity characteristics at the same time is of great practical importance in laser cutting. This paper discusses the application of the preference selection index (PSI) method for discrete optimization of the CO2 laser cutting of stainless steel. The main motivation for application of the PSI method is that it represents an almost unexplored multi-criteria decision making (MCDM) method, and moreover, this method does not require assessment of the considered criteria relative significances. After reviewing and comparing the existing approaches for determination of laser cutting parameter settings, the application of the PSI method was explained in detail. Experiment realization was conducted by using Taguchi's L27 orthogonal array. Roughness of the cut surface, heat affected zone (HAZ), kerf width and material removal rate (MRR) were considered as optimization criteria. The proposed methodology is found to be very useful in real manufacturing environment since it involves simple calculations which are easy to understand and implement. However, while applying the PSI method it was observed that it can not be useful in situations where there exist a large number of alternatives which have attribute values (performances) very close to those which are preferred.
van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F
2013-08-01
Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.
Impey, Danielle; de la Salle, Sara; Knott, Verner
2016-06-01
Transcranial direct current stimulation (tDCS) is a non-invasive form of brain stimulation which uses a very weak constant current to temporarily excite (anodal stimulation) or inhibit (cathodal stimulation) activity in the brain area of interest via small electrodes placed on the scalp. Currently, tDCS of the frontal cortex is being used as a tool to investigate cognition in healthy controls and to improve symptoms in neurological and psychiatric patients. tDCS has been found to facilitate cognitive performance on measures of attention, memory, and frontal-executive functions. Recently, a short session of anodal tDCS over the temporal lobe has been shown to increase auditory sensory processing as indexed by the Mismatch Negativity (MMN) event-related potential (ERP). This preliminary pilot study examined the separate and interacting effects of both anodal and cathodal tDCS on MMN-indexed auditory pitch discrimination. In a randomized, double blind design, the MMN was assessed before (baseline) and after tDCS (2mA, 20min) in 2 separate sessions, one involving 'sham' stimulation (the device is turned off), followed by anodal stimulation (to temporarily excite cortical activity locally), and one involving cathodal stimulation (to temporarily decrease cortical activity locally), followed by anodal stimulation. Results demonstrated that anodal tDCS over the temporal cortex increased MMN-indexed auditory detection of pitch deviance, and while cathodal tDCS decreased auditory discrimination in baseline-stratified groups, subsequent anodal stimulation did not significantly alter MMN amplitudes. These findings strengthen the position that tDCS effects on cognition extend to the neural processing of sensory input and raise the possibility that this neuromodulatory technique may be useful for investigating sensory processing deficits in clinical populations. Copyright © 2016 Elsevier Inc. All rights reserved.
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.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
International Nuclear Information System (INIS)
Moropoulou, A.; Delegou, E.T.; Vlahakis, V.; Karaviti, E.
2007-01-01
In this work, digital processing of scanning-electron-microscopy images utilized to assess cleaning interventions applied on the Pentelic marble surfaces of the National Archaeological Museum and National Library in Athens, Greece. Beside mineralogical and chemical characterization that took place by scanning-electron-microscopy with Energy Dispersive X-ray Spectroscopy, the image-analysis program EDGE was applied for estimating three evaluation indexes of the marble micro-structure. The EDGE program was developed by the U.S. Geological Survey for the evaluation of cleaning interventions applied on Philadelphia City Hall. This computer program analyzes scanning-electron-microscopy images of stone specimens cut in cross-section for measuring the fractal dimension of the exposed surfaces, the stone near-surface fracture density, the shape factor (a surface roughness factor) and the friability index which represents the physico-chemical and physico-mechanical stability of the stone surface. The results indicated that the evaluation of the marble surface micro-structure before and after cleaning is achieved by the suggested indexes, while the performance of cleaning interventions on the marble surfaces can be assessed
Energy Technology Data Exchange (ETDEWEB)
Smith-Perera, Aida [Universidad Metropolitana de Caracas, Departamento de Gestion Tecnologica, Caracas 1071, Edo Miranda (Venezuela); Garcia-Melon, Monica; Poveda-Bautista, Rocio; Pastor-Ferrando, Juan-Pascual [Universidad Politecnica de Valencia, Departamento de Proyectos de Ingenieria, Camino de vera s/n 46022 Valencia (Spain)
2010-08-15
In this paper a new approach to prioritize project portfolio in an efficient and reliable way is presented. It is based on strategic objectives of the company and multicriteria decision methods. The paper introduces a rigorous method with acceptable complexity which seeks to assist managers of a big Electrical Company of Venezuela to distribute the annual budget among the possible improvement actions to be conducted on the electrical network of Caracas. A total of 15 network improvement actions grouped into three clusters according to the strategic objectives of the company have been analyzed using the Project Strategic Index (PSI) proposed. The approach combines the use of the Analytic Network Process (ANP) method with the information obtained from the experts during the decision-making process. The ANP method allows the aggregation of the experts' judgments on each of the indicators used into one Project Strategic Index. In addition, ANP is based on utility ratio functions which are the most appropriate for the analysis of uncertain data, like experts' estimations. Finally, unlike the other multicriteria techniques, ANP allows the decision problem to be modelled using the relationships among dependent criteria. The participating experts coincided in the appreciation that the method proposed in this paper is useful and an improvement from traditional budget distribution techniques. They find the results obtained coherent, the process seems sufficiently rigorous and precise, and the use of resources is significantly less than in other methods. (author)
International Nuclear Information System (INIS)
Smith-Perera, Aida; Garcia-Melon, Monica; Poveda-Bautista, Rocio; Pastor-Ferrando, Juan-Pascual
2010-01-01
In this paper a new approach to prioritize project portfolio in an efficient and reliable way is presented. It is based on strategic objectives of the company and multicriteria decision methods. The paper introduces a rigorous method with acceptable complexity which seeks to assist managers of a big Electrical Company of Venezuela to distribute the annual budget among the possible improvement actions to be conducted on the electrical network of Caracas. A total of 15 network improvement actions grouped into three clusters according to the strategic objectives of the company have been analyzed using the Project Strategic Index (PSI) proposed. The approach combines the use of the Analytic Network Process (ANP) method with the information obtained from the experts during the decision-making process. The ANP method allows the aggregation of the experts' judgments on each of the indicators used into one Project Strategic Index. In addition, ANP is based on utility ratio functions which are the most appropriate for the analysis of uncertain data, like experts' estimations. Finally, unlike the other multicriteria techniques, ANP allows the decision problem to be modelled using the relationships among dependent criteria. The participating experts coincided in the appreciation that the method proposed in this paper is useful and an improvement from traditional budget distribution techniques. They find the results obtained coherent, the process seems sufficiently rigorous and precise, and the use of resources is significantly less than in other methods. (author)
A Bayesian method for construction of Markov models to describe dynamics on various time-scales.
Rains, Emily K; Andersen, Hans C
2010-10-14
The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Second Order Optimality in Markov Decision Chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2017-01-01
Roč. 53, č. 6 (2017), s. 1086-1099 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : Markov decision chains * second order optimality * optimalilty conditions for transient, discounted and average models * policy and value iterations Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/sladky-0485146.pdf
Analysis of a quantum Markov chain
International Nuclear Information System (INIS)
Marbeau, J.; Gudder, S.
1990-01-01
A quantum chain is analogous to a classical stationary Markov chain except that the probability measure is replaced by a complex amplitude measure and the transition probability matrix is replaced by a transition amplitude matrix. After considering the general situation, we study a particular example of a quantum chain whose transition amplitude matrix has the form of a Dirichlet matrix. Such matrices generate a discrete analog of the usual continuum Feynman amplitude. We then compute the probability distribution for these quantum chains
Modelling of cyclical stratigraphy using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Kulatilake, P.H.S.W.
1987-07-01
State-of-the-art on modelling of cyclical stratigraphy using first-order Markov chains is reviewed. Shortcomings of the presently available procedures are identified. A procedure which eliminates all the identified shortcomings is presented. Required statistical tests to perform this modelling are given in detail. An example (the Oficina formation in eastern Venezuela) is given to illustrate the presented procedure. 12 refs., 3 tabs. 1 fig.
Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.
Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine
2010-09-01
Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.
The bacterial sequential Markov coalescent
De Maio, N; Wilson, DJ
2017-01-01
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 that are not consistent with the hypothesis of a si...
a multi-period markov model for monthly rainfall in lagos, nigeria
African Journals Online (AJOL)
PUBLICATIONS1
A twelve-period. Markov model has been developed for the monthly rainfall data for Lagos, along the coast of .... autoregressive process to model river flow; Deo et al. (2015) utilized an ...... quences for the analysis of river basins by simulation.
M.J.C. Nuijten (Mark); D.L. Andress (Dennis); S.E. Marx (Steven); R. Sterz (Raimund)
2009-01-01
textabstractObjective: The objective of this study was to determine the cost effectiveness of paricalcitol versus calcitriol for the treatment of secondary hyperparathyroidism in patients with chronic kidney disease in the United States setting. Methods: A Markov process model was developed
Temperature scaling method for Markov chains.
Crosby, Lonnie D; Windus, Theresa L
2009-01-22
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
Event-related potential N270 as an index of social information conflict in explicit processing.
Wang, Pei; Tan, Chen-Hao; Li, Yu; Zhang, Qin; Wang, Yi-Bo; Luo, Jun-Long
2018-01-01
As N270 has been widely shown to be sensitive to nonsocial information conflict, the present study investigated whether social information conflict can elicit increased N270 in either explicit or implicit processing conditions. Gender stereotype-related picture-word pairs and picture-word pairs in specific colors were used as social and nonsocial information, respectively. Participants performed an explicit task based on the S1-S2 paradigm in Study 1, and both social and nonsocial information conditions elicited larger N270 than the no-conflict condition. In Study 2, participants performed a word judgment task that was modified from the S1-S2 paradigm of Study 1. However, neither social information nor nonsocial information elicited larger N270 within the conflict condition. Social trials generally elicited a more negative ERP waveform than nonsocial trials overall. These findings suggest that N270 may reflect the processing of social information conflict only in explicit conditions and also that the cognitive basis of N270 is thus a general but explicit processing of working memory representation conflict. Copyright © 2017. Published by Elsevier B.V.
Optimal Time-Abstract Schedulers for CTMDPs and Markov Games
Directory of Open Access Journals (Sweden)
Markus Rabe
2010-06-01
Full Text Available We study time-bounded reachability in continuous-time Markov decision processes for time-abstract scheduler classes. Such reachability problems play a paramount role in dependability analysis and the modelling of manufacturing and queueing systems. Consequently, their analysis has been studied intensively, and techniques for the approximation of optimal control are well understood. From a mathematical point of view, however, the question of approximation is secondary compared to the fundamental question whether or not optimal control exists. We demonstrate the existence of optimal schedulers for the time-abstract scheduler classes for all CTMDPs. Our proof is constructive: We show how to compute optimal time-abstract strategies with finite memory. It turns out that these optimal schedulers have an amazingly simple structure---they converge to an easy-to-compute memoryless scheduling policy after a finite number of steps. Finally, we show that our argument can easily be lifted to Markov games: We show that both players have a likewise simple optimal strategy in these more general structures.
Hidden Markov latent variable models with multivariate longitudinal data.
Song, Xinyuan; Xia, Yemao; Zhu, Hongtu
2017-03-01
Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (MCECM) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use. © 2016, The International Biometric Society.