A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

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.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

NASA Astrophysics Data System (ADS)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

Graph transformation method for calculating waiting times in Markov chains.

PubMed

Trygubenko, Semen A; Wales, David J

2006-06-21

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a nonstochastic and noniterative fashion. In particular, we can calculate the mean first-passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

An abstract specification language for Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, R. W.

1985-01-01

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

An abstract language for specifying Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

1986-01-01

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding.

PubMed

Radford, Isolde H; Fersht, Alan R; Settanni, Giovanni

2011-06-09

Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

Observation uncertainty in reversible Markov chains.

PubMed

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+) .

Time-patterns of antibiotic exposure in poultry production--a Markov chains exploratory study of nature and consequences.

PubMed

Chauvin, C; Clement, C; Bruneau, M; Pommeret, D

2007-07-16

This article describes the use of Markov chains to explore the time-patterns of antimicrobial exposure in broiler poultry. The transition in antimicrobial exposure status (exposed/not exposed to an antimicrobial, with a distinction between exposures to the different antimicrobial classes) in extensive data collected in broiler chicken flocks from November 2003 onwards, was investigated. All Markov chains were first-order chains. Mortality rate, geographical location and slaughter semester were sources of heterogeneity between transition matrices. Transitions towards a 'no antimicrobial' exposure state were highly predominant, whatever the initial state. From a 'no antimicrobial' exposure state, the transition to beta-lactams was predominant among transitions to an antimicrobial exposure state. Transitions between antimicrobial classes were rare and variable. Switches between antimicrobial classes and repeats of a particular class were both observed. Application of Markov chains analysis to the database of the nation-wide antimicrobial resistance monitoring programme pointed out that transition probabilities between antimicrobial exposure states increased with the number of resistances in Escherichia coli strains.

Transition-Independent Decentralized Markov Decision Processes

NASA Technical Reports Server (NTRS)

Becker, Raphen; Silberstein, Shlomo; Lesser, Victor; Goldman, Claudia V.; Morris, Robert (Technical Monitor)

2003-01-01

There has been substantial progress with formal models for sequential decision making by individual agents using the Markov decision process (MDP). However, similar treatment of multi-agent systems is lacking. A recent complexity result, showing that solving decentralized MDPs is NEXP-hard, provides a partial explanation. To overcome this complexity barrier, we identify a general class of transition-independent decentralized MDPs that is widely applicable. The class consists of independent collaborating agents that are tied up by a global reward function that depends on both of their histories. We present a novel algorithm for solving this class of problems and examine its properties. The result is the first effective technique to solve optimally a class of decentralized MDPs. This lays the foundation for further work in this area on both exact and approximate solutions.

Patchwork sampling of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kürsten, Rüdiger; Behn, Ulrich

2016-03-01

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

Markov chains: computing limit existence and approximations with DNA.

PubMed

Cardona, M; Colomer, M A; Conde, J; Miret, J M; Miró, J; Zaragoza, A

2005-09-01

We present two algorithms to perform computations over Markov chains. The first one determines whether the sequence of powers of the transition matrix of a Markov chain converges or not to a limit matrix. If it does converge, the second algorithm enables us to estimate this limit. The combination of these algorithms allows the computation of a limit using DNA computing. In this sense, we have encoded the states and the transition probabilities using strands of DNA for generating paths of the Markov chain.

Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion

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

Wei, Qingda, E-mail: weiqd@hqu.edu.cn; Chen, Xian, E-mail: chenxian@amss.ac.cn

In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation andmore » obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.« less

A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains

NASA Astrophysics Data System (ADS)

Gan, Tingyue; Cameron, Maria

2017-06-01

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical timescales at which the qualitative behavior of a given Markov chain changes, and give an effective description of the dynamics on each of them. This approach is valid for both time-reversible and time-irreversible Markov processes, with or without symmetry. Central to this approach are two graph algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the critical timescales and the hierarchies of Typical Transition Graphs or T-graphs indicating the most likely transitions in the system without and with symmetry, respectively. The sequence of critical timescales includes the subsequence of the reciprocals of the real parts of eigenvalues. Under a certain assumption, we prove sharp asymptotic estimates for eigenvalues (including pre-factors) and show how one can extract them from the output of Algorithm 1. We discuss the relationship between Algorithms 1 and 2 and explain how one needs to interpret the output of Algorithm 1 if it is applied in the case with symmetry instead of Algorithm 2. Finally, we analyze an example motivated by R. D. Astumian's model of the dynamics of kinesin, a molecular motor, by means of Algorithm 2.

Dynamic Noise and its Role in Understanding Epidemiological Processes

NASA Astrophysics Data System (ADS)

Stollenwerk, Nico; Aguiar, Maíra

2010-09-01

We investigate the role of dynamic noise in understanding epidemiological systems, such as influenza or dengue fever by deriving stochastic ordinary differential equations from markov processes for discrete populations. This approach allows for an easy analysis of dynamical noise transitions between co-existing attractors.

First and second order semi-Markov chains for wind speed modeling

NASA Astrophysics Data System (ADS)

Prattico, F.; Petroni, F.; D'Amico, G.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [3] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [1], by using two models, first-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. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution, Renewable Energy, 28/2003 1787-1802. [2] 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 generation of wind speed time series, Energy 30/2005 693-708. [3] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Renewable Energy 29/2004, 1407-1418.

A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions.

PubMed

Aralis, Hilary; Brookmeyer, Ron

2017-01-01

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

Modeling the coupled return-spread high frequency dynamics of large tick assets

NASA Astrophysics Data System (ADS)

Curato, Gianbiagio; Lillo, Fabrizio

2015-01-01

Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We present an approach based on the hidden Markov model, also known in econometrics as the Markov switching model, for the dynamics of price changes, where the latent Markov process is described by the transitions between spreads. We then use a finite Markov mixture of logit regressions on past squared price changes to describe temporal dependencies in the dynamics of price changes. The model can thus be seen as a double chain Markov model. We show that the model describes the shape of the price change distribution at different time scales, volatility clustering, and the anomalous decrease of kurtosis. We calibrate our models based on Nasdaq stocks and we show that this model reproduces remarkably well the statistical properties of real data.

Dynamic neutron scattering from conformational dynamics. I. Theory and Markov models

NASA Astrophysics Data System (ADS)

Lindner, Benjamin; Yi, Zheng; Prinz, Jan-Hendrik; Smith, Jeremy C.; Noé, Frank

2013-11-01

The dynamics of complex molecules can be directly probed by inelastic neutron scattering experiments. However, many of the underlying dynamical processes may exist on similar timescales, which makes it difficult to assign processes seen experimentally to specific structural rearrangements. Here, we show how Markov models can be used to connect structural changes observed in molecular dynamics simulation directly to the relaxation processes probed by scattering experiments. For this, a conformational dynamics theory of dynamical neutron and X-ray scattering is developed, following our previous approach for computing dynamical fingerprints of time-correlation functions [F. Noé, S. Doose, I. Daidone, M. Löllmann, J. Chodera, M. Sauer, and J. Smith, Proc. Natl. Acad. Sci. U.S.A. 108, 4822 (2011)]. Markov modeling is used to approximate the relaxation processes and timescales of the molecule via the eigenvectors and eigenvalues of a transition matrix between conformational substates. This procedure allows the establishment of a complete set of exponential decay functions and a full decomposition into the individual contributions, i.e., the contribution of every atom and dynamical process to each experimental relaxation process.

Nonparametric model validations for hidden Markov models with applications in financial econometrics.

PubMed

Zhao, Zhibiao

2011-06-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.

Twelve years of succession on sandy substrates in a post-mining landscape: a Markov chain analysis.

PubMed

Baasch, Annett; Tischew, Sabine; Bruelheide, Helge

2010-06-01

Knowledge of succession rates and pathways is crucial for devising restoration strategies for highly disturbed ecosystems such as surface-mined land. As these processes have often only been described in qualitative terms, we used Markov models to quantify transitions between successional stages. However, Markov models are often considered not attractive for some reasons, such as model assumptions (e.g., stationarity in space and time, or the high expenditure of time required to estimate successional transitions in the field). Here we present a solution for converting multivariate ecological time series into transition matrices and demonstrate the applicability of this approach for a data set that resulted from monitoring the succession of sandy dry grassland in a post-mining landscape. We analyzed five transition matrices, four one-step matrices referring to specific periods of transition (1995-1998, 1998-2001, 2001-2004, 2004-2007), and one matrix for the whole study period (stationary model, 1995-2007). Finally, the stationary model was enhanced to a partly time-variable model. Applying the stationary and the time-variable models, we started a prediction well outside our calibration period, beginning with 100% bare soil in 1974 as the known start of the succession, and generated the coverage of 12 predefined vegetation types in three-year intervals. Transitions among vegetation types changed significantly in space and over time. While the probability of colonization was almost constant over time, the replacement rate tended to increase, indicating that the speed of succession accelerated with time or fluctuations became stronger. The predictions of both models agreed surprisingly well with the vegetation data observed more than two decades later. This shows that our dry grassland succession in a post-mining landscape can be adequately described by comparably simple types of Markov models, although some model assumptions have not been fulfilled and within-plot transitions have not been observed with point exactness. The major achievement of our proposed way to convert vegetation time series into transition matrices is the estimation of probability of events--a strength not provided by other frequently used statistical methods in vegetation science.

Stochastic Dynamics through Hierarchically Embedded Markov Chains

NASA Astrophysics Data System (ADS)

Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.

2017-02-01

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.

Constructing 1/omegaalpha noise from reversible Markov chains.

PubMed

Erland, Sveinung; Greenwood, Priscilla E

2007-09-01

This paper gives sufficient conditions for the output of 1/omegaalpha noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/omegaalpha condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/omega noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/omegaalpha noise which also has a long memory.

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

PubMed

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.

Convergence of Transition Probability Matrix in CLVMarkov Models

NASA Astrophysics Data System (ADS)

Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.

2018-04-01

A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.

On the Mathematical Consequences of Binning Spike Trains.

PubMed

Cessac, Bruno; Le Ny, Arnaud; Löcherbach, Eva

2017-01-01

We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process that is no longer Markov but is instead a variable-length Markov chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, that is, to tell "how good" our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future, and we discuss how binning may affect our conclusions on this ability. We finally comment on the possible consequences of binning in the detection of spurious phase transitions or in the detection of incorrect evidence of criticality.

Discrete time Markov chains (DTMC) susceptible infected susceptible (SIS) epidemic model with two pathogens in two patches

NASA Astrophysics Data System (ADS)

Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami

2017-06-01

The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Nonparametric model validations for hidden Markov models with applications in financial econometrics

PubMed Central

Zhao, Zhibiao

2011-01-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise. PMID:21750601

ASSIST: User's manual

NASA Technical Reports Server (NTRS)

Johnson, S. C.

1986-01-01

Semi-Markov models can be used to compute the reliability of virtually any fault-tolerant system. However, the process of delineating all of the states and transitions in a model of a complex system can be devastingly tedious and error-prone. The ASSIST program allows the user to describe the semi-Markov model in a high-level language. Instead of specifying the individual states of the model, the user specifies the rules governing the behavior of the system and these are used by ASSIST to automatically generate the model. The ASSIST program is described and illustrated by examples.

Transition records of stationary Markov chains.

PubMed

Naudts, Jan; Van der Straeten, Erik

2006-10-01

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk Assessment

NASA Technical Reports Server (NTRS)

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.

Statistical significance test for transition matrices of atmospheric Markov chains

NASA Technical Reports Server (NTRS)

Vautard, Robert; Mo, Kingtse C.; Ghil, Michael

1990-01-01

Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.

Analysis of single-molecule fluorescence spectroscopic data with a Markov-modulated Poisson process.

PubMed

Jäger, Mark; Kiel, Alexander; Herten, Dirk-Peter; Hamprecht, Fred A

2009-10-05

We present a photon-by-photon analysis framework for the evaluation of data from single-molecule fluorescence spectroscopy (SMFS) experiments using a Markov-modulated Poisson process (MMPP). A MMPP combines a discrete (and hidden) Markov process with an additional Poisson process reflecting the observation of individual photons. The algorithmic framework is used to automatically analyze the dynamics of the complex formation and dissociation of Cu2+ ions with the bidentate ligand 2,2'-bipyridine-4,4'dicarboxylic acid in aqueous media. The process of association and dissociation of Cu2+ ions is monitored with SMFS. The dcbpy-DNA conjugate can exist in two or more distinct states which influence the photon emission rates. The advantage of a photon-by-photon analysis is that no information is lost in preprocessing steps. Different model complexities are investigated in order to best describe the recorded data and to determine transition rates on a photon-by-photon basis. The main strength of the method is that it allows to detect intermittent phenomena which are masked by binning and that are difficult to find using correlation techniques when they are short-lived.

Towards automatic Markov reliability modeling of computer architectures

NASA Technical Reports Server (NTRS)

Liceaga, C. A.; Siewiorek, D. P.

1986-01-01

The analysis and evaluation of reliability measures using time-varying Markov models is required for Processor-Memory-Switch (PMS) structures that have competing processes such as standby redundancy and repair, or renewal processes such as transient or intermittent faults. The task of generating these models is tedious and prone to human error due to the large number of states and transitions involved in any reasonable system. Therefore model formulation is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model formulation. This paper presents an overview of the Automated Reliability Modeling (ARM) program, under development at NASA Langley Research Center. ARM will accept as input a description of the PMS interconnection graph, the behavior of the PMS components, the fault-tolerant strategies, and the operational requirements. The output of ARM will be the reliability of availability Markov model formulated for direct use by evaluation programs. The advantages of such an approach are (a) utility to a large class of users, not necessarily expert in reliability analysis, and (b) a lower probability of human error in the computation.

Copula-based prediction of economic movements

NASA Astrophysics Data System (ADS)

García, J. E.; González-López, V. A.; Hirsh, I. D.

2016-06-01

In this paper we model the discretized returns of two paired time series BM&FBOVESPA Dividend Index and BM&FBOVESPA Public Utilities Index using multivariate Markov models. The discretization corresponds to three categories, high losses, high profits and the complementary periods of the series. In technical terms, the maximal memory that can be considered for a Markov model, can be derived from the size of the alphabet and dataset. The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain. In this case the size of the database is not large enough for a consistent estimation of the model. We apply a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consist on obtaining a partition of the state space which is constructed from a combination, of the partitions corresponding to the two marginal processes and the partition corresponding to the multivariate Markov chain. In order to estimate the transition probabilities, all the partitions are linked using a copula. In our application this strategy provides a significant improvement in the movement predictions.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Building Simple Hidden Markov Models. Classroom Notes

ERIC Educational Resources Information Center

Ching, Wai-Ki; Ng, Michael K.

2004-01-01

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

Constructing 1/ωα noise from reversible Markov chains

NASA Astrophysics Data System (ADS)

Erland, Sveinung; Greenwood, Priscilla E.

2007-09-01

This paper gives sufficient conditions for the output of 1/ωα noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/ωα condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/ω noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/ωα noise which also has a long memory.

Metastable Distributions of Markov Chains with Rare Transitions

NASA Astrophysics Data System (ADS)

Freidlin, M.; Koralov, L.

2017-06-01

In this paper we consider Markov chains X^\\varepsilon _t with transition rates that depend on a small parameter \\varepsilon . We are interested in the long time behavior of X^\\varepsilon _t at various \\varepsilon -dependent time scales t = t(\\varepsilon ). The asymptotic behavior depends on how the point (1/\\varepsilon , t(\\varepsilon )) approaches infinity. We introduce a general notion of complete asymptotic regularity (a certain asymptotic relation between the ratios of transition rates), which ensures the existence of the metastable distribution for each initial point and a given time scale t(\\varepsilon ). The technique of i-graphs allows one to describe the metastable distribution explicitly. The result may be viewed as a generalization of the ergodic theorem to the case of parameter-dependent Markov chains.

Quantum Markov chains

NASA Astrophysics Data System (ADS)

Gudder, Stanley

2008-07-01

A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum operation. A quantum Markov chain is defined to be a pair (G,E) where G is a directed graph and E =[Eij] is a TOM whose entry Eij labels the edge from vertex j to vertex i. We think of the vertices of G as sites that a quantum system can occupy and Eij is the transition operation from site j to site i in one time step. The discrete dynamics of the system is obtained by iterating the TOM E. We next consider a special type of TOM called a transition effect matrix. In this case, there are two types of dynamics, a state dynamics and an operator dynamics. Although these two types are not identical, they are statistically equivalent. We next give examples that illustrate various properties of quantum Markov chains. We conclude by showing that our formalism generalizes the usual framework for quantum random walks.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Milestoning with coarse memory

NASA Astrophysics Data System (ADS)

Hawk, Alexander T.

2013-04-01

Milestoning is a method used to calculate the kinetics of molecular processes occurring on timescales inaccessible to traditional molecular dynamics (MD) simulations. In the method, the phase space of the system is partitioned by milestones (hypersurfaces), trajectories are initialized on each milestone, and short MD simulations are performed to calculate transitions between neighboring milestones. Long trajectories of the system are then reconstructed with a semi-Markov process from the observed statistics of transition. The procedure is typically justified by the assumption that trajectories lose memory between crossing successive milestones. Here we present Milestoning with Coarse Memory (MCM), a generalization of Milestoning that relaxes the memory loss assumption of conventional Milestoning. In the method, milestones are defined and sample transitions are calculated in the standard Milestoning way. Then, after it is clear where trajectories sample milestones, the milestones are broken up into distinct neighborhoods (clusters), and each sample transition is associated with two clusters: the cluster containing the coordinates the trajectory was initialized in, and the cluster (on the terminal milestone) containing trajectory's final coordinates. Long trajectories of the system are then reconstructed with a semi-Markov process in an extended state space built from milestone and cluster indices. To test the method, we apply it to a process that is particularly ill suited for Milestoning: the dynamics of a polymer confined to a narrow cylinder. We show that Milestoning calculations of both the mean first passage time and the mean transit time of reversal—which occurs when the end-to-end vector reverses direction—are significantly improved when MCM is applied. Finally, we note the overhead of performing MCM on top of conventional Milestoning is negligible.

Generating probabilistic Boolean networks from a prescribed transition probability matrix.

PubMed

Ching, W-K; Chen, X; Tsing, N-K

2009-11-01

Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. This is an interesting inverse problem in network inference using steady-state data. The problem is important as most microarray data sets are assumed to be obtained from sampling the steady-state.

ASSIST user manual

NASA Technical Reports Server (NTRS)

Johnson, Sally C.; Boerschlein, David P.

1995-01-01

Semi-Markov models can be used to analyze the reliability of virtually any fault-tolerant system. However, the process of delineating all the states and transitions in a complex system model can be devastatingly tedious and error prone. The Abstract Semi-Markov Specification Interface to the SURE Tool (ASSIST) computer program allows the user to describe the semi-Markov model in a high-level language. Instead of listing the individual model states, the user specifies the rules governing the behavior of the system, and these are used to generate the model automatically. A few statements in the abstract language can describe a very large, complex model. Because no assumptions are made about the system being modeled, ASSIST can be used to generate models describing the behavior of any system. The ASSIST program and its input language are described and illustrated by examples.

Current recommendations on the estimation of transition probabilities in Markov cohort models for use in health care decision-making: a targeted literature review.

PubMed

Olariu, Elena; Cadwell, Kevin K; Hancock, Elizabeth; Trueman, David; Chevrou-Severac, Helene

2017-01-01

Although Markov cohort models represent one of the most common forms of decision-analytic models used in health care decision-making, correct implementation of such models requires reliable estimation of transition probabilities. This study sought to identify consensus statements or guidelines that detail how such transition probability matrices should be estimated. A literature review was performed to identify relevant publications in the following databases: Medline, Embase, the Cochrane Library, and PubMed. Electronic searches were supplemented by manual-searches of health technology assessment (HTA) websites in Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and the UK. One reviewer assessed studies for eligibility. Of the 1,931 citations identified in the electronic searches, no studies met the inclusion criteria for full-text review, and no guidelines on transition probabilities in Markov models were identified. Manual-searching of the websites of HTA agencies identified ten guidelines on economic evaluations (Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and UK). All identified guidelines provided general guidance on how to develop economic models, but none provided guidance on the calculation of transition probabilities. One relevant publication was identified following review of the reference lists of HTA agency guidelines: the International Society for Pharmacoeconomics and Outcomes Research taskforce guidance. This provided limited guidance on the use of rates and probabilities. There is limited formal guidance available on the estimation of transition probabilities for use in decision-analytic models. Given the increasing importance of cost-effectiveness analysis in the decision-making processes of HTA bodies and other medical decision-makers, there is a need for additional guidance to inform a more consistent approach to decision-analytic modeling. Further research should be done to develop more detailed guidelines on the estimation of transition probabilities.

A methodology for stochastic analysis of share prices as Markov chains with finite states.

PubMed

Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey

2014-01-01

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

Markov model of the loan portfolio dynamics considering influence of management and external economic factors

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana; Timofeeva, Galina

2016-12-01

Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors are macroeconomic indicators, such as inflation and unemployment rates, exchange rates, consumer price indices, etc. Changes in corrective actions adjust the intensity of transitions in the migration matrix. The mathematical model for forecasting the credit portfolio structure taking into account a cumulative impact of internal and external changes is obtained.

A network of conformational transitions in an unfolding process of HP-35 revealed by high-temperature MD simulation and a Markov state model

NASA Astrophysics Data System (ADS)

Shao, Dandan; Gao, Kaifu

2018-01-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 11175068 and 11474117) and the Self-determined Research Funds of CCNU from the Colleges Basic Research and Operation of MOE, China (Grant No. 230-20205170054).

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Effect of Parametric Dichotomic Markov Noise on the Properties of Chaotic Transitions in Dynamical Systems

NASA Astrophysics Data System (ADS)

Gac, J. M.; Żebrowski, J. J.

A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.

The spectral method and the central limit theorem for general Markov chains

NASA Astrophysics Data System (ADS)

Nagaev, S. V.

2017-12-01

We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

Maximally reliable Markov chains under energy constraints.

PubMed

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.

Integrated Thermal Response Modeling System For Hypersonic Entry Vehicles

NASA Technical Reports Server (NTRS)

Chen, Y.-K.; Milos, F. S.; Partridge, Harry (Technical Monitor)

2000-01-01

We describe all extension of the Markov decision process model in which a continuous time dimension is included ill the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Exact Solutions to Time-dependent Mdps

NASA Technical Reports Server (NTRS)

Boyan, Justin A.; Littman, Michael L.

2000-01-01

We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Saccade selection when reward probability is dynamically manipulated using Markov chains

PubMed Central

Lovejoy, Lee P.; Krauzlis, Richard J.

2012-01-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200–600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection. PMID:18330552

Saccade selection when reward probability is dynamically manipulated using Markov chains.

PubMed

Nummela, Samuel U; Lovejoy, Lee P; Krauzlis, Richard J

2008-05-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200-600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection.

Enhancement of Markov chain model by integrating exponential smoothing: A case study on Muslims marriage and divorce

NASA Astrophysics Data System (ADS)

Jamaluddin, Fadhilah; Rahim, Rahela Abdul

2015-12-01

Markov Chain has been introduced since the 1913 for the purpose of studying the flow of data for a consecutive number of years of the data and also forecasting. The important feature in Markov Chain is obtaining the accurate Transition Probability Matrix (TPM). However to obtain the suitable TPM is hard especially in involving long-term modeling due to unavailability of data. This paper aims to enhance the classical Markov Chain by introducing Exponential Smoothing technique in developing the appropriate TPM.

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

Sieve estimation in a Markov illness-death process under dual censoring.

PubMed

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.

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

PubMed Central

Crawford, Forrest W.; Suchard, Marc A.

2011-01-01

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λn and a particle dies with instantaneous rate μn. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics. PMID:21984359

[Succession caused by beaver (Castor fiber L.) life activity: I. What is learnt from the calibration of a simple Markov model].

PubMed

Logofet, D O; Evstigneev, O I; Aleĭnikov, A A; Morozova, A O

2014-01-01

A homogeneous Markov chain of three aggregated states "pond--swamp--wood" is proposed as a model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity in a forest biogeocoenosis. To calibrate the chain transition matrix, the data have appeared sufficient that were gained from field studies undertaken in "Bryanskii Les" Reserve in the years of 2002-2008. Major outcomes of the calibrated model ensue from the formulae of finite homogeneous Markov chain theory: the stationary probability distribution of states, thematrix (T) of mean first passage times, and the mean durations (M(j)) of succession stages. The former illustrates the distribution of relative areas under succession stages if the current trends and transition rates of succession are conserved in the long-term--it has appeared close to the observed distribution. Matrix T provides for quantitative characteristics of the cyclic process, specifying the ranges the experts proposed for the duration of stages in the conceptual scheme of succession. The calculated values of M(j) detect potential discrepancies between empirical data, the expert knowledge that summarizes the data, and the postulates accepted in the mathematical model. The calculated M2 value falls outside the expert range, which gives a reason to doubt the validity of expert estimation proposed, the aggregation mode chosen for chain states, or/and the accuracy-of data available, i.e., to draw certain "lessons" from partially successful calibration. Refusal to postulate the time homogeneity or the Markov property of the chain is also discussed among possible ways to improve the model.

Sanov and central limit theorems for output statistics of quantum Markov chains

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

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

A compositional framework for Markov processes

NASA Astrophysics Data System (ADS)

Baez, John C.; Fong, Brendan; Pollard, Blake S.

2016-03-01

We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.

Projection of postgraduate students flow with a smoothing matrix transition diagram of Markov chain

NASA Astrophysics Data System (ADS)

Rahim, Rahela; Ibrahim, Haslinda; Adnan, Farah Adibah

2013-04-01

This paper presents a case study of modeling postgraduate students flow at the College of Art and Sciences, Universiti Utara Malaysia. First, full time postgraduate students and the semester they were in are identified. Then administrative data were used to estimate the transitions between these semesters for the year 2001-2005 periods. Markov chain model is developed to calculate the -5 and -10 years projection of postgraduate students flow at the college. The optimization question addressed in this study is 'Which transitions would sustain the desired structure in the dynamic situation such as trend towards graduation?' The smoothed transition probabilities are proposed to estimate the transition probabilities matrix of 16 × 16. The results shows that using smoothed transition probabilities, the projection number of postgraduate students enrolled in the respective semesters are closer to actual than using the conventional steady states transition probabilities.

A Markov State-based Quantitative Kinetic Model of Sodium Release from the Dopamine Transporter

NASA Astrophysics Data System (ADS)

Razavi, Asghar M.; Khelashvili, George; Weinstein, Harel

2017-01-01

The dopamine transporter (DAT) belongs to the neurotransmitter:sodium symporter (NSS) family of membrane proteins that are responsible for reuptake of neurotransmitters from the synaptic cleft to terminate a neuronal signal and enable subsequent neurotransmitter release from the presynaptic neuron. The release of one sodium ion from the crystallographically determined sodium binding site Na2 had been identified as an initial step in the transport cycle which prepares the transporter for substrate translocation by stabilizing an inward-open conformation. We have constructed Markov State Models (MSMs) from extensive molecular dynamics simulations of human DAT (hDAT) to explore the mechanism of this sodium release. Our results quantify the release process triggered by hydration of the Na2 site that occurs concomitantly with a conformational transition from an outward-facing to an inward-facing state of the transporter. The kinetics of the release process are computed from the MSM, and transition path theory is used to identify the most probable sodium release pathways. An intermediate state is discovered on the sodium release pathway, and the results reveal the importance of various modes of interaction of the N-terminus of hDAT in controlling the pathways of release.

Transition probabilities of health states for workers in Malaysia using a Markov chain model

NASA Astrophysics Data System (ADS)

Samsuddin, Shamshimah; Ismail, Noriszura

2017-04-01

The aim of our study is to estimate the transition probabilities of health states for workers in Malaysia who contribute to the Employment Injury Scheme under the Social Security Organization Malaysia using the Markov chain model. Our study uses four states of health (active, temporary disability, permanent disability and death) based on the data collected from the longitudinal studies of workers in Malaysia for 5 years. The transition probabilities vary by health state, age and gender. The results show that men employees are more likely to have higher transition probabilities to any health state compared to women employees. The transition probabilities can be used to predict the future health of workers in terms of a function of current age, gender and health state.

[Development of Markov models for economics evaluation of strategies on hepatitis B vaccination and population-based antiviral treatment in China].

PubMed

Yang, P C; Zhang, S X; Sun, P P; Cai, Y L; Lin, Y; Zou, Y H

2017-07-10

Objective: To construct the Markov models to reflect the reality of prevention and treatment interventions against hepatitis B virus (HBV) infection, simulate the natural history of HBV infection in different age groups and provide evidence for the economics evaluations of hepatitis B vaccination and population-based antiviral treatment in China. Methods: According to the theory and techniques of Markov chain, the Markov models of Chinese HBV epidemic were developed based on the national data and related literature both at home and abroad, including the settings of Markov model states, allowable transitions and initial and transition probabilities. The model construction, operation and verification were conducted by using software TreeAge Pro 2015. Results: Several types of Markov models were constructed to describe the disease progression of HBV infection in neonatal period, perinatal period or adulthood, the progression of chronic hepatitis B after antiviral therapy, hepatitis B prevention and control in adults, chronic hepatitis B antiviral treatment and the natural progression of chronic hepatitis B in general population. The model for the newborn was fundamental which included ten states, i.e . susceptiblity to HBV, HBsAg clearance, immune tolerance, immune clearance, low replication, HBeAg negative CHB, compensated cirrhosis, decompensated cirrhosis, hepatocellular carcinoma (HCC) and death. The susceptible state to HBV was excluded in the perinatal period model, and the immune tolerance state was excluded in the adulthood model. The model for general population only included two states, survive and death. Among the 5 types of models, there were 9 initial states assigned with initial probabilities, and 27 states for transition probabilities. The results of model verifications showed that the probability curves were basically consistent with the situation of HBV epidemic in China. Conclusion: The Markov models developed can be used in economics evaluation of hepatitis B vaccination and treatment for the elimination of HBV infection in China though the structures and parameters in the model have uncertainty with dynamic natures.

Filtering Using Nonlinear Expectations

DTIC Science & Technology

2016-04-16

gives a solution to estimating a Markov chain observed in Gaussian noise when the variance of the noise is unkown. This paper is accepted for the IEEE...Optimization, an A* journal. A short third paper discusses how to estimate a change in the transition dynamics of a noisily observed Markov chain ...The change point time is hidden in a hidden Markov chain , so a second level of discovery is involved. This paper is accepted for Communications in

Markov chain model for demersal fish catch analysis in Indonesia

NASA Astrophysics Data System (ADS)

Firdaniza; Gusriani, N.

2018-03-01

As an archipelagic country, Indonesia has considerable potential fishery resources. One of the fish resources that has high economic value is demersal fish. Demersal fish is a fish with a habitat in the muddy seabed. Demersal fish scattered throughout the Indonesian seas. Demersal fish production in each Indonesia’s Fisheries Management Area (FMA) varies each year. In this paper we have discussed the Markov chain model for demersal fish yield analysis throughout all Indonesia’s Fisheries Management Area. Data of demersal fish catch in every FMA in 2005-2014 was obtained from Directorate of Capture Fisheries. From this data a transition probability matrix is determined by the number of transitions from the catch that lie below the median or above the median. The Markov chain model of demersal fish catch data was an ergodic Markov chain model, so that the limiting probability of the Markov chain model can be determined. The predictive value of demersal fishing yields was obtained by calculating the combination of limiting probability with average catch results below the median and above the median. The results showed that for 2018 and long-term demersal fishing results in most of FMA were below the median value.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

NASA Astrophysics Data System (ADS)

Li, Zhiqiang; Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-04-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling

NASA Astrophysics Data System (ADS)

Plattner, Nuria; Doerr, Stefan; de Fabritiis, Gianni; Noé, Frank

2017-10-01

Protein-protein association is fundamental to many life processes. However, a microscopic model describing the structures and kinetics during association and dissociation is lacking on account of the long lifetimes of associated states, which have prevented efficient sampling by direct molecular dynamics (MD) simulations. Here we demonstrate protein-protein association and dissociation in atomistic resolution for the ribonuclease barnase and its inhibitor barstar by combining adaptive high-throughput MD simulations and hidden Markov modelling. The model reveals experimentally consistent intermediate structures, energetics and kinetics on timescales from microseconds to hours. A variety of flexibly attached intermediates and misbound states funnel down to a transition state and a native basin consisting of the loosely bound near-native state and the tightly bound crystallographic state. These results offer a deeper level of insight into macromolecular recognition and our approach opens the door for understanding and manipulating a wide range of macromolecular association processes.

Copula-based analysis of rhythm

NASA Astrophysics Data System (ADS)

García, J. E.; González-López, V. A.; Viola, M. L. Lanfredi

2016-06-01

In this paper we establish stochastic profiles of the rhythm for three languages: English, Japanese and Spanish. We model the increase or decrease of the acoustical energy, collected into three bands coming from the acoustic signal. The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain. In this case the size of the database is not large enough for a consistent estimation of the model. We apply a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consist on obtaining a partition of the state space which is constructed from a combination of the partitions corresponding to the three marginal processes, one for each band of energy, and the partition coming from to the multivariate Markov chain. Then, all the partitions are linked using a copula, in order to estimate the transition probabilities.

From empirical data to time-inhomogeneous continuous Markov processes.

PubMed

Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G

2016-03-01

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

Markov State Models of gene regulatory networks.

PubMed

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

2017-02-06

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

Stability analysis for virus spreading in complex networks with quarantine and non-homogeneous transition rates

NASA Astrophysics Data System (ADS)

Alarcon-Ramos, L. A.; Schaum, A.; Rodríguez Lucatero, C.; Bernal Jaquez, R.

2014-03-01

Virus propagations in complex networks have been studied in the framework of discrete time Markov process dynamical systems. These studies have been carried out under the assumption of homogeneous transition rates, yielding conditions for virus extinction in terms of the transition probabilities and the largest eigenvalue of the connectivity matrix. Nevertheless the assumption of homogeneous rates is rather restrictive. In the present study we consider non-homogeneous transition rates, assigned according to a uniform distribution, with susceptible, infected and quarantine states, thus generalizing the previous studies. A remarkable result of this analysis is that the extinction depends on the weakest element in the network. Simulation results are presented for large free-scale networks, that corroborate our theoretical findings.

A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer

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

Liu, Yifang; Lee, Chi-Guhn; Chan, Timothy C. Y., E-mail: tcychan@mie.utoronto.ca

2014-02-15

Purpose: To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy. Methods: The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxelsmore » on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity. Results: The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict. Conclusions: By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.« less

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Document Ranking Based upon Markov Chains.

ERIC Educational Resources Information Center

Danilowicz, Czeslaw; Balinski, Jaroslaw

2001-01-01

Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)

Estimating parameters of hidden Markov models based on marked individuals: use of robust design data

USGS Publications Warehouse

Kendall, William L.; White, Gary C.; Hines, James E.; Langtimm, Catherine A.; Yoshizaki, Jun

2012-01-01

Development and use of multistate mark-recapture models, which provide estimates of parameters of Markov processes in the face of imperfect detection, have become common over the last twenty years. Recently, estimating parameters of hidden Markov models, where the state of an individual can be uncertain even when it is detected, has received attention. Previous work has shown that ignoring state uncertainty biases estimates of survival and state transition probabilities, thereby reducing the power to detect effects. Efforts to adjust for state uncertainty have included special cases and a general framework for a single sample per period of interest. We provide a flexible framework for adjusting for state uncertainty in multistate models, while utilizing multiple sampling occasions per period of interest to increase precision and remove parameter redundancy. These models also produce direct estimates of state structure for each primary period, even for the case where there is just one sampling occasion. We apply our model to expected value data, and to data from a study of Florida manatees, to provide examples of the improvement in precision due to secondary capture occasions. We also provide user-friendly software to implement these models. This general framework could also be used by practitioners to consider constrained models of particular interest, or model the relationship between within-primary period parameters (e.g., state structure) and between-primary period parameters (e.g., state transition probabilities).

Forecasting client transitions in British Columbia's Long-Term Care Program.

PubMed Central

Lane, D; Uyeno, D; Stark, A; Gutman, G; McCashin, B

1987-01-01

This article presents a model for the annual transitions of clients through various home and facility placements in a long-term care program. The model, an application of Markov chain analysis, is developed, tested, and applied to over 9,000 clients (N = 9,483) in British Columbia's Long Term Care Program (LTC) over the period 1978-1983. Results show that the model gives accurate forecasts of the progress of groups of clients from state to state in the long-term care system from time of admission until eventual death. Statistical methods are used to test the modeling hypothesis that clients' year-over-year transitions occur in constant proportions from state to state within the long-term care system. Tests are carried out by examining actual year-over-year transitions of each year's new admission cohort (1978-1983). Various subsets of the available data are analyzed and, after accounting for clear differences among annual cohorts, the most acceptable model of the actual client transition data occurred when clients were separated into male and female groups, i.e., the transition behavior of each group is describable by a different Markov model. To validate the model, we develop model estimates for the numbers of existing clients in each state of the long-term care system for the period (1981-1983) for which actual data are available. When these estimates are compared with the actual data, total weighted absolute deviations do not exceed 10 percent of actuals. Finally, we use the properties of the Markov chain probability transition matrix and simulation methods to develop three-year forecasts with prediction intervals for the distribution of the existing total clients into each state of the system. The tests, forecasts, and Markov model supplemental information are contained in a mechanized procedure suitable for a microcomputer. The procedure provides a powerful, efficient tool for decision makers planning facilities and services in response to the needs of long-term care clients. PMID:3121537

Inferring the parameters of a Markov process from snapshots of the steady state

NASA Astrophysics Data System (ADS)

Dettmer, Simon L.; Berg, Johannes

2018-02-01

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous configurations. We apply the method to non-equilibrium models from statistical physics and theoretical biology, including the asymmetric simple exclusion process (ASEP), the kinetic Ising model, and replicator dynamics.

Improving Markov Chain Models for Road Profiles Simulation via Definition of States

DTIC Science & Technology

2012-04-01

wavelet transform in pavement profile analysis," Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, vol. 47, no. 4...34Estimating Markov Transition Probabilities from Micro -Unit Data," Journal of the Royal Statistical Society. Series C (Applied Statistics), pp. 355-371

The Ground-Based Transmission Spectrum of HD 189733b as Generated Through Multiple Broadband Filter Observations

NASA Astrophysics Data System (ADS)

Kasper, David; Cole, Jackson L.; Gardner, Cristilyn N.; Garver, Bethany; Jarka, Kyla L.; Kar, Aman; McGough, Aylin M.; PeQueen, David J.; Rivera, Daniel Ivan; Jang-Condell, Hannah; Kobulnicky, Henry A.; Dale, Daniel A.

2018-06-01

We present new multi-broadband transit photometry of HD 189733b observed with the Wyoming Infrared Observatory. With an ensemble of Sloan filter observations across multiple transits we have created an ultra-low resolution transmission spectrum to discern the nature of the exoplanet atmosphere. This data set exemplifies the capabilities of the 2.3 m observatory. The analysis was performed with a Markov-Chain Monte-Carlo method assisted by a Gaussian-processes regression model. These observations were taken as part of the University of Wyoming's 2017 Research Experience for Undergraduates (REU) and represent one of multiple hot Jupiter exoplanet targets for which we have transit event observations in multiple broadband filters.

Relaxation mode analysis and Markov state relaxation mode analysis for chignolin in aqueous solution near a transition temperature

NASA Astrophysics Data System (ADS)

Mitsutake, Ayori; Takano, Hiroshi

2015-09-01

It is important to extract reaction coordinates or order parameters from protein simulations in order to investigate the local minimum-energy states and the transitions between them. The most popular method to obtain such data is principal component analysis, which extracts modes of large conformational fluctuations around an average structure. We recently applied relaxation mode analysis for protein systems, which approximately estimates the slow relaxation modes and times from a simulation and enables investigations of the dynamic properties underlying the structural fluctuations of proteins. In this study, we apply this relaxation mode analysis to extract reaction coordinates for a system in which there are large conformational changes such as those commonly observed in protein folding/unfolding. We performed a 750-ns simulation of chignolin protein near its folding transition temperature and observed many transitions between the most stable, misfolded, intermediate, and unfolded states. We then applied principal component analysis and relaxation mode analysis to the system. In the relaxation mode analysis, we could automatically extract good reaction coordinates. The free-energy surfaces provide a clearer understanding of the transitions not only between local minimum-energy states but also between the folded and unfolded states, even though the simulation involved large conformational changes. Moreover, we propose a new analysis method called Markov state relaxation mode analysis. We applied the new method to states with slow relaxation, which are defined by the free-energy surface obtained in the relaxation mode analysis. Finally, the relaxation times of the states obtained with a simple Markov state model and the proposed Markov state relaxation mode analysis are compared and discussed.

Diagonal couplings of quantum Markov chains

NASA Astrophysics Data System (ADS)

Kümmerer, Burkhard; Schwieger, Kay

2016-05-01

In this paper we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

Open Markov Processes and Reaction Networks

ERIC Educational Resources Information Center

Swistock Pollard, Blake Stephen

2017-01-01

We begin by defining the concept of "open" Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain "boundary" states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow…

Identification of the protein folding transition state from molecular dynamics trajectories

NASA Astrophysics Data System (ADS)

Muff, S.; Caflisch, A.

2009-03-01

The rate of protein folding is governed by the transition state so that a detailed characterization of its structure is essential for understanding the folding process. In vitro experiments have provided a coarse-grained description of the folding transition state ensemble (TSE) of small proteins. Atomistic details could be obtained by molecular dynamics (MD) simulations but it is not straightforward to extract the TSE directly from the MD trajectories, even for small peptides. Here, the structures in the TSE are isolated by the cut-based free-energy profile (cFEP) using the network whose nodes and links are configurations sampled by MD and direct transitions among them, respectively. The cFEP is a barrier-preserving projection that does not require arbitrarily chosen progress variables. First, a simple two-dimensional free-energy surface is used to illustrate the successful determination of the TSE by the cFEP approach and to explain the difficulty in defining boundary conditions of the Markov state model for an entropically stabilized free-energy minimum. The cFEP is then used to extract the TSE of a β-sheet peptide with a complex free-energy surface containing multiple basins and an entropic region. In contrast, Markov state models with boundary conditions defined by projected variables and conventional histogram-based free-energy profiles are not able to identify the TSE of the β-sheet peptide.

Controlling protein molecular dynamics: How to accelerate folding while preserving the native state

NASA Astrophysics Data System (ADS)

Jensen, Christian H.; Nerukh, Dmitry; Glen, Robert C.

2008-12-01

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1μs. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Free energies from dynamic weighted histogram analysis using unbiased Markov state model.

PubMed

Rosta, Edina; Hummer, Gerhard

2015-01-13

The weighted histogram analysis method (WHAM) is widely used to obtain accurate free energies from biased molecular simulations. However, WHAM free energies can exhibit significant errors if some of the biasing windows are not fully equilibrated. To account for the lack of full equilibration, we develop the dynamic histogram analysis method (DHAM). DHAM uses a global Markov state model to obtain the free energy along the reaction coordinate. A maximum likelihood estimate of the Markov transition matrix is constructed by joint unbiasing of the transition counts from multiple umbrella-sampling simulations along discretized reaction coordinates. The free energy profile is the stationary distribution of the resulting Markov matrix. For this matrix, we derive an explicit approximation that does not require the usual iterative solution of WHAM. We apply DHAM to model systems, a chemical reaction in water treated using quantum-mechanics/molecular-mechanics (QM/MM) simulations, and the Na(+) ion passage through the membrane-embedded ion channel GLIC. We find that DHAM gives accurate free energies even in cases where WHAM fails. In addition, DHAM provides kinetic information, which we here use to assess the extent of convergence in each of the simulation windows. DHAM may also prove useful in the construction of Markov state models from biased simulations in phase-space regions with otherwise low population.

Information distribution in distributed microprocessor based flight control systems

NASA Technical Reports Server (NTRS)

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

1977-01-01

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

Nonlinear Markov Control Processes and Games

DTIC Science & Technology

2012-11-15

the analysis of a new class of stochastic games , nonlinear Markov games , as they arise as a ( competitive ) controlled version of nonlinear Markov... competitive interests) a nonlinear Markov game that we are investigating. I 0. :::tUt::JJt:.l.. I I t:t11VI;:, nonlinear Markov game , nonlinear Markov...corresponding stochastic game Γ+(T, h). In a slightly different setting one can assume that changes in a competitive control process occur as a

Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis.

PubMed

Chiba, Tomoaki; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru

2017-01-01

In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group's sales beat GM's sales, which is a reasonable scenario.

Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis

PubMed Central

Chiba, Tomoaki; Akaho, Shotaro; Murata, Noboru

2017-01-01

In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group’s sales beat GM’s sales, which is a reasonable scenario. PMID:28076383

Real-time network security situation visualization and threat assessment based on semi-Markov process

NASA Astrophysics Data System (ADS)

Chen, Junhua

2013-03-01

To cope with a large amount of data in current sensed environments, decision aid tools should provide their understanding of situations in a time-efficient manner, so there is an increasing need for real-time network security situation awareness and threat assessment. In this study, the state transition model of vulnerability in the network based on semi-Markov process is proposed at first. Once events are triggered by an attacker's action or system response, the current states of the vulnerabilities are known. Then we calculate the transition probabilities of the vulnerability from the current state to security failure state. Furthermore in order to improve accuracy of our algorithms, we adjust the probabilities that they exploit the vulnerability according to the attacker's skill level. In the light of the preconditions and post-conditions of vulnerabilities in the network, attack graph is built to visualize security situation in real time. Subsequently, we predict attack path, recognize attack intention and estimate the impact through analysis of attack graph. These help administrators to insight into intrusion steps, determine security state and assess threat. Finally testing in a network shows that this method is reasonable and feasible, and can undertake tremendous analysis task to facilitate administrators' work.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

NASA Astrophysics Data System (ADS)

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-09-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

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

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlapmore » with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.« less

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

PubMed Central

Nedialkova, Lilia V.; Amat, Miguel A.; Kevrekidis, Ioannis G.; Hummer, Gerhard

2014-01-01

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space. PMID:25240340

The explicit form of the rate function for semi-Markov processes and its contractions

NASA Astrophysics Data System (ADS)

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.

Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

PubMed Central

Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

2018-01-01

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit. PMID:29765629

Modeling of dialogue regimes of distance robot control

NASA Astrophysics Data System (ADS)

Larkin, E. V.; Privalov, A. N.

2017-02-01

Process of distance control of mobile robots is investigated. Petri-Markov net for modeling of dialogue regime is worked out. It is shown, that sequence of operations of next subjects: a human operator, a dialogue computer and an onboard computer may be simulated with use the theory of semi-Markov processes. From the semi-Markov process of the general form Markov process was obtained, which includes only states of transaction generation. It is shown, that a real transaction flow is the result of «concurrency» in states of Markov process. Iteration procedure for evaluation of transaction flow parameters, which takes into account effect of «concurrency», is proposed.

Analysis and design of a second-order digital phase-locked loop

NASA Technical Reports Server (NTRS)

Blasche, P. R.

1979-01-01

A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.

Tracking Skill Acquisition with Cognitive Diagnosis Models: A Higher-Order, Hidden Markov Model with Covariates

ERIC Educational Resources Information Center

Wang, Shiyu; Yang, Yan; Culpepper, Steven Andrew; Douglas, Jeffrey A.

2018-01-01

A family of learning models that integrates a cognitive diagnostic model and a higher-order, hidden Markov model in one framework is proposed. This new framework includes covariates to model skill transition in the learning environment. A Bayesian formulation is adopted to estimate parameters from a learning model. The developed methods are…

Kinetics from Replica Exchange Molecular Dynamics Simulations.

PubMed

Stelzl, Lukas S; Hummer, Gerhard

2017-08-08

Transitions between metastable states govern many fundamental processes in physics, chemistry and biology, from nucleation events in phase transitions to the folding of proteins. The free energy surfaces underlying these processes can be obtained from simulations using enhanced sampling methods. However, their altered dynamics makes kinetic and mechanistic information difficult or impossible to extract. Here, we show that, with replica exchange molecular dynamics (REMD), one can not only sample equilibrium properties but also extract kinetic information. For systems that strictly obey first-order kinetics, the procedure to extract rates is rigorous. For actual molecular systems whose long-time dynamics are captured by kinetic rate models, accurate rate coefficients can be determined from the statistics of the transitions between the metastable states at each replica temperature. We demonstrate the practical applicability of the procedure by constructing master equation (Markov state) models of peptide and RNA folding from REMD simulations.

Localization Transition Induced by Learning in Random Searches

NASA Astrophysics Data System (ADS)

Falcón-Cortés, Andrea; Boyer, Denis; Giuggioli, Luca; Majumdar, Satya N.

2017-10-01

We solve an adaptive search model where a random walker or Lévy flight stochastically resets to previously visited sites on a d -dimensional lattice containing one trapping site. Because of reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which nondiffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker's return probability in the memoryless case. The transition belongs to the same class as the self-consistent theory of Anderson localization. These results show that similarly to many living organisms and unlike the well-studied Markovian walks, non-Markov movement processes can allow agents to learn about their environment and promise to bring adaptive solutions in search tasks.

A Self-Organizing Incremental Spatiotemporal Associative Memory Networks Model for Problems with Hidden State

PubMed Central

2016-01-01

Identifying the hidden state is important for solving problems with hidden state. We prove any deterministic partially observable Markov decision processes (POMDP) can be represented by a minimal, looping hidden state transition model and propose a heuristic state transition model constructing algorithm. A new spatiotemporal associative memory network (STAMN) is proposed to realize the minimal, looping hidden state transition model. STAMN utilizes the neuroactivity decay to realize the short-term memory, connection weights between different nodes to represent long-term memory, presynaptic potentials, and synchronized activation mechanism to complete identifying and recalling simultaneously. Finally, we give the empirical illustrations of the STAMN and compare the performance of the STAMN model with that of other methods. PMID:27891146

Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

PubMed

Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li

2018-02-01

In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.

Statistical learning of music- and language-like sequences and tolerance for spectral shifts.

PubMed

Daikoku, Tatsuya; Yatomi, Yutaka; Yumoto, Masato

2015-02-01

In our previous study (Daikoku, Yatomi, & Yumoto, 2014), we demonstrated that the N1m response could be a marker for the statistical learning process of pitch sequence, in which each tone was ordered by a Markov stochastic model. The aim of the present study was to investigate how the statistical learning of music- and language-like auditory sequences is reflected in the N1m responses based on the assumption that both language and music share domain generality. By using vowel sounds generated by a formant synthesizer, we devised music- and language-like auditory sequences in which higher-ordered transitional rules were embedded according to a Markov stochastic model by controlling fundamental (F0) and/or formant frequencies (F1-F2). In each sequence, F0 and/or F1-F2 were spectrally shifted in the last one-third of the tone sequence. Neuromagnetic responses to the tone sequences were recorded from 14 right-handed normal volunteers. In the music- and language-like sequences with pitch change, the N1m responses to the tones that appeared with higher transitional probability were significantly decreased compared with the responses to the tones that appeared with lower transitional probability within the first two-thirds of each sequence. Moreover, the amplitude difference was even retained within the last one-third of the sequence after the spectral shifts. However, in the language-like sequence without pitch change, no significant difference could be detected. The pitch change may facilitate the statistical learning in language and music. Statistically acquired knowledge may be appropriated to process altered auditory sequences with spectral shifts. The relative processing of spectral sequences may be a domain-general auditory mechanism that is innate to humans. Copyright © 2014 Elsevier Inc. All rights reserved.

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

[Succession caused by beaver (Castor fiber L.) life activity: II. A refined Markov model].

PubMed

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 has not eliminated all the contradictions between the model results and expert knowledge, which suggests a further model development towards a "logically inhomogeneous" version or/and refusal to postulate the Markov property in the conceptual scheme of succession.

A reward semi-Markov process with memory for wind speed modeling

NASA Astrophysics Data System (ADS)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-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.

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

NASA Astrophysics Data System (ADS)

Sinitskiy, Anton V.; Pande, Vijay S.

2018-01-01

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit time scale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule has never been formally proved. In this work, we present analytical results for the slowest time scale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit time scale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit time scale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit time scale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest time scales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

On a Result for Finite Markov Chains

ERIC Educational Resources Information Center

Kulathinal, Sangita; Ghosh, Lagnojita

2006-01-01

In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

A nonstationary Markov transition model for computing the relative risk of dementia before death

PubMed Central

Yu, Lei; Griffith, William S.; Tyas, Suzanne L.; Snowdon, David A.; Kryscio, Richard J.

2010-01-01

This paper investigates the long-term behavior of the k-step transition probability matrix for a nonstationary discrete time Markov chain in the context of modeling transitions from intact cognition to dementia with mild cognitive impairment (MCI) and global impairment (GI) as intervening cognitive states. The authors derive formulas for the following absorption statistics: (1) the relative risk of absorption between competing absorbing states, and (2) the mean and variance of the number of visits among the transient states before absorption. Since absorption is not guaranteed, sufficient conditions are discussed to ensure that the substochastic matrix associated with transitions among transient states converges to zero in limit. Results are illustrated with an application to the Nun Study, a cohort of 678 participants, 75 to 107 years of age, followed longitudinally with up to ten cognitive assessments over a fifteen-year period. PMID:20087848

Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

NASA Astrophysics Data System (ADS)

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.

Classification of customer lifetime value models using Markov chain

NASA Astrophysics Data System (ADS)

Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi

2017-10-01

A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.

Semi-Markov adjunction to the Computer-Aided Markov Evaluator (CAME)

NASA Technical Reports Server (NTRS)

Rosch, Gene; Hutchins, Monica A.; Leong, Frank J.; Babcock, Philip S., IV

1988-01-01

The rule-based Computer-Aided Markov Evaluator (CAME) program was expanded in its ability to incorporate the effect of fault-handling processes into the construction of a reliability model. The fault-handling processes are modeled as semi-Markov events and CAME constructs and appropriate semi-Markov model. To solve the model, the program outputs it in a form which can be directly solved with the Semi-Markov Unreliability Range Evaluator (SURE) program. As a means of evaluating the alterations made to the CAME program, the program is used to model the reliability of portions of the Integrated Airframe/Propulsion Control System Architecture (IAPSA 2) reference configuration. The reliability predictions are compared with a previous analysis. The results bear out the feasibility of utilizing CAME to generate appropriate semi-Markov models to model fault-handling processes.

Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

NASA Astrophysics Data System (ADS)

Yao, Deyin; Lu, Renquan; Xu, Yong; Ren, Hongru

2017-10-01

In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

Multistage Fuzzy Decision Making in Bilateral Negotiation with Finite Termination Times

NASA Astrophysics Data System (ADS)

Richter, Jan; Kowalczyk, Ryszard; Klusch, Matthias

In this paper we model the negotiation process as a multistage fuzzy decision problem where the agents preferences are represented by a fuzzy goal and fuzzy constraints. The opponent is represented by a fuzzy Markov decision process in the form of offer-response patterns which enables utilization of limited and uncertain information, e.g. the characteristics of the concession behaviour. We show that we can obtain adaptive negotiation strategies by only using the negotiation threads of two past cases to create and update the fuzzy transition matrix. The experimental evaluation demonstrates that our approach is adaptive towards different negotiation behaviours and that the fuzzy representation of the preferences and the transition matrix allows for application in many scenarios where the available information, preferences and constraints are soft or imprecise.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

PubMed

Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter

2012-01-01

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

A coupled hidden Markov model for disease interactions

PubMed Central

Sherlock, Chris; Xifara, Tatiana; Telfer, Sandra; Begon, Mike

2013-01-01

To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis–Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites. PMID:24223436

Exploring sensitivity of a multistate occupancy model to inform management decisions

USGS Publications Warehouse

Green, A.W.; Bailey, L.L.; Nichols, J.D.

2011-01-01

Dynamic occupancy models are often used to investigate questions regarding the processes that influence patch occupancy and are prominent in the fields of population and community ecology and conservation biology. Recently, multistate occupancy models have been developed to investigate dynamic systems involving more than one occupied state, including reproductive states, relative abundance states and joint habitat-occupancy states. Here we investigate the sensitivities of the equilibrium-state distribution of multistate occupancy models to changes in transition rates. We develop equilibrium occupancy expressions and their associated sensitivity metrics for dynamic multistate occupancy models. To illustrate our approach, we use two examples that represent common multistate occupancy systems. The first example involves a three-state dynamic model involving occupied states with and without successful reproduction (California spotted owl Strix occidentalis occidentalis), and the second involves a novel way of using a multistate occupancy approach to accommodate second-order Markov processes (wood frog Lithobates sylvatica breeding and metamorphosis). In many ways, multistate sensitivity metrics behave in similar ways as standard occupancy sensitivities. When equilibrium occupancy rates are low, sensitivity to parameters related to colonisation is high, while sensitivity to persistence parameters is greater when equilibrium occupancy rates are high. Sensitivities can also provide guidance for managers when estimates of transition probabilities are not available. Synthesis and applications. Multistate models provide practitioners a flexible framework to define multiple, distinct occupied states and the ability to choose which state, or combination of states, is most relevant to questions and decisions about their own systems. In addition to standard multistate occupancy models, we provide an example of how a second-order Markov process can be modified to fit a multistate framework. Assuming the system is near equilibrium, our sensitivity analyses illustrate how to investigate the sensitivity of the system-specific equilibrium state(s) to changes in transition rates. Because management will typically act on these transition rates, sensitivity analyses can provide valuable information about the potential influence of different actions and when it may be prudent to shift the focus of management among the various transition rates. ?? 2011 The Authors. Journal of Applied Ecology ?? 2011 British Ecological Society.

Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems

NASA Astrophysics Data System (ADS)

Meng, Luming; Sheong, Fu Kit; Zeng, Xiangze; Zhu, Lizhe; Huang, Xuhui

2017-07-01

Constructing Markov state models from large-scale molecular dynamics simulation trajectories is a promising approach to dissect the kinetic mechanisms of complex chemical and biological processes. Combined with transition path theory, Markov state models can be applied to identify all pathways connecting any conformational states of interest. However, the identified pathways can be too complex to comprehend, especially for multi-body processes where numerous parallel pathways with comparable flux probability often coexist. Here, we have developed a path lumping method to group these parallel pathways into metastable path channels for analysis. We define the similarity between two pathways as the intercrossing flux between them and then apply the spectral clustering algorithm to lump these pathways into groups. We demonstrate the power of our method by applying it to two systems: a 2D-potential consisting of four metastable energy channels and the hydrophobic collapse process of two hydrophobic molecules. In both cases, our algorithm successfully reveals the metastable path channels. We expect this path lumping algorithm to be a promising tool for revealing unprecedented insights into the kinetic mechanisms of complex multi-body processes.

Distributed fault detection over sensor networks with Markovian switching topologies

NASA Astrophysics Data System (ADS)

Ge, Xiaohua; Han, Qing-Long

2014-05-01

This paper deals with the distributed fault detection for discrete-time Markov jump linear systems over sensor networks with Markovian switching topologies. The sensors are scatteredly deployed in the sensor field and the fault detectors are physically distributed via a communication network. The system dynamics changes and sensing topology variations are modeled by a discrete-time Markov chain with incomplete mode transition probabilities. Each of these sensor nodes firstly collects measurement outputs from its all underlying neighboring nodes, processes these data in accordance with the Markovian switching topologies, and then transmits the processed data to the remote fault detector node. Network-induced delays and accumulated data packet dropouts are incorporated in the data transmission between the sensor nodes and the distributed fault detector nodes through the communication network. To generate localized residual signals, mode-independent distributed fault detection filters are proposed. By means of the stochastic Lyapunov functional approach, the residual system performance analysis is carried out such that the overall residual system is stochastically stable and the error between each residual signal and the fault signal is made as small as possible. Furthermore, a sufficient condition on the existence of the mode-independent distributed fault detection filters is derived in the simultaneous presence of incomplete mode transition probabilities, Markovian switching topologies, network-induced delays, and accumulated data packed dropouts. Finally, a stirred-tank reactor system is given to show the effectiveness of the developed theoretical results.

Predicting landscape vegetation dynamics using state-and-transition simulation models

Treesearch

Colin J. Daniel; Leonardo Frid

2012-01-01

This paper outlines how state-and-transition simulation models (STSMs) can be used to project changes in vegetation over time across a landscape. STSMs are stochastic, empirical simulation models that use an adapted Markov chain approach to predict how vegetation will transition between states over time, typically in response to interactions between succession,...

Markov-modulated Markov chains and the covarion process of molecular evolution.

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Open Markov Processes and Reaction Networks

NASA Astrophysics Data System (ADS)

Swistock Pollard, Blake Stephen

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Modeling Driver Behavior near Intersections in Hidden Markov Model

PubMed Central

Li, Juan; He, Qinglian; Zhou, Hang; Guan, Yunlin; Dai, Wei

2016-01-01

Intersections are one of the major locations where safety is a big concern to drivers. Inappropriate driver behaviors in response to frequent changes when approaching intersections often lead to intersection-related crashes or collisions. Thus to better understand driver behaviors at intersections, especially in the dilemma zone, a Hidden Markov Model (HMM) is utilized in this study. With the discrete data processing, the observed dynamic data of vehicles are used for the inference of the Hidden Markov Model. The Baum-Welch (B-W) estimation algorithm is applied to calculate the vehicle state transition probability matrix and the observation probability matrix. When combined with the Forward algorithm, the most likely state of the driver can be obtained. Thus the model can be used to measure the stability and risk of driver behavior. It is found that drivers’ behaviors in the dilemma zone are of lower stability and higher risk compared with those in other regions around intersections. In addition to the B-W estimation algorithm, the Viterbi Algorithm is utilized to predict the potential dangers of vehicles. The results can be applied to driving assistance systems to warn drivers to avoid possible accidents. PMID:28009838

Oncology Modeling for Fun and Profit! Key Steps for Busy Analysts in Health Technology Assessment.

PubMed

Beca, Jaclyn; Husereau, Don; Chan, Kelvin K W; Hawkins, Neil; Hoch, Jeffrey S

2018-01-01

In evaluating new oncology medicines, two common modeling approaches are state transition (e.g., Markov and semi-Markov) and partitioned survival. Partitioned survival models have become more prominent in oncology health technology assessment processes in recent years. Our experience in conducting and evaluating models for economic evaluation has highlighted many important and practical pitfalls. As there is little guidance available on best practices for those who wish to conduct them, we provide guidance in the form of 'Key steps for busy analysts,' who may have very little time and require highly favorable results. Our guidance highlights the continued need for rigorous conduct and transparent reporting of economic evaluations regardless of the modeling approach taken, and the importance of modeling that better reflects reality, which includes better approaches to considering plausibility, estimating relative treatment effects, dealing with post-progression effects, and appropriate characterization of the uncertainty from modeling itself.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

NASA Astrophysics Data System (ADS)

Jensen, Christian H.; Nerukh, Dmitry; Glen, Robert C.

2008-03-01

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Stochastic modeling of sunshine number data

NASA Astrophysics Data System (ADS)

Brabec, Marek; Paulescu, Marius; Badescu, Viorel

2013-11-01

In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar Radiation Monitoring Station of the West University of Timisoara.

Stochastic modeling of sunshine number data

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

Brabec, Marek, E-mail: mbrabec@cs.cas.cz; Paulescu, Marius; Badescu, Viorel

2013-11-13

In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation ofmore » Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar Radiation Monitoring Station of the West University of Timisoara.« less

Markov Chain Models for Stochastic Behavior in Resonance Overlap Regions

NASA Astrophysics Data System (ADS)

McCarthy, Morgan; Quillen, Alice

2018-01-01

We aim to predict lifetimes of particles in chaotic zoneswhere resonances overlap. A continuous-time Markov chain model isconstructed using mean motion resonance libration timescales toestimate transition times between resonances. The model is applied todiffusion in the co-rotation region of a planet. For particles begunat low eccentricity, the model is effective for early diffusion, butnot at later time when particles experience close encounters to the planet.

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

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.

Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.

Finding exact constants in a Markov model of Zipfs law generation

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

2017-12-01

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

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

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

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

Cai, H.

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 ofmore » the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability).« less

Plant calendar pattern based on rainfall forecast and the probability of its success in Deli Serdang regency of Indonesia

NASA Astrophysics Data System (ADS)

Darnius, O.; Sitorus, S.

2018-03-01

The objective of this study was to determine the pattern of plant calendar of three types of crops; namely, palawija, rice, andbanana, based on rainfall in Deli Serdang Regency. In the first stage, we forecasted rainfall by using time series analysis, and obtained appropriate model of ARIMA (1,0,0) (1,1,1)12. Based on the forecast result, we designed a plant calendar pattern for the three types of plant. Furthermore, the probability of success in the plant types following the plant calendar pattern was calculated by using the Markov process by discretizing the continuous rainfall data into three categories; namely, Below Normal (BN), Normal (N), and Above Normal (AN) to form the probability transition matrix. Finally, the combination of rainfall forecasting models and the Markov process were used to determine the pattern of cropping calendars and the probability of success in the three crops. This research used rainfall data of Deli Serdang Regency taken from the office of BMKG (Meteorologist Climatology and Geophysics Agency), Sampali Medan, Indonesia.

TOTAL user manual

NASA Technical Reports Server (NTRS)

Johnson, Sally C.; Boerschlein, David P.

1994-01-01

Semi-Markov models can be used to analyze the reliability of virtually any fault-tolerant system. However, the process of delineating all of the states and transitions in the model of a complex system can be devastatingly tedious and error-prone. Even with tools such as the Abstract Semi-Markov Specification Interface to the SURE Tool (ASSIST), the user must describe a system by specifying the rules governing the behavior of the system in order to generate the model. With the Table Oriented Translator to the ASSIST Language (TOTAL), the user can specify the components of a typical system and their attributes in the form of a table. The conditions that lead to system failure are also listed in a tabular form. The user can also abstractly specify dependencies with causes and effects. The level of information required is appropriate for system designers with little or no background in the details of reliability calculations. A menu-driven interface guides the user through the system description process, and the program updates the tables as new information is entered. The TOTAL program automatically generates an ASSIST input description to match the system description.

SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems.

PubMed

Chae, Seunghwan; Nguang, Sing Kiong

2014-07-01

In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

PubMed

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.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.

PubMed

Djordjevic, Ivan B

2015-08-24

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

PubMed Central

Djordjevic, Ivan B.

2015-01-01

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled. PMID:26305258

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Using Markov Chains to predict the natural progression of diabetic retinopathy.

PubMed

Srikanth, Priyanka

2015-01-01

To study the natural progression of diabetic retinopathy in patients with type 2 diabetes. This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy (NPDR) were treated. Markov Chains and Chi-square test were used for statistical analysis. We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference (P=0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07y in moderate NPDR, be in the severe NPDR state for 1.33y before moving into PDR for roughly 8y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29y. Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR. However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy (PDR) and stay in that state for long periods before transitioning into blindness.

Processing and Conversion of Algae to Bioethanol

NASA Astrophysics Data System (ADS)

Kampfe, Sara Katherine

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

An agent-based simulation model for Clostridium difficile infection control.

PubMed

Codella, James; Safdar, Nasia; Heffernan, Rick; Alagoz, Oguzhan

2015-02-01

Control of Clostridium difficile infection (CDI) is an increasingly difficult problem for health care institutions. There are commonly recommended strategies to combat CDI transmission, such as oral vancomycin for CDI treatment, increased hand hygiene with soap and water for health care workers, daily environmental disinfection of infected patient rooms, and contact isolation of diseased patients. However, the efficacy of these strategies, particularly for endemic CDI, has not been well studied. The objective of this research is to develop a valid, agent-based simulation model (ABM) to study C. difficile transmission and control in a midsized hospital. We develop an ABM of a midsized hospital with agents such as patients, health care workers, and visitors. We model the natural progression of CDI in a patient using a Markov chain and the transmission of CDI through agent and environmental interactions. We derive input parameters from aggregate patient data from the 2007-2010 Wisconsin Hospital Association and published medical literature. We define a calibration process, which we use to estimate transition probabilities of the Markov model by comparing simulation results to benchmark values found in published literature. In a comparison of CDI control strategies implemented individually, routine bleach disinfection of CDI-positive patient rooms provides the largest reduction in nosocomial asymptomatic colonization (21.8%) and nosocomial CDIs (42.8%). Additionally, vancomycin treatment provides the largest reduction in relapse CDIs (41.9%), CDI-related mortalities (68.5%), and total patient length of stay (21.6%). We develop a generalized ABM for CDI control that can be customized and further expanded to specific institutions and/or scenarios. Additionally, we estimate transition probabilities for a Markov model of natural CDI progression in a patient through calibration. © The Author(s) 2014.

Poissonian steady states: from stationary densities to stationary intensities.

PubMed

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

Poissonian steady states: From stationary densities to stationary intensities

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling

PubMed Central

Williams, Claire; Lewsey, James D.; Mackay, Daniel F.; Briggs, Andrew H.

2016-01-01

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results. PMID:27698003

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling.

PubMed

Williams, Claire; Lewsey, James D; Mackay, Daniel F; Briggs, Andrew H

2017-05-01

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results.

Status and future transition of rapid urbanizing landscape in central Western Ghats - CA based approach

NASA Astrophysics Data System (ADS)

Bharath, S..; Rajan, K. S.; Ramachandra, T. V.

2014-11-01

The land use changes in forested landscape are highly complex and dynamic, affected by the natural, socio-economic, cultural, political and other factors. The remote sensing (RS) and geographical information system (GIS) techniques coupled with multi-criteria evaluation functions such as Markov-cellular automata (CA-Markov) model helps in analysing intensity, extent and future forecasting of human activities affecting the terrestrial biosphere. Karwar taluk of Central Western Ghats in Karnataka state, India has seen rapid transitions in its forest cover due to various anthropogenic activities, primarily driven by major industrial activities. A study based on Landsat and IRS derived data along with CA-Markov method has helped in characterizing the patterns and trends of land use changes over a period of 2004-2013, expected transitions was predicted for a set of scenarios through 2013-2022. The analysis reveals the loss of pristine forest cover from 75.51% to 67.36% (1973 to 2013) and increase in agriculture land as well as built-up area of 8.65% (2013), causing impact on local flora and fauna. The other factors driving these changes are the aggregated level of demand for land, local and regional effects of land use activities such as deforestation, improper practices in expansion of agriculture and infrastructure development, deteriorating natural resources availability. The spatio temporal models helped in visualizing on-going changes apart from prediction of likely changes. The CA-Markov based analysis provides us insights into the localized changes impacting these regions and can be useful in developing appropriate mitigation management approaches based on the modelled future impacts. This necessitates immediate measures for minimizing the future impacts.

Net Surface Flux Budget Over Tropical Oceans Estimated from the Tropical Rainfall Measuring Mission (TRMM)

NASA Astrophysics Data System (ADS)

Fan, Tai-Fang

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Magneto - Optical Imaging of Superconducting MgB2 Thin Films

NASA Astrophysics Data System (ADS)

Hummert, Stephanie Maria

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Boron Carbide Filled Neutron Shielding Textile Polymers

NASA Astrophysics Data System (ADS)

Manzlak, Derrick Anthony

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Parallel Unstructured Grid Generation for Complex Real-World Aerodynamic Simulations

NASA Astrophysics Data System (ADS)

Zagaris, George

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Polymeric Radiation Shielding for Applications in Space: Polyimide Synthesis and Modeling of Multi-Layered Polymeric Shields

NASA Astrophysics Data System (ADS)

Schiavone, Clinton Cleveland

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

The Development of the CALIPSO LiDAR Simulator

NASA Astrophysics Data System (ADS)

Powell, Kathleen A.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Exploring a Novel Approach to Technical Nuclear Forensics Utilizing Atomic Force Microscopy

NASA Astrophysics Data System (ADS)

Peeke, Richard Scot

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Modeling of Critically-Stratified Gravity Flows: Application to the Eel River Continental Shelf, Northern California

NASA Astrophysics Data System (ADS)

Scully, Malcolm E.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Production of Cyclohexylene-Containing Diamines in Pursuit of Novel Radiation Shielding Materials

NASA Astrophysics Data System (ADS)

Bate, Norah G.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Development of Boron-Containing Polyimide Materials and Poly(arylene Ether)s for Radiation Shielding

NASA Astrophysics Data System (ADS)

Collins, Brittani May

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Magnetization Dynamics and Anisotropy in Ferromagnetic/Antiferromagnetic Ni/NiO Bilayers

NASA Astrophysics Data System (ADS)

Petersen, Andreas

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

A Network of Conformational Transitions in the Apo Form of NDM-1 Enzyme Revealed by MD Simulation and a Markov State Model.

PubMed

Gao, Kaifu; Zhao, Yunjie

2017-04-13

New Delhi metallo-β-lactamase-1 (NDM-1) is a novel β-lactamase enzyme that confers enteric bacteria with nearly complete resistance to all β-lactam antibiotics, so it raises a formidable and global threat to human health. However, the binding mechanism between apo-NDM-1 and antibiotics as well as related conformational changes remains poorly understood, which largely hinders the overcoming of its antibiotic resistance. In our study, long-time conventional molecular dynamics simulation and Markov state models were applied to reveal both the dynamical and conformational landscape of apo-NDM-1: the MD simulation demonstrates that loop L3, which is responsible for antibiotic binding, is the most flexible and undergoes dramatic conformational changes; moreover, the Markov state model built from the simulation maps four metastable states including open, semiopen, and closed conformations of loop L3 as well as frequent transitions between the states. Our findings propose a possible conformational selection model for the binding mechanism between apo-NDM-1 and antibiotics, which facilitates the design of novel inhibitors and antibiotics.

Using hidden Markov models to align multiple sequences.

PubMed

Mount, David W

2009-07-01

A hidden Markov model (HMM) is a probabilistic model of a multiple sequence alignment (msa) of proteins. In the model, each column of symbols in the alignment is represented by a frequency distribution of the symbols (called a "state"), and insertions and deletions are represented by other states. One moves through the model along a particular path from state to state in a Markov chain (i.e., random choice of next move), trying to match a given sequence. The next matching symbol is chosen from each state, recording its probability (frequency) and also the probability of going to that state from a previous one (the transition probability). State and transition probabilities are multiplied to obtain a probability of the given sequence. The hidden nature of the HMM is due to the lack of information about the value of a specific state, which is instead represented by a probability distribution over all possible values. This article discusses the advantages and disadvantages of HMMs in msa and presents algorithms for calculating an HMM and the conditions for producing the best HMM.

Indexed semi-Markov process for wind speed modeling.

NASA Astrophysics Data System (ADS)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-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. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [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 generation 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, Renewable 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 distribution, Renewable Energy 28 (2003) 1787-1802.

Detecting memory and structure in human navigation patterns using Markov chain models of varying order.

PubMed

Singer, Philipp; Helic, Denis; Taraghi, Behnam; Strohmaier, Markus

2014-01-01

One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work.

Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order

PubMed Central

Singer, Philipp; Helic, Denis; Taraghi, Behnam; Strohmaier, Markus

2014-01-01

One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work. PMID:25013937

Multiensemble Markov models of molecular thermodynamics and kinetics.

PubMed

Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank

2016-06-07

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model.

Multiensemble Markov models of molecular thermodynamics and kinetics

PubMed Central

Wu, Hao; Paul, Fabian; Noé, Frank

2016-01-01

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model. PMID:27226302

Markov and semi-Markov processes as a failure rate

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

Grabski, Franciszek

2016-06-08

In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

NASA Astrophysics Data System (ADS)

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.

Camera-Model Identification Using Markovian Transition Probability Matrix

NASA Astrophysics Data System (ADS)

Xu, Guanshuo; Gao, Shang; Shi, Yun Qing; Hu, Ruimin; Su, Wei

Detecting the (brands and) models of digital cameras from given digital images has become a popular research topic in the field of digital forensics. As most of images are JPEG compressed before they are output from cameras, we propose to use an effective image statistical model to characterize the difference JPEG 2-D arrays of Y and Cb components from the JPEG images taken by various camera models. Specifically, the transition probability matrices derived from four different directional Markov processes applied to the image difference JPEG 2-D arrays are used to identify statistical difference caused by image formation pipelines inside different camera models. All elements of the transition probability matrices, after a thresholding technique, are directly used as features for classification purpose. Multi-class support vector machines (SVM) are used as the classification tool. The effectiveness of our proposed statistical model is demonstrated by large-scale experimental results.

Conditioned Limit Theorems for Some Null Recurrent Markov Processes

DTIC Science & Technology

1976-08-01

Chapter 1 INTRODUCTION 1.1 Summary of Results Let (Vk, k ! 0) be a discrete time Markov process with state space EC(- , ) and let S be...explain our results in some detail. 2 We begin by stating our three basic assumptions: (1) vk s k 2 0 Is a Markov process with state space E C(-o,%); (Ii... 12 n 3. CONDITIONING ON T (, > n.................................1.9 3.1 Preliminary Results

A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models.

PubMed

Jones, Edmund; Epstein, David; García-Mochón, Leticia

2017-10-01

For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.

Decision analysis with cumulative prospect theory.

PubMed

Bayoumi, A M; Redelmeier, D A

2000-01-01

Individuals sometimes express preferences that do not follow expected utility theory. Cumulative prospect theory adjusts for some phenomena by using decision weights rather than probabilities when analyzing a decision tree. The authors examined how probability transformations from cumulative prospect theory might alter a decision analysis of a prophylactic therapy in AIDS, eliciting utilities from patients with HIV infection (n = 75) and calculating expected outcomes using an established Markov model. They next focused on transformations of three sets of probabilities: 1) the probabilities used in calculating standard-gamble utility scores; 2) the probabilities of being in discrete Markov states; 3) the probabilities of transitioning between Markov states. The same prophylaxis strategy yielded the highest quality-adjusted survival under all transformations. For the average patient, prophylaxis appeared relatively less advantageous when standard-gamble utilities were transformed. Prophylaxis appeared relatively more advantageous when state probabilities were transformed and relatively less advantageous when transition probabilities were transformed. Transforming standard-gamble and transition probabilities simultaneously decreased the gain from prophylaxis by almost half. Sensitivity analysis indicated that even near-linear probability weighting transformations could substantially alter quality-adjusted survival estimates. The magnitude of benefit estimated in a decision-analytic model can change significantly after using cumulative prospect theory. Incorporating cumulative prospect theory into decision analysis can provide a form of sensitivity analysis and may help describe when people deviate from expected utility theory.

An Alignment-Free Algorithm in Comparing the Similarity of Protein Sequences Based on Pseudo-Markov Transition Probabilities among Amino Acids

PubMed Central

Li, Yushuang; Yang, Jiasheng; Zhang, Yi

2016-01-01

In this paper, we have proposed a novel alignment-free method for comparing the similarity of protein sequences. We first encode a protein sequence into a 440 dimensional feature vector consisting of a 400 dimensional Pseudo-Markov transition probability vector among the 20 amino acids, a 20 dimensional content ratio vector, and a 20 dimensional position ratio vector of the amino acids in the sequence. By evaluating the Euclidean distances among the representing vectors, we compare the similarity of protein sequences. We then apply this method into the ND5 dataset consisting of the ND5 protein sequences of 9 species, and the F10 and G11 datasets representing two of the xylanases containing glycoside hydrolase families, i.e., families 10 and 11. As a result, our method achieves a correlation coefficient of 0.962 with the canonical protein sequence aligner ClustalW in the ND5 dataset, much higher than those of other 5 popular alignment-free methods. In addition, we successfully separate the xylanases sequences in the F10 family and the G11 family and illustrate that the F10 family is more heat stable than the G11 family, consistent with a few previous studies. Moreover, we prove mathematically an identity equation involving the Pseudo-Markov transition probability vector and the amino acids content ratio vector. PMID:27918587

Markov Chain-Based Acute Effect Estimation of Air Pollution on Elder Asthma Hospitalization

PubMed Central

Luo, Li; Zhang, Fengyi; Sun, Lin; Li, Chunyang; Huang, Debin; Han, Gao; Wang, Bin

2017-01-01

Background Asthma caused substantial economic and health care burden and is susceptible to air pollution. Particularly, when it comes to elder asthma patient (older than 65), the phenomenon is more significant. The aim of this study is to investigate the Markov-based acute effects of air pollution on elder asthma hospitalizations, in forms of transition probabilities. Methods A retrospective, population-based study design was used to assess temporal patterns in hospitalizations for asthma in a region of Sichuan province, China. Approximately 12 million residents were covered during this period. Relative risk analysis and Markov chain model were employed on daily hospitalization state estimation. Results Among PM2.5, PM10, NO2, and SO2, only SO2 was significant. When air pollution is severe, the transition probability from a low-admission state (previous day) to high-admission state (next day) is 35.46%, while it is 20.08% when air pollution is mild. In particular, for female-cold subgroup, the counterparts are 30.06% and 0.01%, respectively. Conclusions SO2 was a significant risk factor for elder asthma hospitalization. When air pollution worsened, the transition probabilities from each state to high admission states increase dramatically. This phenomenon appeared more evidently, especially in female-cold subgroup (which is in cold season for female admissions). Based on our work, admission amount forecast, asthma intervention, and corresponding healthcare allocation can be done. PMID:29147496

Using Markov Chains to predict the natural progression of diabetic retinopathy

PubMed Central

Srikanth, Priyanka

2015-01-01

AIM To study the natural progression of diabetic retinopathy in patients with type 2 diabetes. METHODS This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy (NPDR) were treated. Markov Chains and Chi-square test were used for statistical analysis. RESULTS We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference (P=0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07y in moderate NPDR, be in the severe NPDR state for 1.33y before moving into PDR for roughly 8y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29y. CONCLUSION Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR. However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy (PDR) and stay in that state for long periods before transitioning into blindness. PMID:25709923

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

Network Security Risk Assessment System Based on Attack Graph and Markov Chain

NASA Astrophysics Data System (ADS)

Sun, Fuxiong; Pi, Juntao; Lv, Jin; Cao, Tian

2017-10-01

Network security risk assessment technology can be found in advance of the network problems and related vulnerabilities, it has become an important means to solve the problem of network security. Based on attack graph and Markov chain, this paper provides a Network Security Risk Assessment Model (NSRAM). Based on the network infiltration tests, NSRAM generates the attack graph by the breadth traversal algorithm. Combines with the international standard CVSS, the attack probability of atomic nodes are counted, and then the attack transition probabilities of ones are calculated by Markov chain. NSRAM selects the optimal attack path after comprehensive measurement to assessment network security risk. The simulation results show that NSRAM can reflect the actual situation of network security objectively.

A big-data model for multi-modal public transportation with application to macroscopic control and optimisation

NASA Astrophysics Data System (ADS)

Faizrahnemoon, Mahsa; Schlote, Arieh; Maggi, Lorenzo; Crisostomi, Emanuele; Shorten, Robert

2015-11-01

This paper describes a Markov-chain-based approach to modelling multi-modal transportation networks. An advantage of the model is the ability to accommodate complex dynamics and handle huge amounts of data. The transition matrix of the Markov chain is built and the model is validated using the data extracted from a traffic simulator. A realistic test-case using multi-modal data from the city of London is given to further support the ability of the proposed methodology to handle big quantities of data. Then, we use the Markov chain as a control tool to improve the overall efficiency of a transportation network, and some practical examples are described to illustrate the potentials of the approach.

Handling target obscuration through Markov chain observations

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Wu, Biao

2008-04-01

Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.

SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

PubMed

Thiede, Erik; VAN Koten, Brian; Weare, Jonathan

For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.

High-Performance Nanocomposites Designed for Radiation Shielding in Space and an Application of GIS for Analyzing Nanopowder Dispersion in Polymer Matrixes

NASA Astrophysics Data System (ADS)

Auslander, Joseph Simcha

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Time-Resolved Magneto-Optical Imaging of Superconducting YBCO Thin Films in the High-Frequency AC Current Regime

NASA Astrophysics Data System (ADS)

Frey, Alexander

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Use of Remote Sensing to Identify Essential Habitat for Aeschynomene virginica (L.) BSP, a Threatened Tidal Freshwater Wetland Plant

NASA Astrophysics Data System (ADS)

Mountz, Elizabeth M.

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Silver-Polyimide Nanocomposite Films: Single-Stage Synthesis and Analysis of Metalized Partially-Fluorinated Polyimide BTDA/4-BDAF Prepared from Silver(I) Complexes

NASA Astrophysics Data System (ADS)

Abelard, Joshua Erold Robert

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Multifunctional Polymer Synthesis and Incorporation of Gadolinium Compounds and Modified Tungsten Nanoparticles for Improvement of Radiation Shielding for use in Outer Space

NASA Astrophysics Data System (ADS)

Harbert, Emily Grace

We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

Molecular dynamics of conformational substates for a simplified protein model

NASA Astrophysics Data System (ADS)

Grubmüller, Helmut; Tavan, Paul

1994-09-01

Extended molecular dynamics simulations covering a total of 0.232 μs have been carried out on a simplified protein model. Despite its simplified structure, that model exhibits properties similar to those of more realistic protein models. In particular, the model was found to undergo transitions between conformational substates at a time scale of several hundred picoseconds. The computed trajectories turned out to be sufficiently long as to permit a statistical analysis of that conformational dynamics. To check whether effective descriptions neglecting memory effects can reproduce the observed conformational dynamics, two stochastic models were studied. A one-dimensional Langevin effective potential model derived by elimination of subpicosecond dynamical processes could not describe the observed conformational transition rates. In contrast, a simple Markov model describing the transitions between but neglecting dynamical processes within conformational substates reproduced the observed distribution of first passage times. These findings suggest, that protein dynamics generally does not exhibit memory effects at time scales above a few hundred picoseconds, but confirms the existence of memory effects at a picosecond time scale.

Implicit Value Updating Explains Transitive Inference Performance: The Betasort Model

PubMed Central

Jensen, Greg; Muñoz, Fabian; Alkan, Yelda; Ferrera, Vincent P.; Terrace, Herbert S.

2015-01-01

Transitive inference (the ability to infer that B > D given that B > C and C > D) is a widespread characteristic of serial learning, observed in dozens of species. Despite these robust behavioral effects, reinforcement learning models reliant on reward prediction error or associative strength routinely fail to perform these inferences. We propose an algorithm called betasort, inspired by cognitive processes, which performs transitive inference at low computational cost. This is accomplished by (1) representing stimulus positions along a unit span using beta distributions, (2) treating positive and negative feedback asymmetrically, and (3) updating the position of every stimulus during every trial, whether that stimulus was visible or not. Performance was compared for rhesus macaques, humans, and the betasort algorithm, as well as Q-learning, an established reward-prediction error (RPE) model. Of these, only Q-learning failed to respond above chance during critical test trials. Betasort’s success (when compared to RPE models) and its computational efficiency (when compared to full Markov decision process implementations) suggests that the study of reinforcement learning in organisms will be best served by a feature-driven approach to comparing formal models. PMID:26407227

Implicit Value Updating Explains Transitive Inference Performance: The Betasort Model.

PubMed

Jensen, Greg; Muñoz, Fabian; Alkan, Yelda; Ferrera, Vincent P; Terrace, Herbert S

2015-01-01

Transitive inference (the ability to infer that B > D given that B > C and C > D) is a widespread characteristic of serial learning, observed in dozens of species. Despite these robust behavioral effects, reinforcement learning models reliant on reward prediction error or associative strength routinely fail to perform these inferences. We propose an algorithm called betasort, inspired by cognitive processes, which performs transitive inference at low computational cost. This is accomplished by (1) representing stimulus positions along a unit span using beta distributions, (2) treating positive and negative feedback asymmetrically, and (3) updating the position of every stimulus during every trial, whether that stimulus was visible or not. Performance was compared for rhesus macaques, humans, and the betasort algorithm, as well as Q-learning, an established reward-prediction error (RPE) model. Of these, only Q-learning failed to respond above chance during critical test trials. Betasort's success (when compared to RPE models) and its computational efficiency (when compared to full Markov decision process implementations) suggests that the study of reinforcement learning in organisms will be best served by a feature-driven approach to comparing formal models.

Estimation of sojourn time in chronic disease screening without data on interval cases.

PubMed

Chen, T H; Kuo, H S; Yen, M F; Lai, M S; Tabar, L; Duffy, S W

2000-03-01

Estimation of the sojourn time on the preclinical detectable period in disease screening or transition rates for the natural history of chronic disease usually rely on interval cases (diagnosed between screens). However, to ascertain such cases might be difficult in developing countries due to incomplete registration systems and difficulties in follow-up. To overcome this problem, we propose three Markov models to estimate parameters without using interval cases. A three-state Markov model, a five-state Markov model related to regional lymph node spread, and a five-state Markov model pertaining to tumor size are applied to data on breast cancer screening in female relatives of breast cancer cases in Taiwan. Results based on a three-state Markov model give mean sojourn time (MST) 1.90 (95% CI: 1.18-4.86) years for this high-risk group. Validation of these models on the basis of data on breast cancer screening in the age groups 50-59 and 60-69 years from the Swedish Two-County Trial shows the estimates from a three-state Markov model that does not use interval cases are very close to those from previous Markov models taking interval cancers into account. For the five-state Markov model, a reparameterized procedure using auxiliary information on clinically detected cancers is performed to estimate relevant parameters. A good fit of internal and external validation demonstrates the feasibility of using these models to estimate parameters that have previously required interval cancers. This method can be applied to other screening data in which there are no data on interval cases.

Stochastic thermodynamics across scales: Emergent inter-attractoral discrete Markov jump process and its underlying continuous diffusion

NASA Astrophysics Data System (ADS)

Santillán, Moisés; Qian, Hong

2013-01-01

We investigate the internal consistency of a recently developed mathematical thermodynamic structure across scales, between a continuous stochastic nonlinear dynamical system, i.e., a diffusion process with Langevin and Fokker-Planck equations, and its emergent discrete, inter-attractoral Markov jump process. We analyze how the system’s thermodynamic state functions, e.g. free energy F, entropy S, entropy production ep, free energy dissipation Ḟ, etc., are related when the continuous system is described with coarse-grained discrete variables. It is shown that the thermodynamics derived from the underlying, detailed continuous dynamics gives rise to exactly the free-energy representation of Gibbs and Helmholtz. That is, the system’s thermodynamic structure is the same as if one only takes a middle road and starts with the natural discrete description, with the corresponding transition rates empirically determined. By natural we mean in the thermodynamic limit of a large system, with an inherent separation of time scales between inter- and intra-attractoral dynamics. This result generalizes a fundamental idea from chemistry, and the theory of Kramers, by incorporating thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by a discrete representation, in terms of exponential rate laws and a stochastic thermodynamics.

Closed-form solution of decomposable stochastic models

NASA Technical Reports Server (NTRS)

Sjogren, Jon A.

1990-01-01

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Ultrafast dynamics of photoexcited charge and spin currents in semiconductor nanostructures

NASA Astrophysics Data System (ADS)

Meier, Torsten; Pasenow, Bernhard; Duc, Huynh Thanh; Vu, Quang Tuyen; Haug, Hartmut; Koch, Stephan W.

2007-02-01

Employing the quantum interference among one- and two-photon excitations induced by ultrashort two-color laser pulses it is possible to generate charge and spin currents in semiconductors and semiconductor nanostructures on femtosecond time scales. Here, it is reviewed how the excitation process and the dynamics of such photocurrents can be described on the basis of a microscopic many-body theory. Numerical solutions of the semiconductor Bloch equations (SBE) provide a detailed description of the time-dependent material excitations. Applied to the case of photocurrents, numerical solutions of the SBE for a two-band model including many-body correlations on the second-Born Markov level predict an enhanced damping of the spin current relative to that of the charge current. Interesting effects are obtained when the scattering processes are computed beyond the Markovian limit. Whereas the overall decay of the currents is basically correctly described already within the Markov approximation, quantum-kinetic calculations show that memory effects may lead to additional oscillatory signatures in the current transients. When transitions to coupled heavy- and light-hole valence bands are incorporated into the SBE, additional charge and spin currents, which are not described by the two-band model, appear.

A Latent Transition Analysis of Academic Intrinsic Motivation from Childhood through Adolescence

ERIC Educational Resources Information Center

Marcoulides, George A.; Gottfried, Adele Eskeles; Gottfried, Allen W.; Oliver, Pamella H.

2008-01-01

A longitudinal modeling approach was utilized to determine the existence of latent classes with regard to academic intrinsic motivation and the points of stability and transition of individuals between and within classes. A special type of latent Markov Chain model using "Mplus" was fit to data from the Fullerton Longitudinal Study, with…

Modeling Land Use/Cover Changes in an African Rural Landscape

NASA Astrophysics Data System (ADS)

Kamusoko, C.; Aniya, M.

2006-12-01

Land use/cover changes are analyzed in the Bindura district of Zimbabwe, Africa through the integration of data from a time series of Landsat imagery (1973, 1989 and 2000), a household survey and GIS coverages. We employed a hybrid supervised/unsupervised classification approach to generate land use/cover maps from which landscape metrics were calculated. Population and other household variables were derived from a sample of surveyed villages, while road accessibility and slope were obtained from topographic maps and digital elevation model, respectively. Markov-cellular automata modeling approach that incorporates Markov chain analysis, cellular automata and multi-criteria evaluation (MCE) / multi-objective allocation (MOLA) procedures was used to simulate land use/cover changes. A GIS-based MCE technique computed transition potential maps, whereas transition areas were derived from the 1973-2000 land use/cover maps using the Markov chain analysis. A 5 x 5 cellular automata filter was used to develop a spatially explicit contiguity- weighting factor to change the cells based on its previous state and those of its neighbors, while MOLA resolved land use/cover class allocation conflicts. The kappa index of agreement was used for model validation. Observed trends in land use/cover changes indicate that deforestation and the encroachment of cultivation in woodland areas is a continuous trend in the study area. This suggests that economic activities driven by agricultural expansion were the main causes of landscape fragmentation, leading to landscape degradation. Rigorous calibration of transition potential maps done by a MCE algorithm and Markovian transition probabilities produced accurate inputs for the simulation of land use/cover changes. Overall standard kappa index of agreement ranged from 0.73 to 0.83, which is sufficient for simulating land use/cover changes in the study area. Land use/cover simulations under the 1989 and 2000 scenario indicated further landscape degradation in the rural areas of the Bindura district. Keywords: Zimbabwe, land use/cover changes, landscape fragmentation, GIS, land use/cover change modeling, multi-criteria evaluation/multi-objective allocation procedures, Markov-cellular automata

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

PubMed Central

Liu, Yu-Ying; Li, Shuang; Li, Fuxin; Song, Le; Rehg, James M.

2016-01-01

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset. PMID:27019571

Effect of Clustering Algorithm on Establishing Markov State Model for Molecular Dynamics Simulations.

PubMed

Li, Yan; Dong, Zigang

2016-06-27

Recently, the Markov state model has been applied for kinetic analysis of molecular dynamics simulations. However, discretization of the conformational space remains a primary challenge in model building, and it is not clear how the space decomposition by distinct clustering strategies exerts influence on the model output. In this work, different clustering algorithms are employed to partition the conformational space sampled in opening and closing of fatty acid binding protein 4 as well as inactivation and activation of the epidermal growth factor receptor. Various classifications are achieved, and Markov models are set up accordingly. On the basis of the models, the total net flux and transition rate are calculated between two distinct states. Our results indicate that geometric and kinetic clustering perform equally well. The construction and outcome of Markov models are heavily dependent on the data traits. Compared to other methods, a combination of Bayesian and hierarchical clustering is feasible in identification of metastable states.

Entropy, complexity, and Markov diagrams for random walk cancer models.

PubMed

Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-19

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

Entropy, complexity, and Markov diagrams for random walk cancer models

NASA Astrophysics Data System (ADS)

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

ASSIST - THE ABSTRACT SEMI-MARKOV SPECIFICATION INTERFACE TO THE SURE TOOL PROGRAM (SUN VERSION)

NASA Technical Reports Server (NTRS)

Johnson, S. C.

1994-01-01

ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, is an interface that will enable reliability engineers to accurately design large semi-Markov models. The user describes the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. The abstract language allows efficient description of large, complex systems; a one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. Instead of listing the individual states of the Markov model, reliability engineers can specify the rules governing the behavior of a system, and these are used to automatically generate the model. ASSIST reads an input file describing the failure behavior of a system in an abstract language and generates a Markov model in the format needed for input to SURE, the semi-Markov Unreliability Range Evaluator program, and PAWS/STEM, the Pade Approximation with Scaling program and Scaled Taylor Exponential Matrix. A Markov model consists of a number of system states and transitions between them. Each state in the model represents a possible state of the system in terms of which components have failed, which ones have been removed, etc. Within ASSIST, each state is defined by a state vector, where each element of the vector takes on an integer value within a defined range. An element can represent any meaningful characteristic, such as the number of working components of one type in the system, or the number of faulty components of another type in use. Statements representing transitions between states in the model have three parts: a condition expression, a destination expression, and a rate expression. The first expression is a Boolean expression describing the state space variable values of states for which the transition is valid. The second expression defines the destination state for the transition in terms of state space variable values. The third expression defines the distribution of elapsed time for the transition. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. ASSIST was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The VMS version (LAR14193) is written in C-language and can be compiled with the VAX C compiler. The standard distribution medium for the VMS version of ASSIST is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The Sun version (LAR14923) is written in ANSI C-language. An ANSI compliant C compiler is required in order to compile this package. The standard distribution medium for the Sun version of ASSIST is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the documentation in PostScript, TeX, and DVI formats are provided on the distribution medium. (The VMS distribution lacks the .DVI format files, however.) ASSIST was developed in 1986 and last updated in 1992. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

ASSIST - THE ABSTRACT SEMI-MARKOV SPECIFICATION INTERFACE TO THE SURE TOOL PROGRAM (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Johnson, S. C.

1994-01-01

ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, is an interface that will enable reliability engineers to accurately design large semi-Markov models. The user describes the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. The abstract language allows efficient description of large, complex systems; a one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. Instead of listing the individual states of the Markov model, reliability engineers can specify the rules governing the behavior of a system, and these are used to automatically generate the model. ASSIST reads an input file describing the failure behavior of a system in an abstract language and generates a Markov model in the format needed for input to SURE, the semi-Markov Unreliability Range Evaluator program, and PAWS/STEM, the Pade Approximation with Scaling program and Scaled Taylor Exponential Matrix. A Markov model consists of a number of system states and transitions between them. Each state in the model represents a possible state of the system in terms of which components have failed, which ones have been removed, etc. Within ASSIST, each state is defined by a state vector, where each element of the vector takes on an integer value within a defined range. An element can represent any meaningful characteristic, such as the number of working components of one type in the system, or the number of faulty components of another type in use. Statements representing transitions between states in the model have three parts: a condition expression, a destination expression, and a rate expression. The first expression is a Boolean expression describing the state space variable values of states for which the transition is valid. The second expression defines the destination state for the transition in terms of state space variable values. The third expression defines the distribution of elapsed time for the transition. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. ASSIST was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The VMS version (LAR14193) is written in C-language and can be compiled with the VAX C compiler. The standard distribution medium for the VMS version of ASSIST is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The Sun version (LAR14923) is written in ANSI C-language. An ANSI compliant C compiler is required in order to compile this package. The standard distribution medium for the Sun version of ASSIST is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the documentation in PostScript, TeX, and DVI formats are provided on the distribution medium. (The VMS distribution lacks the .DVI format files, however.) ASSIST was developed in 1986 and last updated in 1992. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

Markov Modeling of Component Fault Growth over a Derived Domain of Feasible Output Control Effort Modifications

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

This paper introduces a novel Markov process formulation of stochastic fault growth modeling, in order to facilitate the development and analysis of prognostics-based control adaptation. A metric representing the relative deviation between the nominal output of a system and the net output that is actually enacted by an implemented prognostics-based control routine, will be used to define the action space of the formulated Markov process. The state space of the Markov process will be defined in terms of an abstracted metric representing the relative health remaining in each of the system s components. The proposed formulation of component fault dynamics will conveniently relate feasible system output performance modifications to predictions of future component health deterioration.

The application of Markov decision process with penalty function in restaurant delivery robot

NASA Astrophysics Data System (ADS)

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.

Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method

PubMed Central

Kim, Kyungmok; Lee, Jaewook

2016-01-01

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones. PMID:28773359

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.

PubMed

Namikawa, Jun

2005-08-01

Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

A hidden Markov model approach to neuron firing patterns.

PubMed

Camproux, A C; Saunier, F; Chouvet, G; Thalabard, J C; Thomas, G

1996-11-01

Analysis and characterization of neuronal discharge patterns are of interest to neurophysiologists and neuropharmacologists. In this paper we present a hidden Markov model approach to modeling single neuron electrical activity. Basically the model assumes that each interspike interval corresponds to one of several possible states of the neuron. Fitting the model to experimental series of interspike intervals by maximum likelihood allows estimation of the number of possible underlying neuron states, the probability density functions of interspike intervals corresponding to each state, and the transition probabilities between states. We present an application to the analysis of recordings of a locus coeruleus neuron under three pharmacological conditions. The model distinguishes two states during halothane anesthesia and during recovery from halothane anesthesia, and four states after administration of clonidine. The transition probabilities yield additional insights into the mechanisms of neuron firing.

Betting on change: modeling transitional probabilities to guide therapy development for opioid dependence.

PubMed

Carpenter, Kenneth M; Jiang, Huiping; Sullivan, Maria A; Bisaga, Adam; Comer, Sandra D; Raby, Wilfrid Noel; Brooks, Adam C; Nunes, Edward V

2009-03-01

This study investigated the process of change by modeling transitions among four clinical states encountered in 64 detoxified opiate-dependent individuals treated with daily oral naltrexone: no opiate use, blocked opiate use (i.e., opiate use while adhering to oral naltrexone), unblocked opiate use (i.e., opiate use after having discontinued oral naltrexone), and treatment dropout. The effects of baseline characteristics and two psychosocial interventions of differing intensity, behavioral naltrexone therapy (BNT) and compliance enhancement (CE), on these transitions were studied. Participants using greater quantities of opiates were more likely than other participants to be retained in BNT relative to CE. Markov modeling indicated a transition from abstinence to treatment dropout was approximately 3.56 times greater among participants in CE relative to participants in BNT, indicating the more comprehensive psychosocial intervention kept participants engaged in treatment longer. Transitions to stopping treatment were more likely to occur after unblocked opiate use in both treatments. Continued opiate use while being blocked accounted for a relatively low proportion of transitions to abstinence and may have more deleterious effects later in a treatment episode. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Multi-state Markov model for disability: A case of Malaysia Social Security (SOCSO)

NASA Astrophysics Data System (ADS)

Samsuddin, Shamshimah; Ismail, Noriszura

2016-06-01

Studies of SOCSO's contributor outcomes like disability are usually restricted to a single outcome. In this respect, the study has focused on the approach of multi-state Markov model for estimating the transition probabilities among SOCSO's contributor in Malaysia between states: work, temporary disability, permanent disability and death at yearly intervals on age, gender, year and disability category; ignoring duration and past disability experience which is not consider of how or when someone arrived in that category. These outcomes represent different states which depend on health status among the workers.

Artificial emotion triggered stochastic behavior transitions with motivational gain effects for multi-objective robot tasks

NASA Astrophysics Data System (ADS)

Dağlarli, Evren; Temeltaş, Hakan

2007-04-01

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

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

PubMed

Dixit, Purushottam D; Dill, Ken A

2018-02-13

Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C 2 M 2 ), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

Markovian prediction of future values for food grains in the economic survey

NASA Astrophysics Data System (ADS)

Sathish, S.; Khadar Babu, S. K.

2017-11-01

Now-a-days prediction and forecasting are plays a vital role in research. For prediction, regression is useful to predict the future value and current value on production process. In this paper, we assume food grain production exhibit Markov chain dependency and time homogeneity. The economic generative performance evaluation the balance time artificial fertilization different level in Estrusdetection using a daily Markov chain model. Finally, Markov process prediction gives better performance compare with Regression model.

A Markov Environment-dependent Hurricane Intensity Model and Its Comparison with Multiple Dynamic Models

NASA Astrophysics Data System (ADS)

Jing, R.; Lin, N.; Emanuel, K.; Vecchi, G. A.; Knutson, T. R.

2017-12-01

A Markov environment-dependent hurricane intensity model (MeHiM) is developed to simulate the climatology of hurricane intensity given the surrounding large-scale environment. The model considers three unobserved discrete states representing respectively storm's slow, moderate, and rapid intensification (and deintensification). Each state is associated with a probability distribution of intensity change. The storm's movement from one state to another, regarded as a Markov chain, is described by a transition probability matrix. The initial state is estimated with a Bayesian approach. All three model components (initial intensity, state transition, and intensity change) are dependent on environmental variables including potential intensity, vertical wind shear, midlevel relative humidity, and ocean mixing characteristics. This dependent Markov model of hurricane intensity shows a significant improvement over previous statistical models (e.g., linear, nonlinear, and finite mixture models) in estimating the distributions of 6-h and 24-h intensity change, lifetime maximum intensity, and landfall intensity, etc. Here we compare MeHiM with various dynamical models, including a global climate model [High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR)], a regional hurricane model (Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model), and a simplified hurricane dynamic model [Coupled Hurricane Intensity Prediction System (CHIPS)] and its newly developed fast simulator. The MeHiM developed based on the reanalysis data is applied to estimate the intensity of simulated storms to compare with the dynamical-model predictions under the current climate. The dependences of hurricanes on the environment under current and future projected climates in the various models will also be compared statistically.

Inferring energy dissipation from violation of the fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Wang, Shou-Wen

2018-05-01

The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.

General simulation algorithm for autocorrelated binary processes.

PubMed

Serinaldi, Francesco; Lombardo, Federico

2017-02-01

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Time-course variation of statistics embedded in music: Corpus study on implicit learning and knowledge.

PubMed

Daikoku, Tatsuya

2018-01-01

Learning and knowledge of transitional probability in sequences like music, called statistical learning and knowledge, are considered implicit processes that occur without intention to learn and awareness of what one knows. This implicit statistical knowledge can be alternatively expressed via abstract medium such as musical melody, which suggests this knowledge is reflected in melodies written by a composer. This study investigates how statistics in music vary over a composer's lifetime. Transitional probabilities of highest-pitch sequences in Ludwig van Beethoven's Piano Sonata were calculated based on different hierarchical Markov models. Each interval pattern was ordered based on the sonata opus number. The transitional probabilities of sequential patterns that are musical universal in music gradually decreased, suggesting that time-course variations of statistics in music reflect time-course variations of a composer's statistical knowledge. This study sheds new light on novel methodologies that may be able to evaluate the time-course variation of composer's implicit knowledge using musical scores.

Transition model for ricin-aptamer interactions with multiple pathways and energy barriers

NASA Astrophysics Data System (ADS)

Wang, Bin; Xu, Bingqian

2014-02-01

We develop a transition model to interpret single-molecule ricin-aptamer interactions with multiple unbinding pathways and energy barriers measured by atomic force microscopy dynamic force spectroscopy. Molecular simulations establish the relationship between binding conformations and the corresponding unbinding pathways. Each unbinding pathway follows a Bell-Evans multiple-barrier model. Markov-type transition matrices are developed to analyze the redistribution of unbinding events among the pathways under different loading rates. Our study provides detailed information about complex behaviors in ricin-aptamer unbinding events.

Predictability of Circulation Transitions (Observed and Modeled): Non-diffusive Dynamics, Markov Chains and Error Growth.

NASA Astrophysics Data System (ADS)

Straus, D. M.

2006-12-01

The transitions between portions of the state space of the large-scale flow is studied from daily wintertime data over the Pacific North America region using the NCEP reanalysis data set (54 winters) and very large suites of hindcasts made with the COLA atmospheric GCM with observed SST (55 members for each of 18 winters). The partition of the large-scale state space is guided by cluster analysis, whose statistical significance and relationship to SST is reviewed (Straus and Molteni, 2004; Straus, Corti and Molteni, 2006). The determination of the global nature of the flow through state space is studied using Markov Chains (Crommelin, 2004). In particular the non-diffusive part of the flow is contrasted in nature (small data sample) and the AGCM (large data sample). The intrinsic error growth associated with different portions of the state space is studied through sets of identical twin AGCM simulations. The goal is to obtain realistic estimates of predictability times for large-scale transitions that should be useful in long-range forecasting.

Markov chain algorithms: a template for building future robust low-power systems

PubMed Central

Deka, Biplab; Birklykke, Alex A.; Duwe, Henry; Mansinghka, Vikash K.; Kumar, Rakesh

2014-01-01

Although computational systems are looking towards post CMOS devices in the pursuit of lower power, the expected inherent unreliability of such devices makes it difficult to design robust systems without additional power overheads for guaranteeing robustness. As such, algorithmic structures with inherent ability to tolerate computational errors are of significant interest. We propose to cast applications as stochastic algorithms based on Markov chains (MCs) as such algorithms are both sufficiently general and tolerant to transition errors. We show with four example applications—Boolean satisfiability, sorting, low-density parity-check decoding and clustering—how applications can be cast as MC algorithms. Using algorithmic fault injection techniques, we demonstrate the robustness of these implementations to transition errors with high error rates. Based on these results, we make a case for using MCs as an algorithmic template for future robust low-power systems. PMID:24842030

A hidden Markov model approach to neuron firing patterns.

PubMed Central

Camproux, A C; Saunier, F; Chouvet, G; Thalabard, J C; Thomas, G

1996-01-01

Analysis and characterization of neuronal discharge patterns are of interest to neurophysiologists and neuropharmacologists. In this paper we present a hidden Markov model approach to modeling single neuron electrical activity. Basically the model assumes that each interspike interval corresponds to one of several possible states of the neuron. Fitting the model to experimental series of interspike intervals by maximum likelihood allows estimation of the number of possible underlying neuron states, the probability density functions of interspike intervals corresponding to each state, and the transition probabilities between states. We present an application to the analysis of recordings of a locus coeruleus neuron under three pharmacological conditions. The model distinguishes two states during halothane anesthesia and during recovery from halothane anesthesia, and four states after administration of clonidine. The transition probabilities yield additional insights into the mechanisms of neuron firing. Images FIGURE 3 PMID:8913581

Understanding eye movements in face recognition using hidden Markov models.

PubMed

Chuk, Tim; Chan, Antoni B; Hsiao, Janet H

2014-09-16

We use a hidden Markov model (HMM) based approach to analyze eye movement data in face recognition. HMMs are statistical models that are specialized in handling time-series data. We conducted a face recognition task with Asian participants, and model each participant's eye movement pattern with an HMM, which summarized the participant's scan paths in face recognition with both regions of interest and the transition probabilities among them. By clustering these HMMs, we showed that participants' eye movements could be categorized into holistic or analytic patterns, demonstrating significant individual differences even within the same culture. Participants with the analytic pattern had longer response times, but did not differ significantly in recognition accuracy from those with the holistic pattern. We also found that correct and wrong recognitions were associated with distinctive eye movement patterns; the difference between the two patterns lies in the transitions rather than locations of the fixations alone. © 2014 ARVO.

Incorporating teleconnection information into reservoir operating policies using Stochastic Dynamic Programming and a Hidden Markov Model

NASA Astrophysics Data System (ADS)

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 to both the El Niño Southern Oscillation and the Indian Ocean Dipole influence local hydro-meteorological processes; statistically significant lag correlations have already been established. Simulation of the derived operating policies, which are benchmarked against standard policies conditioned on the reservoir storage and the antecedent inflow, demonstrates the potential of the proposed approach. Future research will further develop the model for sensitivity analysis and regional studies examining the economic value of incorporating long range forecasts into reservoir operation.

Exact goodness-of-fit tests for Markov chains.

PubMed

Besag, J; Mondal, D

2013-06-01

Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.

Simulating reservoir lithologies by an actively conditioned Markov chain model

NASA Astrophysics Data System (ADS)

Feng, Runhai; Luthi, Stefan M.; Gisolf, Dries

2018-06-01

The coupled Markov chain model can be used to simulate reservoir lithologies between wells, by conditioning them on the observed data in the cored wells. However, with this method, only the state at the same depth as the current cell is going to be used for conditioning, which may be a problem if the geological layers are dipping. This will cause the simulated lithological layers to be broken or to become discontinuous across the reservoir. In order to address this problem, an actively conditioned process is proposed here, in which a tolerance angle is predefined. The states contained in the region constrained by the tolerance angle will be employed for conditioning in the horizontal chain first, after which a coupling concept with the vertical chain is implemented. In order to use the same horizontal transition matrix for different future states, the tolerance angle has to be small. This allows the method to work in reservoirs without complex structures caused by depositional processes or tectonic deformations. Directional artefacts in the modeling process are avoided through a careful choice of the simulation path. The tolerance angle and dipping direction of the strata can be obtained from a correlation between wells, or from seismic data, which are available in most hydrocarbon reservoirs, either by interpretation or by inversion that can also assist the construction of a horizontal probability matrix.

A comparison between MS-VECM and MS-VECMX on economic time series data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Wai; Ismail, Mohd Tahir; Sek, Siok-Kun

2014-07-01

Multivariate Markov switching models able to provide useful information on the study of structural change data since the regime switching model can analyze the time varying data and capture the mean and variance in the series of dependence structure. This paper will investigates the oil price and gold price effects on Malaysia, Singapore, Thailand and Indonesia stock market returns. Two forms of Multivariate Markov switching models are used namely the mean adjusted heteroskedasticity Markov Switching Vector Error Correction Model (MSMH-VECM) and the mean adjusted heteroskedasticity Markov Switching Vector Error Correction Model with exogenous variable (MSMH-VECMX). The reason for using these two models are to capture the transition probabilities of the data since real financial time series data always exhibit nonlinear properties such as regime switching, cointegrating relations, jumps or breaks passing the time. A comparison between these two models indicates that MSMH-VECM model able to fit the time series data better than the MSMH-VECMX model. In addition, it was found that oil price and gold price affected the stock market changes in the four selected countries.

Metadynamics Enhanced Markov Modeling of Protein Dynamics.

PubMed

Biswas, Mithun; Lickert, Benjamin; Stock, Gerhard

2018-05-31

Enhanced sampling techniques represent a versatile approach to account for rare conformational transitions in biomolecules. A particularly promising strategy is to combine massive parallel computing of short molecular dynamics (MD) trajectories (to sample the free energy landscape of the system) with Markov state modeling (to rebuild the kinetics from the sampled data). To obtain well-distributed initial structures for the short trajectories, it is proposed to employ metadynamics MD, which quickly sweeps through the entire free energy landscape of interest. Being only used to generate initial conformations, the implementation of metadynamics can be simple and fast. The conformational dynamics of helical peptide Aib 9 is adopted to discuss various technical issues of the approach, including metadynamics settings, minimal number and length of short MD trajectories, and the validation of the resulting Markov models. Using metadynamics to launch some thousands of nanosecond trajectories, several Markov state models are constructed that reveal that previous unbiased MD simulations of in total 16 μs length cannot provide correct equilibrium populations or qualitative features of the pathway distribution of the short peptide.

Entropy, complexity, and Markov diagrams for random walk cancer models

PubMed Central

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-01-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

Reverse engineering a social agent-based hidden markov model--visage.

PubMed

Chen, Hung-Ching Justin; Goldberg, Mark; Magdon-Ismail, Malik; Wallace, William A

2008-12-01

We present a machine learning approach to discover the agent dynamics that drives the evolution of the social groups in a community. We set up the problem by introducing an agent-based hidden Markov model for the agent dynamics: an agent's actions are determined by micro-laws. Nonetheless, We learn the agent dynamics from the observed communications without knowing state transitions. Our approach is to identify the appropriate micro-laws corresponding to an identification of the appropriate parameters in the model. The model identification problem is then formulated as a mixed optimization problem. To solve the problem, we develop a multistage learning process for determining the group structure, the group evolution, and the micro-laws of a community based on the observed set of communications among actors, without knowing the semantic contents. Finally, to test the quality of our approximations and the feasibility of the approach, we present the results of extensive experiments on synthetic data as well as the results on real communities, such as Enron email and Movie newsgroups. Insight into agent dynamics helps us understand the driving forces behind social evolution.

Optimizing Likelihood Models for Particle Trajectory Segmentation in Multi-State Systems.

PubMed

Young, Dylan Christopher; Scrimgeour, Jan

2018-06-19

Particle tracking offers significant insight into the molecular mechanics that govern the behav- ior of living cells. The analysis of molecular trajectories that transition between different motive states, such as diffusive, driven and tethered modes, is of considerable importance, with even single trajectories containing significant amounts of information about a molecule's environment and its interactions with cellular structures. Hidden Markov models (HMM) have been widely adopted to perform the segmentation of such complex tracks. In this paper, we show that extensive analysis of hidden Markov model outputs using data derived from multi-state Brownian dynamics simulations can be used both for the optimization of the likelihood models used to describe the states of the system and for characterization of the technique's failure mechanisms. This analysis was made pos- sible by the implementation of parallelized adaptive direct search algorithm on a Nvidia graphics processing unit. This approach provides critical information for the visualization of HMM failure and successful design of particle tracking experiments where trajectories contain multiple mobile states. © 2018 IOP Publishing Ltd.

Leaf optical system modeled as a stochastic process. [solar radiation interaction with terrestrial vegetation

NASA Technical Reports Server (NTRS)

Tucker, C. J.; Garratt, M. W.

1977-01-01

A stochastic leaf radiation model based upon physical and physiological properties of dicot leaves has been developed. The model accurately predicts the absorbed, reflected, and transmitted radiation of normal incidence as a function of wavelength resulting from the leaf-irradiance interaction over the spectral interval of 0.40-2.50 micron. The leaf optical system has been represented as Markov process with a unique transition matrix at each 0.01-micron increment between 0.40 micron and 2.50 micron. Probabilities are calculated at every wavelength interval from leaf thickness, structure, pigment composition, and water content. Simulation results indicate that this approach gives accurate estimations of actual measured values for dicot leaf absorption, reflection, and transmission as a function of wavelength.

Delirium superimposed on dementia: defining disease states and course from longitudinal measurements of a multivariate index using latent class analysis and hidden Markov chains.

PubMed

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.

Modeling carbachol-induced hippocampal network synchronization using hidden Markov models

NASA Astrophysics Data System (ADS)

Dragomir, Andrei; Akay, Yasemin M.; Akay, Metin

2010-10-01

In this work we studied the neural state transitions undergone by the hippocampal neural network using a hidden Markov model (HMM) framework. We first employed a measure based on the Lempel-Ziv (LZ) estimator to characterize the changes in the hippocampal oscillation patterns in terms of their complexity. These oscillations correspond to different modes of hippocampal network synchronization induced by the cholinergic agonist carbachol in the CA1 region of mice hippocampus. HMMs are then used to model the dynamics of the LZ-derived complexity signals as first-order Markov chains. Consequently, the signals corresponding to our oscillation recordings can be segmented into a sequence of statistically discriminated hidden states. The segmentation is used for detecting transitions in neural synchronization modes in data recorded from wild-type and triple transgenic mice models (3xTG) of Alzheimer's disease (AD). Our data suggest that transition from low-frequency (delta range) continuous oscillation mode into high-frequency (theta range) oscillation, exhibiting repeated burst-type patterns, occurs always through a mode resembling a mixture of the two patterns, continuous with burst. The relatively random patterns of oscillation during this mode may reflect the fact that the neuronal network undergoes re-organization. Further insight into the time durations of these modes (retrieved via the HMM segmentation of the LZ-derived signals) reveals that the mixed mode lasts significantly longer (p < 10-4) in 3xTG AD mice. These findings, coupled with the documented cholinergic neurotransmission deficits in the 3xTG mice model, may be highly relevant for the case of AD.

On the stochastic dissemination of faults in an admissible network

NASA Technical Reports Server (NTRS)

Kyrala, A.

1987-01-01

The dynamic distribution of faults in a general type network is discussed. The starting point is a uniquely branched network in which each pair of nodes is connected by a single branch. Mathematical expressions for the uniquely branched network transition matrix are derived to show that sufficient stationarity exists to ensure the validity of the use of the Markov Chain model to analyze networks. In addition the conditions for the use of Semi-Markov models are discussed. General mathematical expressions are derived in an examination of branch redundancy techniques commonly used to increase reliability.

Markov Chain Analysis of Musical Dice Games

NASA Astrophysics Data System (ADS)

Volchenkov, D.; Dawin, J. R.

2012-07-01

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.

Musical Markov Chains

NASA Astrophysics Data System (ADS)

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.

Chronic escitalopram treatment attenuated the accelerated rapid eye movement sleep transitions after selective rapid eye movement sleep deprivation: a model-based analysis using Markov chains.

PubMed

Kostyalik, Diána; Vas, Szilvia; Kátai, Zita; Kitka, Tamás; Gyertyán, István; Bagdy, Gyorgy; Tóthfalusi, László

2014-11-19

Shortened rapid eye movement (REM) sleep latency and increased REM sleep amount are presumed biological markers of depression. These sleep alterations are also observable in several animal models of depression as well as during the rebound sleep after selective REM sleep deprivation (RD). Furthermore, REM sleep fragmentation is typically associated with stress procedures and anxiety. The selective serotonin reuptake inhibitor (SSRI) antidepressants reduce REM sleep time and increase REM latency after acute dosing in normal condition and even during REM rebound following RD. However, their therapeutic outcome evolves only after weeks of treatment, and the effects of chronic treatment in REM-deprived animals have not been studied yet. Chronic escitalopram- (10 mg/kg/day, osmotic minipump for 24 days) or vehicle-treated rats were subjected to a 3-day-long RD on day 21 using the flower pot procedure or kept in home cage. On day 24, fronto-parietal electroencephalogram, electromyogram and motility were recorded in the first 2 h of the passive phase. The observed sleep patterns were characterized applying standard sleep metrics, by modelling the transitions between sleep phases using Markov chains and by spectral analysis. Based on Markov chain analysis, chronic escitalopram treatment attenuated the REM sleep fragmentation [accelerated transition rates between REM and non-REM (NREM) stages, decreased REM sleep residence time between two transitions] during the rebound sleep. Additionally, the antidepressant avoided the frequent awakenings during the first 30 min of recovery period. The spectral analysis showed that the SSRI prevented the RD-caused elevation in theta (5-9 Hz) power during slow-wave sleep. Conversely, based on the aggregate sleep metrics, escitalopram had only moderate effects and it did not significantly attenuate the REM rebound after RD. In conclusion, chronic SSRI treatment is capable of reducing several effects on sleep which might be the consequence of the sub-chronic stress caused by the flower pot method. These data might support the antidepressant activity of SSRIs, and may allude that investigating the rebound period following the flower pot protocol could be useful to detect antidepressant drug response. Markov analysis is a suitable method to study the sleep pattern.

MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes

USGS Publications Warehouse

Williams, B.K.

1988-01-01

Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.

Markov and non-Markov processes in complex systems by the dynamical information entropy

NASA Astrophysics Data System (ADS)

Yulmetyev, R. M.; Gafarov, F. M.

1999-12-01

We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.

Open Quantum Systems and Classical Trajectories

NASA Astrophysics Data System (ADS)

Rebolledo, Rolando

2004-09-01

A Quantum Markov Semigroup consists of a family { T} = ({ T}t)_{t ∈ B R+} of normal ω*- continuous completely positive maps on a von Neumann algebra 𝔐 which preserve the unit and satisfy the semigroup property. This class of semigroups has been extensively used to represent open quantum systems. This article is aimed at studying the existence of a { T} -invariant abelian subalgebra 𝔄 of 𝔐. When this happens, the restriction of { T}t to 𝔄 defines a classical Markov semigroup T = (Tt)t ∈ ∝ + say, associated to a classical Markov process X = (Xt)t ∈ ∝ +. The structure (𝔄, T, X) unravels the quantum Markov semigroup { T} , providing a bridge between open quantum systems and classical stochastic processes.

Envelopes of Sets of Measures, Tightness, and Markov Control Processes

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

Gonzalez-Hernandez, J.; Hernandez-Lerma, O.

1999-11-15

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.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.

PubMed

Kapfer, Sebastian C; Krauth, Werner

2017-12-15

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.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

NASA Astrophysics Data System (ADS)

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.

A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

NASA Astrophysics Data System (ADS)

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.

VAMPnets for deep learning of molecular kinetics.

PubMed

Mardt, Andreas; Pasquali, Luca; Wu, Hao; Noé, Frank

2018-01-02

There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.

Markov modeling for the neurosurgeon: a review of the literature and an introduction to cost-effectiveness research.

PubMed

Wali, Arvin R; Brandel, Michael G; Santiago-Dieppa, David R; Rennert, Robert C; Steinberg, Jeffrey A; Hirshman, Brian R; Murphy, James D; Khalessi, Alexander A

2018-05-01

OBJECTIVE Markov modeling is a clinical research technique that allows competing medical strategies to be mathematically assessed in order to identify the optimal allocation of health care resources. The authors present a review of the recently published neurosurgical literature that employs Markov modeling and provide a conceptual framework with which to evaluate, critique, and apply the findings generated from health economics research. METHODS The PubMed online database was searched to identify neurosurgical literature published from January 2010 to December 2017 that had utilized Markov modeling for neurosurgical cost-effectiveness studies. Included articles were then assessed with regard to year of publication, subspecialty of neurosurgery, decision analytical techniques utilized, and source information for model inputs. RESULTS A total of 55 articles utilizing Markov models were identified across a broad range of neurosurgical subspecialties. Sixty-five percent of the papers were published within the past 3 years alone. The majority of models derived health transition probabilities, health utilities, and cost information from previously published studies or publicly available information. Only 62% of the studies incorporated indirect costs. Ninety-three percent of the studies performed a 1-way or 2-way sensitivity analysis, and 67% performed a probabilistic sensitivity analysis. A review of the conceptual framework of Markov modeling and an explanation of the different terminology and methodology are provided. CONCLUSIONS As neurosurgeons continue to innovate and identify novel treatment strategies for patients, Markov modeling will allow for better characterization of the impact of these interventions on a patient and societal level. The aim of this work is to equip the neurosurgical readership with the tools to better understand, critique, and apply findings produced from cost-effectiveness research.

Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks

PubMed Central

Gao, Shouwan; Chen, Pengpeng; Huang, Dan; Niu, Qiang

2016-01-01

This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples. PMID:27104541

Site-percolation threshold of carbon nanotube fibers-Fast inspection of percolation with Markov stochastic theory

NASA Astrophysics Data System (ADS)

Xu, Fangbo; Xu, Zhiping; Yakobson, Boris I.

2014-08-01

We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix-vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at pc=0.1533±0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to pc).

Assessment of variations in control of asthma over time.

PubMed

Combescure, C; Chanez, P; Saint-Pierre, P; Daurès, J P; Proudhon, H; Godard, P

2003-08-01

Control and severity of asthma are two different but complementary concepts. The severity of asthma could influence the control over time. The aim of this study was to demonstrate this relationship. A total 365 patients with persistent asthma (severity) were enrolled and followed-up prospectively. Data were analysed using a continuous time homogeneous Markov model of the natural history of asthma. Control of asthma was defined according to three health states which were qualified: optimal, suboptimal and unacceptable control (states 1, 2 and 3). Transition forces (denoted lambda(ij) from state i to state j) and transition probabilities between control states were assessed and the results stratified by asthma severity were compared. Models were validated by comparing expected and observed numbers of patients in the different states. Transition probabilities stabilised between 100-250 days and more rapidly in patients with mild-to-moderate asthma. Patients with mild-to-moderate asthma in suboptimal or unacceptable control had a high probability of transition directly to optimal control. Patients with severe asthma had a tendency to remain in unacceptable control. A Markov model is a useful tool to model the control of asthma over time. Severity modified clearly the health states. It could be used to compare the performance of different approaches to asthma management.

A nonparametric test for Markovianity in the illness-death model.

PubMed

Rodríguez-Girondo, Mar; de Uña-Álvarez, Jacobo

2012-12-30

Multistate models are useful tools for modeling disease progression when survival is the main outcome, but several intermediate events of interest are observed during the follow-up time. The illness-death model is a special multistate model with important applications in the biomedical literature. It provides a suitable representation of the individual's history when a unique intermediate event can be experienced before the main event of interest. Nonparametric estimation of transition probabilities in this and other multistate models is usually performed through the Aalen-Johansen estimator under a Markov assumption. The Markov assumption claims that given the present state, the future evolution of the illness is independent of the states previously visited and the transition times among them. However, this assumption fails in some applications, leading to inconsistent estimates. In this paper, we provide a new approach for testing Markovianity in the illness-death model. The new method is based on measuring the future-past association along time. This results in a detailed inspection of the process, which often reveals a non-Markovian behavior with different trends in the association measure. A test of significance for zero future-past association at each time point is introduced, and a significance trace is proposed accordingly. Besides, we propose a global test for Markovianity based on a supremum-type test statistic. The finite sample performance of the test is investigated through simulations. We illustrate the new method through the analysis of two biomedical data analysis. Copyright © 2012 John Wiley & Sons, Ltd.

SIMULATION FROM ENDPOINT-CONDITIONED, CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE, WITH APPLICATIONS TO MOLECULAR EVOLUTION.

PubMed

Hobolth, Asger; Stone, Eric A

2009-09-01

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.

Vulnerability to paroxysmal oscillations in delayed neural networks: A basis for nocturnal frontal lobe epilepsy?

NASA Astrophysics Data System (ADS)

Quan, Austin; Osorio, Ivan; Ohira, Toru; Milton, John

2011-12-01

Resonance can occur in bistable dynamical systems due to the interplay between noise and delay (τ) in the absence of a periodic input. We investigate resonance in a two-neuron model with mutual time-delayed inhibitory feedback. For appropriate choices of the parameters and inputs three fixed-point attractors co-exist: two are stable and one is unstable. In the absence of noise, delay-induced transient oscillations (referred to herein as DITOs) arise whenever the initial function is tuned sufficiently close to the unstable fixed-point. In the presence of noisy perturbations, DITOs arise spontaneously. Since the correlation time for the stationary dynamics is ˜τ, we approximated a higher order Markov process by a three-state Markov chain model by rescaling time as t → 2sτ, identifying the states based on whether the sub-intervals were completely confined to one basin of attraction (the two stable attractors) or straddled the separatrix, and then determining the transition probability matrix empirically. The resultant Markov chain model captured the switching behaviors including the statistical properties of the DITOs. Our observations indicate that time-delayed and noisy bistable dynamical systems are prone to generate DITOs as switches between the two attractors occur. Bistable systems arise transiently in situations when one attractor is gradually replaced by another. This may explain, for example, why seizures in certain epileptic syndromes tend to occur as sleep stages change.

The Markov process admits a consistent steady-state thermodynamic formalism

NASA Astrophysics Data System (ADS)

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.

Medical imaging feasibility in body fluids using Markov chains

NASA Astrophysics Data System (ADS)

Kavehrad, M.; Armstrong, A. D.

2017-02-01

A relatively wide field-of-view and high resolution imaging is necessary for navigating the scope within the body, inspecting tissue, diagnosing disease, and guiding surgical interventions. As the large number of modes available in the multimode fibers (MMF) provides higher resolution, MMFs could replace the millimeters-thick bundles of fibers and lenses currently used in endoscopes. However, attributes of body fluids and obscurants such as blood, impose perennial limitations on resolution and reliability of optical imaging inside human body. To design and evaluate optimum imaging techniques that operate under realistic body fluids conditions, a good understanding of the channel (medium) behavior is necessary. In most prior works, Monte-Carlo Ray Tracing (MCRT) algorithm has been used to analyze the channel behavior. This task is quite numerically intensive. The focus of this paper is on investigating the possibility of simplifying this task by a direct extraction of state transition matrices associated with standard Markov modeling from the MCRT computer simulations programs. We show that by tracing a photon's trajectory in the body fluids via a Markov chain model, the angular distribution can be calculated by simple matrix multiplications. We also demonstrate that the new approach produces result that are close to those obtained by MCRT and other known methods. Furthermore, considering the fact that angular, spatial, and temporal distributions of energy are inter-related, mixing time of Monte- Carlo Markov Chain (MCMC) for different types of liquid concentrations is calculated based on Eigen-analysis of the state transition matrix and possibility of imaging in scattering media are investigated. To this end, we have started to characterize the body fluids that reduce the resolution of imaging [1].

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Structure and Randomness of Continuous-Time, Discrete-Event Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2017-10-01

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ɛ -machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

Many roads to synchrony: natural time scales and their algorithms.

PubMed

James, Ryan G; Mahoney, John R; Ellison, Christopher J; Crutchfield, James P

2014-04-01

We consider two important time scales-the Markov and cryptic orders-that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the ε-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the ε-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.

Using the Pearson Distribution for Synthesis of the Suboptimal Algorithms for Filtering Multi-Dimensional Markov Processes

NASA Astrophysics Data System (ADS)

Mit'kin, A. S.; Pogorelov, V. A.; Chub, E. G.

2015-08-01

We consider the method of constructing the suboptimal filter on the basis of approximating the a posteriori probability density of the multidimensional Markov process by the Pearson distributions. The proposed method can efficiently be used for approximating asymmetric, excessive, and finite densities.

A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms.

PubMed

Balbi, Pietro; Massobrio, Paolo; Hellgren Kotaleski, Jeanette

2017-09-01

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour.

Stochastic modelling of a single ion channel: an alternating renewal approach with application to limited time resolution.

PubMed

Milne, R K; Yeo, G F; Edeson, R O; Madsen, B W

1988-04-22

Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.

INCLUDING TRANSITION PROBABILITIES IN NEST SURVIVAL ESTIMATION: A MAYFIELD MARKOV CHAIN

EPA Science Inventory

This manuscript is primarily an exploration of the statistical properties of nest-survival estimates for terrestrial songbirds. The Mayfield formulation described herein should allow researchers to test for complicated effects of stressors on daily survival and overall success, i...

Crime Specialization, Seriousness Progression, and Markov Chains.

ERIC Educational Resources Information Center

Holland, Terrill R.; McGarvey, Bill

1984-01-01

Subjected sequences of violent and nonviolent offenses to log-linear analyses of the stabilities and magnitudes of their transition probabilities. Results were seen to support previous research in which nonviolent criminality emerged as more fundamental than violence in potential for pattern development. (LLL)

Hidden Markov models of biological primary sequence information.

PubMed Central

Baldi, P; Chauvin, Y; Hunkapiller, T; McClure, M A

1994-01-01

Hidden Markov model (HMM) techniques are used to model families of biological sequences. A smooth and convergent algorithm is introduced to iteratively adapt the transition and emission parameters of the models from the examples in a given family. The HMM approach is applied to three protein families: globins, immunoglobulins, and kinases. In all cases, the models derived capture the important statistical characteristics of the family and can be used for a number of tasks, including multiple alignments, motif detection, and classification. For K sequences of average length N, this approach yields an effective multiple-alignment algorithm which requires O(KN2) operations, linear in the number of sequences. PMID:8302831

Vulnerability of networks of interacting Markov chains.

PubMed

Kocarev, L; Zlatanov, N; Trajanov, D

2010-05-13

The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.

Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.

PubMed

Reich, W; Scheuermann, G

2012-12-01

Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.

Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

NASA Astrophysics Data System (ADS)

Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji

2015-12-01

Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.

Markov Transition Model to Dementia with Death as a Competing Event.

PubMed

Wei, Shaoceng; Xu, Liou; Kryscio, Richard J

2014-12-01

This study evaluates the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. A multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model the cognitive panel data; transitions among states depend on four covariates age, education, prior state (intact cognition, or M.C.I., or G.I.) and the presence/absence of an apolipoprotein E-4 allele (APOE4). A Weibull model and a Cox proportional hazards (Cox PH) model are used to fit the survival from death based on age at entry and the APOE4 status. A shared random effect correlates this survival time with the transition model. Simulation studies determine the sensitivity of the maximum likelihood estimates to the violations of the Weibull and Cox PH model assumptions. Results are illustrated with an application to the Nun Study, a longitudinal cohort of 672 participants 75+ years of age at baseline and followed longitudinally with up to ten cognitive assessments per nun.

Markov Transition Model to Dementia with Death as a Competing Event

PubMed Central

Wei, Shaoceng; Xu, Liou; Kryscio, Richard J.

2014-01-01

This study evaluates the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. A multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model the cognitive panel data; transitions among states depend on four covariates age, education, prior state (intact cognition, or M.C.I., or G.I.) and the presence/absence of an apolipoprotein E-4 allele (APOE4). A Weibull model and a Cox proportional hazards (Cox PH) model are used to fit the survival from death based on age at entry and the APOE4 status. A shared random effect correlates this survival time with the transition model. Simulation studies determine the sensitivity of the maximum likelihood estimates to the violations of the Weibull and Cox PH model assumptions. Results are illustrated with an application to the Nun Study, a longitudinal cohort of 672 participants 75+ years of age at baseline and followed longitudinally with up to ten cognitive assessments per nun. PMID:25110380

Capturing the state transitions of seizure-like events using Hidden Markov models.

PubMed

Guirgis, Mirna; Serletis, Demitre; Carlen, Peter L; Bardakjian, Berj L

2011-01-01

The purpose of this study was to investigate the number of states present in the progression of a seizure-like event (SLE). Of particular interest is to determine if there are more than two clearly defined states, as this would suggest that there is a distinct state preceding an SLE. Whole-intact hippocampus from C57/BL mice was used to model epileptiform activity induced by the perfusion of a low Mg(2+)/high K(+) solution while extracellular field potentials were recorded from CA3 pyramidal neurons. Hidden Markov models (HMM) were used to model the state transitions of the recorded SLEs by incorporating various features of the Hilbert transform into the training algorithm; specifically, 2- and 3-state HMMs were explored. Although the 2-state model was able to distinguish between SLE and nonSLE behavior, it provided no improvements compared to visual inspection alone. However, the 3-state model was able to capture two distinct nonSLE states that visual inspection failed to discriminate. Moreover, by developing an HMM based system a priori knowledge of the state transitions was not required making this an ideal platform for seizure prediction algorithms.

Density Control of Multi-Agent Systems with Safety Constraints: A Markov Chain Approach

NASA Astrophysics Data System (ADS)

Demirer, Nazli

The control of systems with autonomous mobile agents has been a point of interest recently, with many applications like surveillance, coverage, searching over an area with probabilistic target locations or exploring an area. In all of these applications, the main goal of the swarm is to distribute itself over an operational space to achieve mission objectives specified by the density of swarm. This research focuses on the problem of controlling the distribution of multi-agent systems considering a hierarchical control structure where the whole swarm coordination is achieved at the high-level and individual vehicle/agent control is managed at the low-level. High-level coordination algorithms uses macroscopic models that describes the collective behavior of the whole swarm and specify the agent motion commands, whose execution will lead to the desired swarm behavior. The low-level control laws execute the motion to follow these commands at the agent level. The main objective of this research is to develop high-level decision control policies and algorithms to achieve physically realizable commanding of the agents by imposing mission constraints on the distribution. We also make some connections with decentralized low-level motion control. This dissertation proposes a Markov chain based method to control the density distribution of the whole system where the implementation can be achieved in a decentralized manner with no communication between agents since establishing communication with large number of agents is highly challenging. The ultimate goal is to guide the overall density distribution of the system to a prescribed steady-state desired distribution while satisfying desired transition and safety constraints. Here, the desired distribution is determined based on the mission requirements, for example in the application of area search, the desired distribution should match closely with the probabilistic target locations. The proposed method is applicable for both systems with a single agent and systems with large number of agents due to the probabilistic nature, where the probability distribution of each agent's state evolves according to a finite-state and discrete-time Markov chain (MC). Hence, designing proper decision control policies requires numerically tractable solution methods for the synthesis of Markov chains. The synthesis problem has the form of a Linear Matrix Inequality Problem (LMI), with LMI formulation of the constraints. To this end, we propose convex necessary and sufficient conditions for safety constraints in Markov chains, which is a novel result in the Markov chain literature. In addition to LMI-based, offline, Markov matrix synthesis method, we also propose a QP-based, online, method to compute a time-varying Markov matrix based on the real-time density feedback. Both problems are convex optimization problems that can be solved in a reliable and tractable way, utilizing existing tools in the literature. A Low Earth Orbit (LEO) swarm simulations are presented to validate the effectiveness of the proposed algorithms. Another problem tackled as a part of this research is the generalization of the density control problem to autonomous mobile agents with two control modes: ON and OFF. Here, each mode consists of a (possibly overlapping) finite set of actions, that is, there exist a set of actions for the ON mode and another set for the OFF mode. We give formulation for a new Markov chain synthesis problem, with additional measurements for the state transitions, where a policy is designed to ensure desired safety and convergence properties for the underlying Markov chain.

Free-energy landscape of ion-channel voltage-sensor–domain activation

PubMed Central

Delemotte, Lucie; Kasimova, Marina A.; Klein, Michael L.; Tarek, Mounir; Carnevale, Vincenzo

2015-01-01

Voltage sensor domains (VSDs) are membrane-bound protein modules that confer voltage sensitivity to membrane proteins. VSDs sense changes in the transmembrane voltage and convert the electrical signal into a conformational change called activation. Activation involves a reorganization of the membrane protein charges that is detected experimentally as transient currents. These so-called gating currents have been investigated extensively within the theoretical framework of so-called discrete-state Markov models (DMMs), whereby activation is conceptualized as a series of transitions across a discrete set of states. Historically, the interpretation of DMM transition rates in terms of transition state theory has been instrumental in shaping our view of the activation process, whose free-energy profile is currently envisioned as composed of a few local minima separated by steep barriers. Here we use atomistic level modeling and well-tempered metadynamics to calculate the configurational free energy along a single transition from first principles. We show that this transition is intrinsically multidimensional and described by a rough free-energy landscape. Remarkably, a coarse-grained description of the system, based on the use of the gating charge as reaction coordinate, reveals a smooth profile with a single barrier, consistent with phenomenological models. Our results bridge the gap between microscopic and macroscopic descriptions of activation dynamics and show that choosing the gating charge as reaction coordinate masks the topological complexity of the network of microstates participating in the transition. Importantly, full characterization of the latter is a prerequisite to rationalize modulation of this process by lipids, toxins, drugs, and genetic mutations. PMID:25535341

Free-energy landscape of ion-channel voltage-sensor-domain activation.

PubMed

Delemotte, Lucie; Kasimova, Marina A; Klein, Michael L; Tarek, Mounir; Carnevale, Vincenzo

2015-01-06

Voltage sensor domains (VSDs) are membrane-bound protein modules that confer voltage sensitivity to membrane proteins. VSDs sense changes in the transmembrane voltage and convert the electrical signal into a conformational change called activation. Activation involves a reorganization of the membrane protein charges that is detected experimentally as transient currents. These so-called gating currents have been investigated extensively within the theoretical framework of so-called discrete-state Markov models (DMMs), whereby activation is conceptualized as a series of transitions across a discrete set of states. Historically, the interpretation of DMM transition rates in terms of transition state theory has been instrumental in shaping our view of the activation process, whose free-energy profile is currently envisioned as composed of a few local minima separated by steep barriers. Here we use atomistic level modeling and well-tempered metadynamics to calculate the configurational free energy along a single transition from first principles. We show that this transition is intrinsically multidimensional and described by a rough free-energy landscape. Remarkably, a coarse-grained description of the system, based on the use of the gating charge as reaction coordinate, reveals a smooth profile with a single barrier, consistent with phenomenological models. Our results bridge the gap between microscopic and macroscopic descriptions of activation dynamics and show that choosing the gating charge as reaction coordinate masks the topological complexity of the network of microstates participating in the transition. Importantly, full characterization of the latter is a prerequisite to rationalize modulation of this process by lipids, toxins, drugs, and genetic mutations.

Deducing the Kinetics of Protein Synthesis In Vivo from the Transition Rates Measured In Vitro

PubMed Central

Rudorf, Sophia; Thommen, Michael; Rodnina, Marina V.; Lipowsky, Reinhard

2014-01-01

The molecular machinery of life relies on complex multistep processes that involve numerous individual transitions, such as molecular association and dissociation steps, chemical reactions, and mechanical movements. The corresponding transition rates can be typically measured in vitro but not in vivo. Here, we develop a general method to deduce the in-vivo rates from their in-vitro values. The method has two basic components. First, we introduce the kinetic distance, a new concept by which we can quantitatively compare the kinetics of a multistep process in different environments. The kinetic distance depends logarithmically on the transition rates and can be interpreted in terms of the underlying free energy barriers. Second, we minimize the kinetic distance between the in-vitro and the in-vivo process, imposing the constraint that the deduced rates reproduce a known global property such as the overall in-vivo speed. In order to demonstrate the predictive power of our method, we apply it to protein synthesis by ribosomes, a key process of gene expression. We describe the latter process by a codon-specific Markov model with three reaction pathways, corresponding to the initial binding of cognate, near-cognate, and non-cognate tRNA, for which we determine all individual transition rates in vitro. We then predict the in-vivo rates by the constrained minimization procedure and validate these rates by three independent sets of in-vivo data, obtained for codon-dependent translation speeds, codon-specific translation dynamics, and missense error frequencies. In all cases, we find good agreement between theory and experiment without adjusting any fit parameter. The deduced in-vivo rates lead to smaller error frequencies than the known in-vitro rates, primarily by an improved initial selection of tRNA. The method introduced here is relatively simple from a computational point of view and can be applied to any biomolecular process, for which we have detailed information about the in-vitro kinetics. PMID:25358034

Markov Processes: Exploring the Use of Dynamic Visualizations to Enhance Student Understanding

ERIC Educational Resources Information Center

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…

On the assumptions underlying milestoning.

PubMed

Vanden-Eijnden, Eric; Venturoli, Maddalena; Ciccotti, Giovanni; Elber, Ron

2008-11-07

Milestoning is a procedure to compute the time evolution of complicated processes such as barrier crossing events or long diffusive transitions between predefined states. Milestoning reduces the dynamics to transition events between intermediates (the milestones) and computes the local kinetic information to describe these transitions via short molecular dynamics (MD) runs between the milestones. The procedure relies on the ability to reinitialize MD trajectories on the milestones to get the right kinetic information about the transitions. It also rests on the assumptions that the transition events between successive milestones and the time lags between these transitions are statistically independent. In this paper, we analyze the validity of these assumptions. We show that sets of optimal milestones exist, i.e., sets such that successive transitions are indeed statistically independent. The proof of this claim relies on the results of transition path theory and uses the isocommittor surfaces of the reaction as milestones. For systems in the overdamped limit, we also obtain the probability distribution to reinitialize the MD trajectories on the milestones, and we discuss why this distribution is not available in closed form for systems with inertia. We explain why the time lags between transitions are not statistically independent even for optimal milestones, but we show that working with such milestones allows one to compute mean first passage times between milestones exactly. Finally, we discuss some practical implications of our results and we compare milestoning with Markov state models in view of our findings.

Electrophysiological correlates reflect the integration of model-based and model-free decision information.

PubMed

Eppinger, Ben; Walter, Maik; Li, Shu-Chen

2017-04-01

In this study, we investigated the interplay of habitual (model-free) and goal-directed (model-based) decision processes by using a two-stage Markov decision task in combination with event-related potentials (ERPs) and computational modeling. To manipulate the demands on model-based decision making, we applied two experimental conditions with different probabilities of transitioning from the first to the second stage of the task. As we expected, when the stage transitions were more predictable, participants showed greater model-based (planning) behavior. Consistent with this result, we found that stimulus-evoked parietal (P300) activity at the second stage of the task increased with the predictability of the state transitions. However, the parietal activity also reflected model-free information about the expected values of the stimuli, indicating that at this stage of the task both types of information are integrated to guide decision making. Outcome-related ERP components only reflected reward-related processes: Specifically, a medial prefrontal ERP component (the feedback-related negativity) was sensitive to negative outcomes, whereas a component that is elicited by reward (the feedback-related positivity) increased as a function of positive prediction errors. Taken together, our data indicate that stimulus-locked parietal activity reflects the integration of model-based and model-free information during decision making, whereas feedback-related medial prefrontal signals primarily reflect reward-related decision processes.

Scalable approximate policies for Markov decision process models of hospital elective admissions.

PubMed

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.

Lotka-Volterra competition models for sessile organisms.

PubMed

Spencer, Matthew; Tanner, Jason E

2008-04-01

Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between states. In most Markov models for communities, these transition probabilities are assumed to be independent of state abundances. This assumption is often suspected to be false and is rarely justified explicitly. Here, we start with simple assumptions about the interactions among sessile organisms and derive a model in which transition probabilities depend on the abundance of destination states. This model is formulated in continuous time and is equivalent to a Lotka-Volterra competition model. We fit this model and a variety of alternatives in which transition probabilities do not depend on state abundances to a long-term coral reef data set. The Lotka-Volterra model describes the data much better than all models we consider other than a saturated model (a model with a separate parameter for each transition at each time interval, which by definition fits the data perfectly). Our approach provides a basis for further development of stochastic models of sessile communities, and many of the methods we use are relevant to other types of community. We discuss possible extensions to spatially explicit models.

Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning

PubMed Central

Matsunaga, Yasuhiro

2018-01-01

Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 μs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins. PMID:29723137

Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning.

PubMed

Matsunaga, Yasuhiro; Sugita, Yuji

2018-05-03

Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 μs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins. © 2018, Matsunaga et al.

Operational Markov Condition for Quantum Processes

NASA Astrophysics Data System (ADS)

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.

Markovian and non-Markovian light-emission channels in strained quantum wires.

PubMed

Lopez-Richard, V; González, J C; Matinaga, F M; Trallero-Giner, C; Ribeiro, E; Sousa Dias, M Rebello; Villegas-Lelovsky, L; Marques, G E

2009-09-01

We have achieved conditions to obtain optical memory effects in semiconductor nanostructures. The system is based on strained InP quantum wires where the tuning of the heavy-light valence band splitting has allowed the existence of two independent optical channels with correlated and uncorrelated excitation and light-emission processes. The presence of an optical channel that preserves the excitation memory is unambiguously corroborated by photoluminescence measurements of free-standing quantum wires under different configurations of the incoming and outgoing light polarizations in various samples. High-resolution transmission electron microscopy and electron diffraction indicate the presence of strain effects in the optical response. By using this effect and under certain growth conditions, we have shown that the optical recombination is mediated by relaxation processes with different natures: one a Markov and another with a non-Markovian signature. Resonance intersubband light-heavy hole transitions assisted by optical phonons provide the desired mechanism for the correlated non-Markovian carrier relaxation process. A multiband calculation for strained InP quantum wires was developed to account for the description of the character of the valence band states and gives quantitative support for light hole-heavy hole transitions assisted by optical phonons.

The Non-linear Trajectory of Change in Play Profiles of Three Children in Psychodynamic Play Therapy.

PubMed

Halfon, Sibel; Çavdar, Alev; Orsucci, Franco; Schiepek, Gunter K; Andreassi, Silvia; Giuliani, Alessandro; de Felice, Giulio

2016-01-01

Aim: Even though there is substantial evidence that play based therapies produce significant change, the specific play processes in treatment remain unexamined. For that purpose, processes of change in long-term psychodynamic play therapy are assessed through a repeated systematic assessment of three children's "play profiles," which reflect patterns of organization among play variables that contribute to play activity in therapy, indicative of the children's coping strategies, and an expression of their internal world. The main aims of the study are to investigate the kinds of play profiles expressed in treatment, and to test whether there is emergence of new and more adaptive play profiles using dynamic systems theory as a methodological framework. Methods and Procedures: Each session from the long-term psychodynamic treatment (mean number of sessions = 55) of three 6-year-old good outcome cases presenting with Separation Anxiety were recorded, transcribed and coded using items from the Children's Play Therapy Instrument (CPTI), created to assess the play activity of children in psychotherapy, generating discrete and measurable units of play activity arranged along a continuum of four play profiles: "Adaptive," "Inhibited," "Impulsive," and "Disorganized." The play profiles were clustered through K -means Algorithm, generating seven discrete states characterizing the course of treatment and the transitions between these states were analyzed by Markov Transition Matrix, Recurrence Quantification Analysis (RQA) and odds ratios comparing the first and second halves of psychotherapy. Results: The Markov Transitions between the states scaled almost perfectly and also showed the ergodicity of the system, meaning that the child can reach any state or shift to another one in play. The RQA and odds ratios showed two trends of change, first concerning the decrease in the use of "less adaptive" strategies, second regarding the reduction of play interruptions. Conclusion: The results support that these children express different psychic states in play, which can be captured through the lens of play profiles, and begin to modify less dysfunctional profiles over the course of treatment. The methodology employed showed the productivity of treating psychodynamic play therapy as a complex system, taking advantage of non-linear methods to study psychotherapeutic play activity.

The transitional behaviour of avalanches in cohesive granular materials

NASA Astrophysics Data System (ADS)

Quintanilla, M. A. S.; Valverde, J. M.; Castellanos, A.

2006-07-01

We present a statistical analysis of avalanches of granular materials that partially fill a slowly rotated horizontal drum. For large sized noncohesive grains the classical coherent oscillation is reproduced, consisting of a quasi-periodic succession of regularly sized avalanches. As the powder cohesiveness is increased by decreasing the particle size, we observe a gradual crossover to a complex dynamics that resembles the transitional behaviour observed in fusion plasmas. For particle size below ~50 µm, avalanches lose a characteristic size, retain a short term memory and turn gradually decorrelated in the long term as described by a Markov process. In contrast, large grains made cohesive by coating them with adhesive microparticles display a distinct phenomenology, characterized by a quasi-regular succession of well defined small precursors and large relaxation events. The transition from a one-peaked distribution (noncohesive large beads) to a flattened distribution (fine cohesive beads) passing through the two-peaked distribution of cohesive large beads had already been predicted using a coupled-map lattice model, as the relaxation mechanism of grain reorganization becomes dominant to the detriment of inertia.

A Multi-Armed Bandit Approach to Following a Markov Chain

DTIC Science & Technology

2017-06-01

focus on the House to Café transition (p1,4). We develop a Multi-Armed Bandit approach for efficiently following this target, where each state takes the...and longitude (each state corresponding to a physical location and a small set of activities). The searcher would then apply our approach on this...the target’s transition probability and the true probability over time. Further, we seek to provide upper bounds (i.e., worst case bounds) on the

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

PubMed Central

2018-01-01

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

Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks.

PubMed

Conesa, D; Martínez-Beneito, M A; Amorós, R; López-Quílez, A

2015-04-01

Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Fuzzy Markov random fields versus chains for multispectral image segmentation.

PubMed

Salzenstein, Fabien; Collet, Christophe

2006-11-01

This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.

Generalization of Faustmann's Formula for Stochastic Forest Growth and Prices with Markov Decision Process Models

Treesearch

Joseph Buongiorno

2001-01-01

Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The...

Finding the best resolution for the Kingman-Tajima coalescent: theory and applications.

PubMed

Sainudiin, Raazesh; Stadler, Tanja; Véber, Amandine

2015-05-01

Many summary statistics currently used in population genetics and in phylogenetics depend only on a rather coarse resolution of the underlying tree (the number of extant lineages, for example). Hence, for computational purposes, working directly on these resolutions appears to be much more efficient. However, this approach seems to have been overlooked in the past. In this paper, we describe six different resolutions of the Kingman-Tajima coalescent together with the corresponding Markov chains, which are essential for inference methods. Two of the resolutions are the well-known n-coalescent and the lineage death process due to Kingman. Two other resolutions were mentioned by Kingman and Tajima, but never explicitly formalized. Another two resolutions are novel, and complete the picture of a multi-resolution coalescent. For all of them, we provide the forward and backward transition probabilities, the probability of visiting a given state as well as the probability of a given realization of the full Markov chain. We also provide a description of the state-space that highlights the computational gain obtained by working with lower-resolution objects. Finally, we give several examples of summary statistics that depend on a coarser resolution of Kingman's coalescent, on which simulations are usually based.

Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

USGS Publications Warehouse

Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.

2009-01-01

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

PubMed Central

Prada-Gracia, Diego; Gómez-Gardeñes, Jesús; Echenique, Pablo; Falo, Fernando

2009-01-01

Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides. PMID:19557191

Exploring the free energy landscape: from dynamics to networks and back.

PubMed

Prada-Gracia, Diego; Gómez-Gardeñes, Jesús; Echenique, Pablo; Falo, Fernando

2009-06-01

Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.

A Hidden Markov Model for Single Particle Tracks Quantifies Dynamic Interactions between LFA-1 and the Actin Cytoskeleton

PubMed Central

Das, Raibatak; Cairo, Christopher W.; Coombs, Daniel

2009-01-01

The extraction of hidden information from complex trajectories is a continuing problem in single-particle and single-molecule experiments. Particle trajectories are the result of multiple phenomena, and new methods for revealing changes in molecular processes are needed. We have developed a practical technique that is capable of identifying multiple states of diffusion within experimental trajectories. We model single particle tracks for a membrane-associated protein interacting with a homogeneously distributed binding partner and show that, with certain simplifying assumptions, particle trajectories can be regarded as the outcome of a two-state hidden Markov model. Using simulated trajectories, we demonstrate that this model can be used to identify the key biophysical parameters for such a system, namely the diffusion coefficients of the underlying states, and the rates of transition between them. We use a stochastic optimization scheme to compute maximum likelihood estimates of these parameters. We have applied this analysis to single-particle trajectories of the integrin receptor lymphocyte function-associated antigen-1 (LFA-1) on live T cells. Our analysis reveals that the diffusion of LFA-1 is indeed approximately two-state, and is characterized by large changes in cytoskeletal interactions upon cellular activation. PMID:19893741

Dynamic Bandwidth Provisioning Using Markov Chain Based on RSVP

DTIC Science & Technology

2013-09-01

AUTHOR(S) Yavuz Sagir 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS (ES) Naval Postgraduate School Monterey, CA 93943-5000 8. PERFORMING...ORGANIZATION REPORT NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS (ES) N/A 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11...is finite or countable. A Markov process is basically a stochastic process in which the past history of the process is irrelevant if the current

The Embedding Problem for Markov Models of Nucleotide Substitution

PubMed Central

Verbyla, Klara L.; Yap, Von Bing; Pahwa, Anuj; Shao, Yunli; Huttley, Gavin A.

2013-01-01

Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor. PMID:23935949

Measurement-based reliability/performability models

NASA Technical Reports Server (NTRS)

Hsueh, Mei-Chen

1987-01-01

Measurement-based models based on real error-data collected on a multiprocessor system are described. Model development from the raw error-data to the estimation of cumulative reward is also described. A workload/reliability model is developed based on low-level error and resource usage data collected on an IBM 3081 system during its normal operation in order to evaluate the resource usage/error/recovery process in a large mainframe system. Thus, both normal and erroneous behavior of the system are modeled. The results provide an understanding of the different types of errors and recovery processes. The measured data show that the holding times in key operational and error states are not simple exponentials and that a semi-Markov process is necessary to model the system behavior. A sensitivity analysis is performed to investigate the significance of using a semi-Markov process, as opposed to a Markov process, to model the measured system.

Markov processes for the prediction of aircraft noise effects on sleep.

PubMed

Basner, Mathias; Siebert, Uwe

2010-01-01

Aircraft noise disturbs sleep and impairs recuperation. Authorities plan to expand Frankfurt airport. To quantitatively assess the effects of a traffic curfew (11 PM to 5 AM) at Frankfurt Airport on sleep structure. Experimental sleep study; polysomnography for 13 consecutive nights. Sleep laboratory. Subjects. 128 healthy subjects, mean age (SD) 38 (13) years, range 19 to 65, 59% female. Intervention. Exposure to aircraft noise via loudspeakers. A 6-state Markov state transition sleep model was used to simulate 3 noise scenarios with first-order Monte Carlo simulations: 1) 2005 traffic at Frankfurt Airport, 2) as simulation 1 but flights between 11 PM and 5 AM cancelled, and 3) as simulation 2, with flights between 11 PM and 5 AM from simulation 1 rescheduled to periods before 11 PM and after 5 AM. Probabilities for transitions between sleep stages were estimated with autoregressive multinomial logistic regression. Compared to a night without curfew, models indicate small improvements in sleep structure in nights with curfew, even if all traffic is rescheduled to periods before and after the curfew period. For those who go to bed before 10:30 PM or after 1 AM, this benefit is likely to be offset by the expected increase of air traffic during late evening and early morning hours. Limitations. Limited ecologic validity due to laboratory setting and subject sample. According to the decision analysis, it is unlikely that the proposed curfew at Frankfurt Airport substantially benefits sleep structure. Extensions of the model could be used to evaluate or propose alternative air traffic regulation strategies for Frankfurt Airport.

A method for using real world data in breast cancer modeling.

PubMed

Pobiruchin, Monika; Bochum, Sylvia; Martens, Uwe M; Kieser, Meinhard; Schramm, Wendelin

2016-04-01

Today, hospitals and other health care-related institutions are accumulating a growing bulk of real world clinical data. Such data offer new possibilities for the generation of disease models for the health economic evaluation. In this article, we propose a new approach to leverage cancer registry data for the development of Markov models. Records of breast cancer patients from a clinical cancer registry were used to construct a real world data driven disease model. We describe a model generation process which maps database structures to disease state definitions based on medical expert knowledge. Software was programmed in Java to automatically derive a model structure and transition probabilities. We illustrate our method with the reconstruction of a published breast cancer reference model derived primarily from clinical study data. In doing so, we exported longitudinal patient data from a clinical cancer registry covering eight years. The patient cohort (n=892) comprised HER2-positive and HER2-negative women treated with or without Trastuzumab. The models generated with this method for the respective patient cohorts were comparable to the reference model in their structure and treatment effects. However, our computed disease models reflect a more detailed picture of the transition probabilities, especially for disease free survival and recurrence. Our work presents an approach to extract Markov models semi-automatically using real world data from a clinical cancer registry. Health care decision makers may benefit from more realistic disease models to improve health care-related planning and actions based on their own data. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains

NASA Astrophysics Data System (ADS)

Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo

2016-09-01

The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.

Comparison of statistical algorithms for detecting homogeneous river reaches along a longitudinal continuum

NASA Astrophysics Data System (ADS)

Leviandier, Thierry; Alber, A.; Le Ber, F.; Piégay, H.

2012-02-01

Seven methods designed to delineate homogeneous river segments, belonging to four families, namely — tests of homogeneity, contrast enhancing, spatially constrained classification, and hidden Markov models — are compared, firstly on their principles, then on a case study, and on theoretical templates. These templates contain patterns found in the case study but not considered in the standard assumptions of statistical methods, such as gradients and curvilinear structures. The influence of data resolution, noise and weak satisfaction of the assumptions underlying the methods is investigated. The control of the number of reaches obtained in order to achieve meaningful comparisons is discussed. No method is found that outperforms all the others on all trials. However, the methods with sequential algorithms (keeping at order n + 1 all breakpoints found at order n) fail more often than those running complete optimisation at any order. The Hubert-Kehagias method and Hidden Markov Models are the most successful at identifying subpatterns encapsulated within the templates. Ergodic Hidden Markov Models are, moreover, liable to exhibit transition areas.

Surface Connectivity and Interocean Exchanges From Drifter-Based Transition Matrices

NASA Astrophysics Data System (ADS)

McAdam, Ronan; van Sebille, Erik

2018-01-01

Global surface transport in the ocean can be represented by using the observed trajectories of drifters to calculate probability distribution functions. The oceanographic applications of the Markov Chain approach to modeling include tracking of floating debris and water masses, globally and on yearly-to-centennial time scales. Here we analyze the error inherent with mapping trajectories onto a grid and the consequences for ocean transport modeling and detection of accumulation structures. A sensitivity analysis of Markov Chain parameters is performed in an idealized Stommel gyre and western boundary current as well as with observed ocean drifters, complementing previous studies on widespread floating debris accumulation. Focusing on two key areas of interocean exchange—the Agulhas system and the North Atlantic intergyre transport barrier—we assess the capacity of the Markov Chain methodology to detect surface connectivity and dynamic transport barriers. Finally, we extend the methodology's functionality to separate the geostrophic and nongeostrophic contributions to interocean exchange in these key regions.

Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain

PubMed Central

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

Transition and duration in disability: New evidence from administrative data.

PubMed

Lopez Casasnovas, Guillem; Nicodemo, Catia

2016-01-01

In recent decades demographic changes (low fertility rates, increased life expectancy…) in most OECD countries, have brought profound changes in the population pyramid, with several effects in the welfare of society. One of them is the increase in the number of people with disabilities, since age is a determining factor in the emergence of this dependency. This paper studies the probability to enter and transit in and from a disability state, as well as its associated mortality, by attending to the distinction between the initial disability level and the process that leads on from it, and by addressing whether and how education, age and income affect this transition. Applying a Markov model and a survival analysis to new Spanish administrative data set (Muestra Continua de Vida Laboral (MCVL)) we estimate the probability that a person changes the state of disability and the duration of her progression in each case. We find that people with an initial state of disability have a higher propensity to change status and take less time to transit amongst different stages than those who have no disability. Men do so more frequently than women and income have negative effects on the transition. These results may help to incorporate into welfare programs some protection mechanisms for delaying transitions and target the most fragile population groups. Copyright © 2016 Elsevier Inc. All rights reserved.

Modeling and evaluating user behavior in exploratory visual analysis

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

Reda, Khairi; Johnson, Andrew E.; Papka, Michael E.

Empirical evaluation methods for visualizations have traditionally focused on assessing the outcome of the visual analytic process as opposed to characterizing how that process unfolds. There are only a handful of methods that can be used to systematically study how people use visualizations, making it difficult for researchers to capture and characterize the subtlety of cognitive and interaction behaviors users exhibit during visual analysis. To validate and improve visualization design, however, it is important for researchers to be able to assess and understand how users interact with visualization systems under realistic scenarios. This paper presents a methodology for modeling andmore » evaluating the behavior of users in exploratory visual analysis. We model visual exploration using a Markov chain process comprising transitions between mental, interaction, and computational states. These states and the transitions between them can be deduced from a variety of sources, including verbal transcripts, videos and audio recordings, and log files. This model enables the evaluator to characterize the cognitive and computational processes that are essential to insight acquisition in exploratory visual analysis, and reconstruct the dynamics of interaction between the user and the visualization system. We illustrate this model with two exemplar user studies, and demonstrate the qualitative and quantitative analytical tools it affords.« less

Evaluation of drought using SPEI drought class transitions and log-linear models for different agro-ecological regions of India

NASA Astrophysics Data System (ADS)

Alam, N. M.; Sharma, G. C.; Moreira, Elsa; Jana, C.; Mishra, P. K.; Sharma, N. K.; Mandal, D.

2017-08-01

Markov chain and 3-dimensional log-linear models were attempted to model drought class transitions derived from the newly developed drought index the Standardized Precipitation Evapotranspiration Index (SPEI) at a 12 month time scale for six major drought prone areas of India. Log-linear modelling approach has been used to investigate differences relative to drought class transitions using SPEI-12 time series derived form 48 yeas monthly rainfall and temperature data. In this study, the probabilities of drought class transition, the mean residence time, the 1, 2 or 3 months ahead prediction of average transition time between drought classes and the drought severity class have been derived. Seasonality of precipitation has been derived for non-homogeneous Markov chains which could be used to explain the effect of the potential retreat of drought. Quasi-association and Quasi-symmetry log-linear models have been fitted to the drought class transitions derived from SPEI-12 time series. The estimates of odds along with their confidence intervals were obtained to explain the progression of drought and estimation of drought class transition probabilities. For initial months as the drought severity increases the calculated odds shows lower value and the odds decreases for the succeeding months. This indicates that the ratio of expected frequencies of occurrence of transition from drought class to the non-drought class decreases as compared to transition to any drought class when the drought severity of the present class increases. From 3-dimensional log-linear model it is clear that during the last 24 years the drought probability has increased for almost all the six regions. The findings from the present study will immensely help to assess the impact of drought on the gross primary production and to develop future contingent planning in similar regions worldwide.

Application du processus de Markov sur les occurrences des précipitations journalières au Congo-Brazzaville

NASA Astrophysics Data System (ADS)

Samba, Gaston; Mpounza, Marcel

2005-11-01

This study deals with the daily precipitation occurrence during the rainy season in different locations in Congo-Brazzaville. The Markov-chain probability model has been used for defining probable dry and wet rainy sequences at each station, and transition probabilities between daily precipitations of two successive days. The main results are: in Congo, the dependence on the preceding day of the daily precipitations occurrence; the confirmation of two main climatic region (equatorial climate to the north and tropical wet to the south); the lack of coherence in the distribution of precipitations. To cite this article: G. Samba, M. Mpounza, C. R. Geoscience 337 (2005).

A brief history of the introduction of generalized ensembles to Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Berg, Bernd A.

2017-03-01

The most efficient weights for Markov chain Monte Carlo calculations of physical observables are not necessarily those of the canonical ensemble. Generalized ensembles, which do not exist in nature but can be simulated on computers, lead often to a much faster convergence. In particular, they have been used for simulations of first order phase transitions and for simulations of complex systems in which conflicting constraints lead to a rugged free energy landscape. Starting off with the Metropolis algorithm and Hastings' extension, I present a minireview which focuses on the explosive use of generalized ensembles in the early 1990s. Illustrations are given, which range from spin models to peptides.

Overeducation Dynamics and Personality

ERIC Educational Resources Information Center

Blazquez, Maite; Budria, Santiago

2012-01-01

In this paper, we use the 2000-2008 waves of the German Socioeconomic Panel to examine overeducation transitions. The results are based on a first-order Markov model that allows us to account for both the initial conditions problem and potential endogeneity in attrition. We found that overeducation dynamics, especially the probability of entering…

Effects of ignoring baseline on modeling transitions from intact cognition to dementia.

PubMed

Yu, Lei; Tyas, Suzanne L; Snowdon, David A; Kryscio, Richard J

2009-07-01

This paper evaluates the effect of ignoring baseline when modeling transitions from intact cognition to dementia with mild cognitive impairment (MCI) and global impairment (GI) as intervening cognitive states. Transitions among states are modeled by a discrete-time Markov chain having three transient (intact cognition, MCI, and GI) and two competing absorbing states (death and dementia). Transition probabilities depend on two covariates, age and the presence/absence of an apolipoprotein E-epsilon4 allele, through a multinomial logistic model with shared random effects. Results are illustrated with an application to the Nun Study, a cohort of 678 participants 75+ years of age at baseline and followed longitudinally with up to ten cognitive assessments per nun.

Exploring first-order phase transitions with population annealing

NASA Astrophysics Data System (ADS)

Barash, Lev Yu.; Weigel, Martin; Shchur, Lev N.; Janke, Wolfhard

2017-03-01

Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example with the Metropolis algorithm. It is hence interesting to see whether such transitions can be more easily studied using population annealing. We report here our preliminary observations from population annealing runs for the two-dimensional Potts model with q > 4, where it undergoes a first-order transition.

Markovian Interpretations of Dual Retrieval Processes

PubMed Central

Gomes, C. F. A.; Nakamura, K.; Reyna, V. F.

2013-01-01

A half-century ago, at the dawn of the all-or-none learning era, Estes showed that finite Markov chains supply a tractable, comprehensive framework for discrete-change data of the sort that he envisioned for shifts in conditioning states in stimulus sampling theory. Shortly thereafter, such data rapidly accumulated in many spheres of human learning and animal conditioning, and Estes’ work stimulated vigorous development of Markov models to handle them. A key outcome was that the data of the workhorse paradigms of episodic memory, recognition and recall, proved to be one- and two-stage Markovian, respectively, to close approximations. Subsequently, Markov modeling of recognition and recall all but disappeared from the literature, but it is now reemerging in the wake of dual-process conceptions of episodic memory. In recall, in particular, Markov models are being used to measure two retrieval operations (direct access and reconstruction) and a slave familiarity operation. In the present paper, we develop this family of models and present the requisite machinery for fit evaluation and significance testing. Results are reviewed from selected experiments in which the recall models were used to understand dual memory processes. PMID:24948840

Stochastic Model of Seasonal Runoff Forecasts

NASA Astrophysics Data System (ADS)

Krzysztofowicz, Roman; Watada, Leslie M.

1986-03-01

Each year the National Weather Service and the Soil Conservation Service issue a monthly sequence of five (or six) categorical forecasts of the seasonal snowmelt runoff volume. To describe uncertainties in these forecasts for the purposes of optimal decision making, a stochastic model is formulated. It is a discrete-time, finite, continuous-space, nonstationary Markov process. Posterior densities of the actual runoff conditional upon a forecast, and transition densities of forecasts are obtained from a Bayesian information processor. Parametric densities are derived for the process with a normal prior density of the runoff and a linear model of the forecast error. The structure of the model and the estimation procedure are motivated by analyses of forecast records from five stations in the Snake River basin, from the period 1971-1983. The advantages of supplementing the current forecasting scheme with a Bayesian analysis are discussed.

Markov switching multinomial logit model: An application to accident-injury severities.

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2009-07-01

In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident-injury severities. These models assume Markov switching over time between two unobserved states of roadway safety as a means of accounting for potential unobserved heterogeneity. The states are distinct in the sense that in different states accident-severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single-state) multinomial logit models for a number of roadway classes and accident types. It is found that the more frequent state of roadway safety is correlated with better weather conditions and that the less frequent state is correlated with adverse weather conditions.

Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function

NASA Astrophysics Data System (ADS)

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.

Phasic Triplet Markov Chains.

PubMed

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.

Recursive recovery of Markov transition probabilities from boundary value data

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

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

Generalization bounds of ERM-based learning processes for continuous-time Markov chains.

PubMed

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.

Availability Control for Means of Transport in Decisive Semi-Markov Models of Exploitation Process

NASA Astrophysics Data System (ADS)

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.

Limiting Distributions of Functionals of Markov Chains.

DTIC Science & Technology

1984-08-01

limiting distributions; periodic * nonhomoger.,!ous Poisson processes . 19 ANS? MACY IConuui oe nonoe’ee if necorglooy and edern thty by block numbers...homogeneous Poisson processes is of interest in itself. The problem considered in this paper is of interest in the theory of partially observable...where we obtain the limiting distribution of the interevent times. Key Words: Markov Chains, Limiting Distributions, Periodic Nonhomogeneous Poisson

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Treesearch

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...

Risk aversion and risk seeking in multicriteria forest management: a Markov decision process approach

Treesearch

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.  The other method used the certainty...

SU-E-J-115: Using Markov Chain Modeling to Elucidate Patterns in Breast Cancer Metastasis Over Time and Space

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

Comen, E; Mason, J; Kuhn, P

2014-06-01

Purpose: Traditionally, breast cancer metastasis is described as a process wherein cancer cells spread from the breast to multiple organ systems via hematogenous and lymphatic routes. Mapping organ specific patterns of cancer spread over time is essential to understanding metastatic progression. In order to better predict sites of metastases, here we demonstrate modeling of the patterned migration of metastasis. Methods: We reviewed the clinical history of 453 breast cancer patients from Memorial Sloan Kettering Cancer Center who were non-metastatic at diagnosis but developed metastasis over time. We used the variables of organ site of metastases as well as time tomore » create a Markov chain model of metastasis. We illustrate the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Results: Based on the clinical histories of 453 breast cancer patients who developed metastasis, we have learned (i) how to create the Markov transition matrix governing the probabilities of cancer progression from site to site; (ii) how to create a systemic network diagram governing disease progression modeled as a random walk on a directed graph; (iii) how to classify metastatic sites as ‘sponges’ that tend to only receive cancer cells or ‘spreaders’ that receive and release them; (iv) how to model the time-scales of disease progression as a Weibull probability distribution function; (v) how to perform Monte Carlo simulations of disease progression; and (vi) how to interpret disease progression as an entropy-increasing stochastic process. Conclusion: Based on our modeling, metastatic spread may follow predictable pathways. Mapping metastasis not simply by organ site, but by function as either a ‘spreader’ or ‘sponge’ fundamentally reframes our understanding of metastatic processes. This model serves as a novel platform from which we may integrate the evolving genomic landscape that drives cancer metastasis. PS-OC Trans-Network Project Grant Award for “Data Assimilation and ensemble statistical forecasting methods applied to the MSKCC longitudinal metastatic breast cancer cohort.”.« less

Numerical research of the optimal control problem in the semi-Markov inventory model

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

Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.

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.

A Markov decision process for managing habitat for Florida scrub-jays

USGS Publications Warehouse

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 (<120 cm or "short"; 120-170 cm or "optimal"; .170 cm or "tall"; and a combination of tall and optimal or "mixed"), and our objective was to calculate a state-dependent management 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 help ensure the persistence of scrub-jays at Merritt Island National Wildlife Refuge. The development of a tailored monitoring program as a component of adaptive management could help reduce uncertainty about controlled and uncontrolled variation in transition probabilities of scrub-height and thus lead to improved decision making.

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

NASA Astrophysics Data System (ADS)

Wang, Ting; Plecháč, Petr

2017-12-01

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

Random Matrix Theory and the Anderson Model

NASA Astrophysics Data System (ADS)

Bellissard, Jean

2004-08-01

This paper is devoted to a discussion of possible strategies to prove rigorously the existence of a metal-insulator Anderson transition for the Anderson model in dimension d≥3. The possible criterions used to define such a transition are presented. It is argued that at low disorder the lowest order in perturbation theory is described by a random matrix model. Various simplified versions for which rigorous results have been obtained in the past are discussed. It includes a free probability approach, the Wegner n-orbital model and a class of models proposed by Disertori, Pinson, and Spencer, Comm. Math. Phys. 232:83-124 (2002). At last a recent work by Magnen, Rivasseau, and the author, Markov Process and Related Fields 9:261-278 (2003) is summarized: it gives a toy modeldescribing the lowest order approximation of Anderson model and it is proved that, for d=2, its density of states is given by the semicircle distribution. A short discussion of its extension to d≥3 follows.

Gender Classification Based on Eye Movements: A Processing Effect During Passive Face Viewing

PubMed Central

Sammaknejad, Negar; Pouretemad, Hamidreza; Eslahchi, Changiz; Salahirad, Alireza; Alinejad, Ashkan

2017-01-01

Studies have revealed superior face recognition skills in females, partially due to their different eye movement strategies when encoding faces. In the current study, we utilized these slight but important differences and proposed a model that estimates the gender of the viewers and classifies them into two subgroups, males and females. An eye tracker recorded participant’s eye movements while they viewed images of faces. Regions of interest (ROIs) were defined for each face. Results showed that the gender dissimilarity in eye movements was not due to differences in frequency of fixations in the ROI s per se. Instead, it was caused by dissimilarity in saccade paths between the ROIs. The difference enhanced when saccades were towards the eyes. Females showed significant increase in transitions from other ROI s to the eyes. Consequently, the extraction of temporal transient information of saccade paths through a transition probability matrix, similar to a first order Markov chain model, significantly improved the accuracy of the gender classification results. PMID:29071007

Gender Classification Based on Eye Movements: A Processing Effect During Passive Face Viewing.

PubMed

Sammaknejad, Negar; Pouretemad, Hamidreza; Eslahchi, Changiz; Salahirad, Alireza; Alinejad, Ashkan

2017-01-01

Studies have revealed superior face recognition skills in females, partially due to their different eye movement strategies when encoding faces. In the current study, we utilized these slight but important differences and proposed a model that estimates the gender of the viewers and classifies them into two subgroups, males and females. An eye tracker recorded participant's eye movements while they viewed images of faces. Regions of interest (ROIs) were defined for each face. Results showed that the gender dissimilarity in eye movements was not due to differences in frequency of fixations in the ROI s per se. Instead, it was caused by dissimilarity in saccade paths between the ROIs. The difference enhanced when saccades were towards the eyes. Females showed significant increase in transitions from other ROI s to the eyes. Consequently, the extraction of temporal transient information of saccade paths through a transition probability matrix, similar to a first order Markov chain model, significantly improved the accuracy of the gender classification results.

Enrollment Planning Using Computer Decision Model: A Case Study at Grambling State University.

ERIC Educational Resources Information Center

Ghosh, Kalyan; Lundy, Harold W.

Achieving enrollment goals continues to be a major administrative concern in higher education. Enrollment management can be assisted through the use of computerized planning and forecast models. Although commercially available Markov transition type curve fitting models have been developed and used, a microcomputer-based decision planning model…

Characterizing and Differentiating Brain State Dynamics via Hidden Markov Models

PubMed Central

Ou, Jinli; Xie, Li; Jin, Changfeng; Li, Xiang; Zhu, Dajiang; Jiang, Rongxin; Chen, Yaowu

2014-01-01

Functional connectivity measured from resting state fMRI (R-fMRI) data has been widely used to examine the brain’s functional activities and has been recently used to characterize and differentiate brain conditions. However, the dynamical transition patterns of the brain’s functional states have been less explored. In this work, we propose a novel computational framework to quantitatively characterize the brain state dynamics via hidden Markov models (HMMs) learned from the observations of temporally dynamic functional connectomics, denoted as functional connectome states. The framework has been applied to the R-fMRI dataset including 44 post-traumatic stress disorder (PTSD) patients and 51 normal control (NC) subjects. Experimental results show that both PTSD and NC brains were undergoing remarkable changes in resting state and mainly transiting amongst a few brain states. Interestingly, further prediction with the best-matched HMM demonstrates that PTSD would enter into, but could not disengage from, a negative mood state. Importantly, 84 % of PTSD patients and 86 % of NC subjects are successfully classified via multiple HMMs using majority voting. PMID:25331991

A hidden Markov model to assess drug-induced sleep fragmentation in the telemetered rat.

PubMed

Diack, C; Ackaert, O; Ploeger, B A; van der Graaf, P H; Gurrell, R; Ivarsson, M; Fairman, D

2011-12-01

Drug-induced sleep fragmentation can cause sleep disturbances either via their intended pharmacological action or as a side effect. Examples of disturbances include excessive daytime sleepiness, insomnia and nightmares. Developing drugs without these side effects requires insight into the mechanisms leading to sleep disturbance. The characterization of the circadian sleep pattern by EEG following drug exposure has improved our understanding of these mechanisms and their translatability across species. The EEG shows frequent transitions between specific sleep states leading to multiple correlated sojourns in these states. We have developed a Markov model to consider the high correlation in the data and quantitatively compared sleep disturbance in telemetered rats induced by methylphenidate, which is known to disturb sleep, and of a new chemical entity (NCE). It was assumed that these drugs could either accelerate or decelerate the transitions between the sleep states. The difference in sleep disturbance of methylphenidate and the NCE were quantitated and different mechanisms of action on rebound sleep were identified. The estimated effect showed that both compounds induce sleep fragmentation with methylphenidate being fivefold more potent compared to the NCE.

Refining Markov state models for conformational dynamics using ensemble-averaged data and time-series trajectories

NASA Astrophysics Data System (ADS)

Matsunaga, Y.; Sugita, Y.

2018-06-01

A data-driven modeling scheme is proposed for conformational dynamics of biomolecules based on molecular dynamics (MD) simulations and experimental measurements. In this scheme, an initial Markov State Model (MSM) is constructed from MD simulation trajectories, and then, the MSM parameters are refined using experimental measurements through machine learning techniques. The second step can reduce the bias of MD simulation results due to inaccurate force-field parameters. Either time-series trajectories or ensemble-averaged data are available as a training data set in the scheme. Using a coarse-grained model of a dye-labeled polyproline-20, we compare the performance of machine learning estimations from the two types of training data sets. Machine learning from time-series data could provide the equilibrium populations of conformational states as well as their transition probabilities. It estimates hidden conformational states in more robust ways compared to that from ensemble-averaged data although there are limitations in estimating the transition probabilities between minor states. We discuss how to use the machine learning scheme for various experimental measurements including single-molecule time-series trajectories.

A fast exact simulation method for a class of Markov jump processes.

PubMed

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.

Development and validation of a Markov microsimulation model for the economic evaluation of treatments in osteoporosis.

PubMed

Hiligsmann, Mickaël; Ethgen, Olivier; Bruyère, Olivier; Richy, Florent; Gathon, Henry-Jean; Reginster, Jean-Yves

2009-01-01

Markov models are increasingly used in economic evaluations of treatments for osteoporosis. Most of the existing evaluations are cohort-based Markov models missing comprehensive memory management and versatility. In this article, we describe and validate an original Markov microsimulation model to accurately assess the cost-effectiveness of prevention and treatment of osteoporosis. We developed a Markov microsimulation model with a lifetime horizon and a direct health-care cost perspective. The patient history was recorded and was used in calculations of transition probabilities, utilities, and costs. To test the internal consistency of the model, we carried out an example calculation for alendronate therapy. Then, external consistency was investigated by comparing absolute lifetime risk of fracture estimates with epidemiologic data. For women at age 70 years, with a twofold increase in the fracture risk of the average population, the costs per quality-adjusted life-year gained for alendronate therapy versus no treatment were estimated at €9105 and €15,325, respectively, under full and realistic adherence assumptions. All the sensitivity analyses in terms of model parameters and modeling assumptions were coherent with expected conclusions and absolute lifetime risk of fracture estimates were within the range of previous estimates, which confirmed both internal and external consistency of the model. Microsimulation models present some major advantages over cohort-based models, increasing the reliability of the results and being largely compatible with the existing state of the art, evidence-based literature. The developed model appears to be a valid model for use in economic evaluations in osteoporosis.

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

[Birth and death process of computer viruses].

PubMed

Segawa, Katsunori; Nakano, Tatsuya; Nakata, Kotoko; Hayashi, Yuzuru

2006-01-01

The daily variations in the number of computer viruses found attaching to e-mails and the number of accesses to the home page of a national institute in Japan are examined. The power spectral densities (PSD) of the variation in the computer viruses show a time-correlation characteristic of Markov process, but the daily access number does not (identified as white noise). Like biological viruses, the variation in the computer viruses can be described by the birth-and-death model known as a Markov process.

Image segmentation using hidden Markov Gauss mixture models.

PubMed

Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M

2007-07-01

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Distance between configurations in Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya

2017-12-01

For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

Symbolic Heuristic Search for Factored Markov Decision Processes

NASA Technical Reports Server (NTRS)

Morris, Robert (Technical Monitor); Feng, Zheng-Zhu; Hansen, Eric A.

2003-01-01

We describe a planning algorithm that integrates two approaches to solving Markov decision processes with large state spaces. State abstraction is used to avoid evaluating states individually. Forward search from a start state, guided by an admissible heuristic, is used to avoid evaluating all states. We combine these two approaches in a novel way that exploits symbolic model-checking techniques and demonstrates their usefulness for decision-theoretic planning.

Using Markov Decision Processes with Heterogeneous Queueing Systems to Examine Military MEDEVAC Dispatching Policies

DTIC Science & Technology

2017-03-23

Air Force Institute of Technology AFIT Scholar Theses and Dissertations 3-23-2017 Using Markov Decision Processes with Heterogeneous Queueing Systems... TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in...POLICIES THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force Institute of Technology

Effects of ignoring baseline on modeling transitions from intact cognition to dementia

PubMed Central

Yu, Lei; Tyas, Suzanne L.; Snowdon, David A.; Kryscio, Richard J.

2009-01-01

This paper evaluates the effect of ignoring baseline when modeling transitions from intact cognition to dementia with mild cognitive impairment (MCI) and global impairment (GI) as intervening cognitive states. Transitions among states are modeled by a discrete-time Markov chain having three transient (intact cognition, MCI, and GI) and two competing absorbing states (death and dementia). Transition probabilities depend on two covariates, age and the presence/absence of an apolipoprotein E-ε4 allele, through a multinomial logistic model with shared random effects. Results are illustrated with an application to the Nun Study, a cohort of 678 participants 75+ years of age at baseline and followed longitudinally with up to ten cognitive assessments per nun. PMID:20161282

Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions

NASA Astrophysics Data System (ADS)

Dinh, Thanh-Chung; Renger, Thomas

2015-01-01

A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.

Origin of Pareto-like spatial distributions in ecosystems.

PubMed

Manor, Alon; Shnerb, Nadav M

2008-12-31

Recent studies of cluster distribution in various ecosystems revealed Pareto statistics for the size of spatial colonies. These results were supported by cellular automata simulations that yield robust criticality for endogenous pattern formation based on positive feedback. We show that this patch statistics is a manifestation of the law of proportionate effect. Mapping the stochastic model to a Markov birth-death process, the transition rates are shown to scale linearly with cluster size. This mapping provides a connection between patch statistics and the dynamics of the ecosystem; the "first passage time" for different colonies emerges as a powerful tool that discriminates between endogenous and exogenous clustering mechanisms. Imminent catastrophic shifts (such as desertification) manifest themselves in a drastic change of the stability properties of spatial colonies.

Discrete-time Markovian stochastic Petri nets

NASA Technical Reports Server (NTRS)

Ciardo, Gianfranco

1995-01-01

We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.

A statistical learning strategy for closed-loop control of fluid flows

NASA Astrophysics Data System (ADS)

Guéniat, Florimond; Mathelin, Lionel; Hussaini, M. Yousuff

2016-12-01

This work discusses a closed-loop control strategy for complex systems utilizing scarce and streaming data. A discrete embedding space is first built using hash functions applied to the sensor measurements from which a Markov process model is derived, approximating the complex system's dynamics. A control strategy is then learned using reinforcement learning once rewards relevant with respect to the control objective are identified. This method is designed for experimental configurations, requiring no computations nor prior knowledge of the system, and enjoys intrinsic robustness. It is illustrated on two systems: the control of the transitions of a Lorenz'63 dynamical system, and the control of the drag of a cylinder flow. The method is shown to perform well.

Spectral simplicity of apparent complexity. I. The nondiagonalizable metadynamics of prediction

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question—correlation, predictability, predictive cost, observer synchronization, and the like—induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the spectral projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II [P. M. Riechers and J. P. Crutchfield, Chaos 28, 033116 (2018)], to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.

Ligand induced change of β2 adrenergic receptor from active to inactive conformation and its implication for the closed/open state of the water channel: insight from molecular dynamics simulation, free energy calculation and Markov state model analysis.

PubMed

Bai, Qifeng; Pérez-Sánchez, Horacio; Zhang, Yang; Shao, Yonghua; Shi, Danfeng; Liu, Huanxiang; Yao, Xiaojun

2014-08-14

The reported crystal structures of β2 adrenergic receptor (β2AR) reveal that the open and closed states of the water channel are correlated with the inactive and active conformations of β2AR. However, more details about the process by which the water channel states are affected by the active to inactive conformational change of β2AR remain illusive. In this work, molecular dynamics simulations are performed to study the dynamical inactive and active conformational change of β2AR induced by inverse agonist ICI 118,551. Markov state model analysis and free energy calculation are employed to explore the open and close states of the water channel. The simulation results show that inverse agonist ICI 118,551 can induce water channel opening during the conformational transition of β2AR. Markov state model (MSM) analysis proves that the energy contour can be divided into seven states. States S1, S2 and S5, which represent the active conformation of β2AR, show that the water channel is in the closed state, while states S4 and S6, which correspond to the intermediate state conformation of β2AR, indicate the water channel opens gradually. State S7, which represents the inactive structure of β2AR, corresponds to the full open state of the water channel. The opening mechanism of the water channel is involved in the ligand-induced conformational change of β2AR. These results can provide useful information for understanding the opening mechanism of the water channel and will be useful for the rational design of potent inverse agonists of β2AR.

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

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

Lin, Yen Ting; Buchler, Nicolas E.

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

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

DOE PAGES

Lin, Yen Ting; Buchler, Nicolas E.

2018-01-31

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

Markov reward processes

NASA Technical Reports Server (NTRS)

Smith, R. M.

1991-01-01

Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.

Characterization of binary string statistics for syntactic landmine detection

NASA Astrophysics Data System (ADS)

Nasif, Ahmed O.; Mark, Brian L.; Hintz, Kenneth J.

2011-06-01

Syntactic landmine detection has been proposed to detect and classify non-metallic landmines using ground penetrating radar (GPR). In this approach, the GPR return is processed to extract characteristic binary strings for landmine and clutter discrimination. In our previous work, we discussed the preprocessing methodology by which the amplitude information of the GPR A-scan signal can be effectively converted into binary strings, which identify the impedance discontinuities in the signal. In this work, we study the statistical properties of the binary string space. In particular, we develop a Markov chain model to characterize the observed bit sequence of the binary strings. The state is defined as the number of consecutive zeros between two ones in the binarized A-scans. Since the strings are highly sparse (the number of zeros is much greater than the number of ones), defining the state this way leads to fewer number of states compared to the case where each bit is defined as a state. The number of total states is further reduced by quantizing the number of consecutive zeros. In order to identify the correct order of the Markov model, the mean square difference (MSD) between the transition matrices of mine strings and non-mine strings is calculated up to order four using training data. The results show that order one or two maximizes this MSD. The specification of the transition probabilities of the chain can be used to compute the likelihood of any given string. Such a model can be used to identify characteristic landmine strings during the training phase. These developments on modeling and characterizing the string statistics can potentially be part of a real-time landmine detection algorithm that identifies landmine and clutter in an adaptive fashion.

Detection limit for rate fluctuations in inhomogeneous Poisson processes

NASA Astrophysics Data System (ADS)

Shintani, Toshiaki; Shinomoto, Shigeru

2012-04-01

Estimations of an underlying rate from data points are inevitably disturbed by the irregular occurrence of events. Proper estimation methods are designed to avoid overfitting by discounting the irregular occurrence of data, and to determine a constant rate from irregular data derived from a constant probability distribution. However, it can occur that rapid or small fluctuations in the underlying density are undetectable when the data are sparse. For an estimation method, the maximum degree of undetectable rate fluctuations is uniquely determined as a phase transition, when considering an infinitely long series of events drawn from a fluctuating density. In this study, we analytically examine an optimized histogram and a Bayesian rate estimator with respect to their detectability of rate fluctuation, and determine whether their detectable-undetectable phase transition points are given by an identical formula defining a degree of fluctuation in an underlying rate. In addition, we numerically examine the variational Bayes hidden Markov model in its detectability of rate fluctuation, and determine whether the numerically obtained transition point is comparable to those of the other two methods. Such consistency among these three principled methods suggests the presence of a theoretical limit for detecting rate fluctuations.

Detection limit for rate fluctuations in inhomogeneous Poisson processes.

PubMed

Shintani, Toshiaki; Shinomoto, Shigeru

2012-04-01

Estimations of an underlying rate from data points are inevitably disturbed by the irregular occurrence of events. Proper estimation methods are designed to avoid overfitting by discounting the irregular occurrence of data, and to determine a constant rate from irregular data derived from a constant probability distribution. However, it can occur that rapid or small fluctuations in the underlying density are undetectable when the data are sparse. For an estimation method, the maximum degree of undetectable rate fluctuations is uniquely determined as a phase transition, when considering an infinitely long series of events drawn from a fluctuating density. In this study, we analytically examine an optimized histogram and a Bayesian rate estimator with respect to their detectability of rate fluctuation, and determine whether their detectable-undetectable phase transition points are given by an identical formula defining a degree of fluctuation in an underlying rate. In addition, we numerically examine the variational Bayes hidden Markov model in its detectability of rate fluctuation, and determine whether the numerically obtained transition point is comparable to those of the other two methods. Such consistency among these three principled methods suggests the presence of a theoretical limit for detecting rate fluctuations.

Operations and support cost modeling using Markov chains

NASA Technical Reports Server (NTRS)

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.

Risk assessment by dynamic representation of vulnerability, exploitation, and impact

NASA Astrophysics Data System (ADS)

Cam, Hasan

2015-05-01

Assessing and quantifying cyber risk accurately in real-time is essential to providing security and mission assurance in any system and network. This paper presents a modeling and dynamic analysis approach to assessing cyber risk of a network in real-time by representing dynamically its vulnerabilities, exploitations, and impact using integrated Bayesian network and Markov models. Given the set of vulnerabilities detected by a vulnerability scanner in a network, this paper addresses how its risk can be assessed by estimating in real-time the exploit likelihood and impact of vulnerability exploitation on the network, based on real-time observations and measurements over the network. The dynamic representation of the network in terms of its vulnerabilities, sensor measurements, and observations is constructed dynamically using the integrated Bayesian network and Markov models. The transition rates of outgoing and incoming links of states in hidden Markov models are used in determining exploit likelihood and impact of attacks, whereas emission rates help quantify the attack states of vulnerabilities. Simulation results show the quantification and evolving risk scores over time for individual and aggregated vulnerabilities of a network.

A Markov chain model for reliability growth and decay

NASA Technical Reports Server (NTRS)

Siegrist, K.

1982-01-01

A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.

Automatic specification of reliability models for fault-tolerant computers

NASA Technical Reports Server (NTRS)

Liceaga, Carlos A.; Siewiorek, Daniel P.

1993-01-01

The calculation of reliability measures using Markov models is required for life-critical processor-memory-switch structures that have standby redundancy or that are subject to transient or intermittent faults or repair. The task of specifying these models is tedious and prone to human error because of the large number of states and transitions required in any reasonable system. Therefore, model specification is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model specification. Automation requires a general system description language (SDL). For practicality, this SDL should also provide a high level of abstraction and be easy to learn and use. The first attempt to define and implement an SDL with those characteristics is presented. A program named Automated Reliability Modeling (ARM) was constructed as a research vehicle. The ARM program uses a graphical interface as its SDL, and it outputs a Markov reliability model specification formulated for direct use by programs that generate and evaluate the model.

Transitions in Prognostic Awareness Among Terminally Ill Cancer Patients in Their Last 6 Months of Life Examined by Multi-State Markov Modeling.

PubMed

Hsiu Chen, Chen; Wen, Fur-Hsing; Hou, Ming-Mo; Hsieh, Chia-Hsun; Chou, Wen-Chi; Chen, Jen-Shi; Chang, Wen-Cheng; Tang, Siew Tzuh

2017-09-01

Developing accurate prognostic awareness, a cornerstone of preference-based end-of-life (EOL) care decision-making, is a dynamic process involving more prognostic-awareness states than knowing or not knowing. Understanding the transition probabilities and time spent in each prognostic-awareness state can help clinicians identify trigger points for facilitating transitions toward accurate prognostic awareness. We examined transition probabilities in distinct prognostic-awareness states between consecutive time points in 247 cancer patients' last 6 months and estimated the time spent in each state. Prognostic awareness was categorized into four states: (a) unknown and not wanting to know, state 1; (b) unknown but wanting to know, state 2; (c) inaccurate awareness, state 3; and (d) accurate awareness, state 4. Transitional probabilities were examined by multistate Markov modeling. Initially, 59.5% of patients had accurate prognostic awareness, whereas the probabilities of being in states 1-3 were 8.1%, 17.4%, and 15.0%, respectively. Patients' prognostic awareness generally remained unchanged (probabilities of remaining in the same state: 45.5%-92.9%). If prognostic awareness changed, it tended to shift toward higher prognostic-awareness states (probabilities of shifting to state 4 were 23.2%-36.6% for patients initially in states 1-3, followed by probabilities of shifting to state 3 for those in states 1 and 2 [9.8%-10.1%]). Patients were estimated to spend 1.29, 0.42, 0.68, and 3.61 months in states 1-4, respectively, in their last 6 months. Terminally ill cancer patients' prognostic awareness generally remained unchanged, with a tendency to become more aware of their prognosis. Health care professionals should facilitate patients' transitions toward accurate prognostic awareness in a timely manner to promote preference-based EOL decisions. Terminally ill Taiwanese cancer patients' prognostic awareness generally remained stable, with a tendency toward developing higher states of awareness. Health care professionals should appropriately assess patients' readiness for prognostic information and respect patients' reluctance to confront their poor prognosis if they are not ready to know, but sensitively coach them to cultivate their accurate prognostic awareness, provide desired and understandable prognostic information for those who are ready to know, and give direct and honest prognostic information to clarify any misunderstandings for those with inaccurate awareness, thus ensuring that they develop accurate and realistic prognostic knowledge in time to make end-of-life care decisions. © AlphaMed Press 2017.

Open-source Software for Exoplanet Atmospheric Modeling

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Blecic, Jasmina; Harrington, Joseph

2018-01-01

I will present a suite of self-standing open-source tools to model and retrieve exoplanet spectra implemented for Python. These include: (1) a Bayesian-statistical package to run Levenberg-Marquardt optimization and Markov-chain Monte Carlo posterior sampling, (2) a package to compress line-transition data from HITRAN or Exomol without loss of information, (3) a package to compute partition functions for HITRAN molecules, (4) a package to compute collision-induced absorption, and (5) a package to produce radiative-transfer spectra of transit and eclipse exoplanet observations and atmospheric retrievals.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding.

PubMed

Taillefumier, Thibaud; Magnasco, Marcelo O

2013-04-16

Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics, and industrial engineering. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its Hölder exponent H. The critical value occurs when the roughness of the boundary equals the roughness of the process, so for diffusive processes the critical value is Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous function of time. For rougher boundaries, H < 1/2, the probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infinity. The critical point Hc = 1/2 corresponds to a widely studied case in the theory of neural coding, in which the external input integrated by a model neuron is a white-noise process, as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue that this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply defined times regardless of the intensity of internal noise.

Quasielastic neutron scattering in biology: Theory and applications

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

Vural, Derya; Univ. of Tennessee, Knoxville, TN; Hu, Xiaohu

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of thismore » in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Lastly, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains.« less

Quasielastic neutron scattering in biology: Theory and applications

DOE PAGES

Vural, Derya; Univ. of Tennessee, Knoxville, TN; Hu, Xiaohu; ...

2016-06-15

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of thismore » in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Lastly, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains.« less

Integration of gene normalization stages and co-reference resolution using a Markov logic network.

PubMed

Dai, Hong-Jie; Chang, Yen-Ching; Tsai, Richard Tzong-Han; Hsu, Wen-Lian

2011-09-15

Gene normalization (GN) is the task of normalizing a textual gene mention to a unique gene database ID. Traditional top performing GN systems usually need to consider several constraints to make decisions in the normalization process, including filtering out false positives, or disambiguating an ambiguous gene mention, to improve system performance. However, these constraints are usually executed in several separate stages and cannot use each other's input/output interactively. In this article, we propose a novel approach that employs a Markov logic network (MLN) to model the constraints used in the GN task. Firstly, we show how various constraints can be formulated and combined in an MLN. Secondly, we are the first to apply the two main concepts of co-reference resolution-discourse salience in centering theory and transitivity-to GN models. Furthermore, to make our results more relevant to developers of information extraction applications, we adopt the instance-based precision/recall/F-measure (PRF) in addition to the article-wide PRF to assess system performance. Experimental results show that our system outperforms baseline and state-of-the-art systems under two evaluation schemes. Through further analysis, we have found several unexplored challenges in the GN task. hongjie@iis.sinica.edu.tw Supplementary data are available at Bioinformatics online.

Influence of credit scoring on the dynamics of Markov chain

NASA Astrophysics Data System (ADS)

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.

Combined risk assessment of nonstationary monthly water quality based on Markov chain and time-varying copula.

PubMed

Shi, Wei; Xia, Jun

2017-02-01

Water quality risk management is a global hot research linkage with the sustainable water resource development. Ammonium nitrogen (NH 3 -N) and permanganate index (COD Mn ) as the focus indicators in Huai River Basin, are selected to reveal their joint transition laws based on Markov theory. The time-varying moments model with either time or land cover index as explanatory variables is applied to build the time-varying marginal distributions of water quality time series. Time-varying copula model, which takes the non-stationarity in the marginal distribution and/or the time variation in dependence structure between water quality series into consideration, is constructed to describe a bivariate frequency analysis for NH 3 -N and COD Mn series at the same monitoring gauge. The larger first-order Markov joint transition probability indicates water quality state Class V w , Class IV and Class III will occur easily in the water body of Bengbu Sluice. Both marginal distribution and copula models are nonstationary, and the explanatory variable time yields better performance than land cover index in describing the non-stationarities in the marginal distributions. In modelling the dependence structure changes, time-varying copula has a better fitting performance than the copula with the constant or the time-trend dependence parameter. The largest synchronous encounter risk probability of NH 3 -N and COD Mn simultaneously reaching Class V is 50.61%, while the asynchronous encounter risk probability is largest when NH 3 -N and COD Mn is inferior to class V and class IV water quality standards, respectively.

Mathematical Analysis of Vehicle Delivery Scale of Bike-Sharing Rental Nodes

NASA Astrophysics Data System (ADS)

Zhai, Y.; Liu, J.; Liu, L.

2018-04-01

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

NASA Astrophysics Data System (ADS)

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.

Performance and state-space analyses of systems using Petri nets

NASA Technical Reports Server (NTRS)

Watson, James Francis, III

1992-01-01

The goal of any modeling methodology is to develop a mathematical description of a system that is accurate in its representation and also permits analysis of structural and/or performance properties. Inherently, trade-offs exist between the level detail in the model and the ease with which analysis can be performed. Petri nets (PN's), a highly graphical modeling methodology for Discrete Event Dynamic Systems, permit representation of shared resources, finite capacities, conflict, synchronization, concurrency, and timing between state changes. By restricting the state transition time delays to the family of exponential density functions, Markov chain analysis of performance problems is possible. One major drawback of PN's is the tendency for the state-space to grow rapidly (exponential complexity) compared to increases in the PN constructs. It is the state space, or the Markov chain obtained from it, that is needed in the solution of many problems. The theory of state-space size estimation for PN's is introduced. The problem of state-space size estimation is defined, its complexities are examined, and estimation algorithms are developed. Both top-down and bottom-up approaches are pursued, and the advantages and disadvantages of each are described. Additionally, the author's research in non-exponential transition modeling for PN's is discussed. An algorithm for approximating non-exponential transitions is developed. Since only basic PN constructs are used in the approximation, theory already developed for PN's remains applicable. Comparison to results from entropy theory show the transition performance is close to the theoretic optimum. Inclusion of non-exponential transition approximations improves performance results at the expense of increased state-space size. The state-space size estimation theory provides insight and algorithms for evaluating this trade-off.

Affective State Level Recognition in Naturalistic Facial and Vocal Expressions.

PubMed

Meng, Hongying; Bianchi-Berthouze, Nadia

2014-03-01

Naturalistic affective expressions change at a rate much slower than the typical rate at which video or audio is recorded. This increases the probability that consecutive recorded instants of expressions represent the same affective content. In this paper, we exploit such a relationship to improve the recognition performance of continuous naturalistic affective expressions. Using datasets of naturalistic affective expressions (AVEC 2011 audio and video dataset, PAINFUL video dataset) continuously labeled over time and over different dimensions, we analyze the transitions between levels of those dimensions (e.g., transitions in pain intensity level). We use an information theory approach to show that the transitions occur very slowly and hence suggest modeling them as first-order Markov models. The dimension levels are considered to be the hidden states in the Hidden Markov Model (HMM) framework. Their discrete transition and emission matrices are trained by using the labels provided with the training set. The recognition problem is converted into a best path-finding problem to obtain the best hidden states sequence in HMMs. This is a key difference from previous use of HMMs as classifiers. Modeling of the transitions between dimension levels is integrated in a multistage approach, where the first level performs a mapping between the affective expression features and a soft decision value (e.g., an affective dimension level), and further classification stages are modeled as HMMs that refine that mapping by taking into account the temporal relationships between the output decision labels. The experimental results for each of the unimodal datasets show overall performance to be significantly above that of a standard classification system that does not take into account temporal relationships. In particular, the results on the AVEC 2011 audio dataset outperform all other systems presented at the international competition.

A fast exact simulation method for a class of Markov jump processes

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

Li, Yao, E-mail: yaoli@math.umass.edu; Hu, Lili, E-mail: lilyhu86@gmail.com

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 itsmore » 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.« less

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Exact solution of the hidden Markov processes.

PubMed

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.

Exact solution of the hidden Markov processes

NASA Astrophysics Data System (ADS)

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 .

OPTIMIZING OBSERVER EFFORT FOR FIELD DETECTION OF REPRODUCTIVE EFFECTS IN BIRDS

EPA Science Inventory

Avian nest survival is best viewed as a Markov process with two absorbing states, death and fledging. We present a column-stochastic Markov chain from which all major Mayfield formulations of daily nest-survival can be derived contingent upon the degree of observer knowledge of e...

Global dynamics of a stochastic neuronal oscillator

NASA Astrophysics Data System (ADS)

Yamanobe, Takanobu

2013-11-01

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

Global dynamics of a stochastic neuronal oscillator.

PubMed

Yamanobe, Takanobu

2013-11-01

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

The Non-linear Trajectory of Change in Play Profiles of Three Children in Psychodynamic Play Therapy

PubMed Central

Halfon, Sibel; Çavdar, Alev; Orsucci, Franco; Schiepek, Gunter K.; Andreassi, Silvia; Giuliani, Alessandro; de Felice, Giulio

2016-01-01

Aim: Even though there is substantial evidence that play based therapies produce significant change, the specific play processes in treatment remain unexamined. For that purpose, processes of change in long-term psychodynamic play therapy are assessed through a repeated systematic assessment of three children’s “play profiles,” which reflect patterns of organization among play variables that contribute to play activity in therapy, indicative of the children’s coping strategies, and an expression of their internal world. The main aims of the study are to investigate the kinds of play profiles expressed in treatment, and to test whether there is emergence of new and more adaptive play profiles using dynamic systems theory as a methodological framework. Methods and Procedures: Each session from the long-term psychodynamic treatment (mean number of sessions = 55) of three 6-year-old good outcome cases presenting with Separation Anxiety were recorded, transcribed and coded using items from the Children’s Play Therapy Instrument (CPTI), created to assess the play activity of children in psychotherapy, generating discrete and measurable units of play activity arranged along a continuum of four play profiles: “Adaptive,” “Inhibited,” “Impulsive,” and “Disorganized.” The play profiles were clustered through K-means Algorithm, generating seven discrete states characterizing the course of treatment and the transitions between these states were analyzed by Markov Transition Matrix, Recurrence Quantification Analysis (RQA) and odds ratios comparing the first and second halves of psychotherapy. Results: The Markov Transitions between the states scaled almost perfectly and also showed the ergodicity of the system, meaning that the child can reach any state or shift to another one in play. The RQA and odds ratios showed two trends of change, first concerning the decrease in the use of “less adaptive” strategies, second regarding the reduction of play interruptions. Conclusion: The results support that these children express different psychic states in play, which can be captured through the lens of play profiles, and begin to modify less dysfunctional profiles over the course of treatment. The methodology employed showed the productivity of treating psychodynamic play therapy as a complex system, taking advantage of non-linear methods to study psychotherapeutic play activity. PMID:27777561

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

Comparing clinical attachment level and pocket depth for predicting periodontal disease progression in healthy sites of patients with chronic periodontitis using multi-state Markov models

PubMed Central

Mdala, Ibrahimu; Olsen, Ingar; Haffajee, Anne D; Socransky, Sigmund S; Thoresen, Magne; de Blasio, Birgitte Freiesleben

2014-01-01

Aim To understand degeneration of healthy sites and identify factors associated with disease progression in patients with chronic periodontitis. Material and Methods Data on healthy sites from 163 American and Swedish subjects were analysed using two-three-state (health, gingivitis, chronic periodontitis) Markov models based on bleeding on probing (BOP), and either clinical attachment level (CAL) + BOP or pocket depth (PD) + BOP. Results In 2 years, 10% (CAL + BOP) and 3% (PD + BOP) of healthy sites developed chronic periodontitis. On average, healthy sites remained healthy for 32 months before transiting in both models. Most transitions (87–97%) from health were to the gingivitis state. The expected duration of the gingivitis lesion was 4–5 months and sites recovered with a high probability (96–98%). Disease severity as measured by number of sites with CAL/PD > 4 mm at baseline and smoking, were associated with fast progression from health to chronic periodontitis within 6 months as were gingival redness in the PD + BOP model only. With age, the rate of disease progression to gingivitis decreased. Conclusion Transition probabilities for gingivitis and chronic periodontitis were higher with CAL + BOP than with PD + BOP. Smoking and disease severity were significant predictors for fast progression. PMID:24888705

Markov decision processes in natural resources management: observability and uncertainty

USGS Publications Warehouse

Williams, Byron K.

2015-01-01

The breadth and complexity of stochastic decision processes in natural resources presents a challenge to analysts who need to understand and use these approaches. The objective of this paper is to describe a class of decision processes that are germane to natural resources conservation and management, namely Markov decision processes, and to discuss applications and computing algorithms under different conditions of observability and uncertainty. A number of important similarities are developed in the framing and evaluation of different decision processes, which can be useful in their applications in natural resources management. The challenges attendant to partial observability are highlighted, and possible approaches for dealing with it are discussed.

Markov Chain Ontology Analysis (MCOA)

PubMed Central

2012-01-01

Background 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. Results 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. Conclusion 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. PMID:22300537

Markov Chain Ontology Analysis (MCOA).

PubMed

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.

Space system operations and support cost analysis using Markov chains

NASA Technical Reports Server (NTRS)

Unal, Resit; Dean, Edwin B.; Moore, Arlene A.; Fairbairn, Robert E.

1990-01-01

This paper evaluates the use of Markov chain process in probabilistic life cycle cost analysis and suggests further uses of the process as a design aid tool. A methodology is developed for estimating operations and support cost and expected life for reusable space transportation systems. Application of the methodology is demonstrated for the case of a hypothetical space transportation vehicle. A sensitivity analysis is carried out to explore the effects of uncertainty in key model inputs.

Modelling Faculty Replacement Strategies Using a Time-Dependent Finite Markov-Chain Process.

ERIC Educational Resources Information Center

Hackett, E. Raymond; Magg, Alexander A.; Carrigan, Sarah D.

1999-01-01

Describes the use of a time-dependent Markov-chain model to develop faculty-replacement strategies within a college at a research university. The study suggests that a stochastic modelling approach can provide valuable insight when planning for personnel needs in the immediate (five-to-ten year) future. (MSE)

Predicting animal home-range structure and transitions using a multistate Ornstein-Uhlenbeck biased random walk

USGS Publications Warehouse

Breed, Greg A.; Golson, Emily A.; Tinker, M. Tim

2017-01-01

The home‐range concept is central in animal ecology and behavior, and numerous mechanistic models have been developed to understand home range formation and maintenance. These mechanistic models usually assume a single, contiguous home range. Here we describe and implement a simple home‐range model that can accommodate multiple home‐range centers, form complex shapes, allow discontinuities in use patterns, and infer how external and internal variables affect movement and use patterns. The model assumes individuals associate with two or more home‐range centers and move among them with some estimable probability. Movement in and around home‐range centers is governed by a two‐dimensional Ornstein‐Uhlenbeck process, while transitions between centers are modeled as a stochastic state‐switching process. We augmented this base model by introducing environmental and demographic covariates that modify transition probabilities between home‐range centers and can be estimated to provide insight into the movement process. We demonstrate the model using telemetry data from sea otters (Enhydra lutris) in California. The model was fit using a Bayesian Markov Chain Monte Carlo method, which estimated transition probabilities, as well as unique Ornstein‐Uhlenbeck diffusion and centralizing tendency parameters. Estimated parameters could then be used to simulate movement and space use that was virtually indistinguishable from real data. We used Deviance Information Criterion (DIC) scores to assess model fit and determined that both wind and reproductive status were predictive of transitions between home‐range centers. Females were less likely to move between home‐range centers on windy days, less likely to move between centers when tending pups, and much more likely to move between centers just after weaning a pup. These tendencies are predicted by theoretical movement rules but were not previously known and show that our model can extract meaningful behavioral insight from complex movement data.

Cascade heterogeneous face sketch-photo synthesis via dual-scale Markov Network

NASA Astrophysics Data System (ADS)

Yao, Saisai; Chen, Zhenxue; Jia, Yunyi; Liu, Chengyun

2018-03-01

Heterogeneous face sketch-photo synthesis is an important and challenging task in computer vision, which has widely applied in law enforcement and digital entertainment. According to the different synthesis results based on different scales, this paper proposes a cascade sketch-photo synthesis method via dual-scale Markov Network. Firstly, Markov Network with larger scale is used to synthesise the initial sketches and the local vertical and horizontal neighbour search (LVHNS) method is used to search for the neighbour patches of test patches in training set. Then, the initial sketches and test photos are jointly entered into smaller scale Markov Network. Finally, the fine sketches are obtained after cascade synthesis process. Extensive experimental results on various databases demonstrate the superiority of the proposed method compared with several state-of-the-art methods.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

PubMed

Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C

2014-04-01

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

Positive contraction mappings for classical and quantum Schrödinger systems

NASA Astrophysics Data System (ADS)

Georgiou, Tryphon T.; Pavon, Michele

2015-03-01

The classical Schrödinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior. Jamison proved that the new law is obtained through a multiplicative functional transformation of the prior. This transformation is characterised by an automorphism on the space of endpoints probability measures, which has been studied by Fortet, Beurling, and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins by establishing solutions to Schrödinger systems for Markov chains. Our approach is based on the Hilbert metric and shows that the solution to the Schrödinger bridge is provided by the fixed point of a contractive map. We approach, in a similar manner, the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map for the cases where the marginals are either uniform or pure states. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.

Relativistic diffusion processes and random walk models

NASA Astrophysics Data System (ADS)

Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-02-01

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

Spontaneous Time Symmetry Breaking in System with Mixed Strategy Nash Equilibrium: Evidences in Experimental Economics Data

NASA Astrophysics Data System (ADS)

Wang, Zhijian; Xu, Bin; Zhejiang Collaboration

2011-03-01

In social science, laboratory experiment with human subjects' interaction is a standard test-bed for studying social processes in micro level. Usually, as in physics, the processes near equilibrium are suggested as stochastic processes with time-reversal symmetry (TRS). To the best of our knowledge, near equilibrium, the breaking time symmetry, as well as the existence of robust time anti-symmetry processes, has not been reported clearly in experimental economics till now. By employing Markov transition method to analysis the data from human subject 2x2 Games with wide parameters and mixed Nash equilibrium, we study the time symmetry of the social interaction process near Nash equilibrium. We find that, the time symmetry is broken, and there exists a robust time anti-symmetry processes. We also report the weight of the time anti-symmetry processes in the total processes of each the games. Evidences in laboratory marketing experiments, at the same time, are provided as one-dimension cases. In these cases, time anti-symmetry cycles can also be captured. The proposition of time anti-symmetry processes is small, but the cycles are distinguishable.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

PyTranSpot: A tool for multiband light curve modeling of planetary transits and stellar spots

NASA Astrophysics Data System (ADS)

Juvan, Ines G.; Lendl, M.; Cubillos, P. E.; Fossati, L.; Tregloan-Reed, J.; Lammer, H.; Guenther, E. W.; Hanslmeier, A.

2018-02-01

Several studies have shown that stellar activity features, such as occulted and non-occulted starspots, can affect the measurement of transit parameters biasing studies of transit timing variations and transmission spectra. We present PyTranSpot, which we designed to model multiband transit light curves showing starspot anomalies, inferring both transit and spot parameters. The code follows a pixellation approach to model the star with its corresponding limb darkening, spots, and transiting planet on a two dimensional Cartesian coordinate grid. We combine PyTranSpot with a Markov chain Monte Carlo framework to study and derive exoplanet transmission spectra, which provides statistically robust values for the physical properties and uncertainties of a transiting star-planet system. We validate PyTranSpot's performance by analyzing eleven synthetic light curves of four different star-planet systems and 20 transit light curves of the well-studied WASP-41b system. We also investigate the impact of starspots on transit parameters and derive wavelength dependent transit depth values for WASP-41b covering a range of 6200-9200 Å, indicating a flat transmission spectrum.

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants.

PubMed

Sumner, Jeremy G; Taylor, Amelia; Holland, Barbara R; Jarvis, Peter D

2017-12-01

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for models with more than two states-for example DNA sequence alignments with four-state models-we find that methods which rely on phylogenetic invariants are incapable of satisfying all three of the stated statistical properties. This is because in these cases the relevant Markov invariants belong to a class of polynomials independent from the phylogenetic invariants.

Dynamic Latent Trait Models with Mixed Hidden Markov Structure for Mixed Longitudinal Outcomes.

PubMed

Zhang, Yue; Berhane, Kiros

2016-01-01

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMM). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study (CHS) to jointly model questionnaire based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

Project MINERVA's Follow-up on Wide-Field, Small Telescope Photometry to Identify Exoplanets

NASA Astrophysics Data System (ADS)

Houghton, Audrey; Henderson, Morgan; Johnson, Samson; Sergi, Anthony; Eastman, Jason D.; Beatty, Thomas G.; McCrady, Nate

2017-01-01

MINERVA is an array of four 0.7-m telescopes equipped for high precision photometry and spectroscopy dedicated to exoplanet observations. During the first 18 months of science operations, MINERVA engaged in a program of photometric follow-up of potential transiting exoplanet targets identified by the Kilodegree Extremely Little Telescope (KELT). Robotically-obtained observations are passed through our data reduction pipeline and we extract light curves via differential photometry. We seek transit signals via a Markov chain Monte Carlo fit using BATMAN. We discuss results for over 100 target stars analyzed to date.

Students' Progress throughout Examination Process as a Markov Chain

ERIC Educational Resources Information Center

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…

Markov Chains for Investigating and Predicting Migration: A Case from Southwestern China

NASA Astrophysics Data System (ADS)

Qin, Bo; Wang, Yiyu; Xu, Haoming

2018-03-01

In order to accurately predict the population’s happiness, this paper conducted two demographic surveys on a new district of a city in western China, and carried out a dynamic analysis using related mathematical methods. This paper argues that the migration of migrants in the city will change the pattern of spatial distribution of human resources in the city and thus affect the social and economic development in all districts. The migration status of the population will change randomly with the passage of time, so it can be predicted and analyzed through the Markov process. The Markov process provides the local government and decision-making bureau a valid basis for the dynamic analysis of the mobility of migrants in the city as well as the ways for promoting happiness of local people’s lives.

Prediction of transfer among multiple states of blood pressure based on Markov model: an 18-year cohort study.

PubMed

Wang, Yunfeng; Ma, Zhimin; Xu, Chaonan; Wang, ZiKun; Yang, Xinghua

2018-05-15

This study aimed to identify the rules of transition between normotension, prehypertension and hypertension states and to establish a prediction model for the incidence of prehypertension and hypertension. Data from the China Health and Nutrition Survey from 1991 to 2009 were used as training data to develop the model. Data of the year 2011 were used for model validation. The multistate Markov model was developed using the msm package in R software. A total of 5265 participants were included at baseline, with an average follow-up of 8.05 ± 5.27 years and 17 640 observations. The ratio of men to women was 1 : 1.17, and the mean age was 37.54 ± 13.80 years. Within 10 years, in men, from normotension, the average probability to prehypertension and hypertension are 34.5 and 35.25%, respectively; from prehypertension, the average probability of recovering to normotension and developing to hypertension are 17.78 and 43.85%, respectively. In women, the average probabilities are 27.49, 28.09, 29.11 and 39.05%. Fat consumption increasing was found to be a protective factor, with 4.5% lower rate of transferring from normotension to prehypertension for a quarter percentage increasing. The model showed a very good prediction ability within 10 years and provided good prediction of blood pressure in the 2011 cohort (χ = 0.781, P = 0.676). The multistate Markov model can be a useful tool to identify the rules of transition among multiple states of blood pressure and predict well prevalence of the normotension, prehypertension and hypertension in cohort populations.

No Magic Bullet: A Theory-Based Meta-Analysis of Markov Transition Probabilities in Studies of Service Systems for Persons With Mental Disabilities.

PubMed

Leff, Hugh Stephen; Chow, Clifton M; Graves, Stephen C

2017-03-01

A random-effects meta-analysis of studies that used Markov transition probabilities (TPs) to describe outcomes for mental health service systems of differing quality for persons with serious mental illness was implemented to improve the scientific understanding of systems performance, to use in planning simulations to project service system costs and outcomes over time, and to test a theory of how outcomes for systems varying in quality differ. Nineteen systems described in 12 studies were coded as basic (B), maintenance (M), and recovery oriented (R) on the basis of descriptions of services provided. TPs for studies were aligned with a common functional-level framework, converted to a one-month time period, synthesized, and compared with theory-based expectations. Meta-regression was employed to explore associations between TPs and characteristics of service recipients and studies. R systems performed better than M and B systems. However, M systems did not perform better than B systems. All systems showed negative as well as positive TPs. For approximately one-third of synthesized TPs, substantial interstudy heterogeneity was noted. Associations were found between TPs and service recipient and study variables Conclusions: Conceptualizing systems as B, M, and R has potential for improving scientific understanding and systems planning. R systems appear more effective than B and M systems, although there is no "magic bullet" system for all service recipients. Interstudy heterogeneity indicates need for common approaches to reporting service recipient states, time periods for TPs, service recipient attributes, and service system characteristics. TPs found should be used in Markov simulations to project system effectiveness and costs of over time.

Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains.

PubMed

Dans, Silvana Laura; Degrati, Mariana; Pedraza, Susana Noemí; Crespo, Enrique Alberto

2012-08-01

In Patagonia, Argentina, watching dolphins, especially dusky dolphins (Lagenorhynchus obscurus), is a new tourist activity. Feeding time decreases and time to return to feeding after feeding is abandoned and time it takes a group of dolphins to feed increase in the presence of boats. Such effects on feeding behavior may exert energetic costs on dolphins and thus reduce an individual's survival and reproductive capacity or maybe associated with shifts in distribution. We sought to predict which behavioral changes modify the activity pattern of dolphins the most. We modeled behavioral sequences of dusky dolphins with Markov chains. We calculated transition probabilities from one activity to another and arranged them in a stochastic matrix model. The proportion of time dolphins dedicated to a given activity (activity budget) and the time it took a dolphin to resume that activity after it had been abandoned (recurrence time) were calculated. We used a sensitivity analysis of Markov chains to calculate the sensitivity of the time budget and the activity-resumption time to changes in behavioral transition probabilities. Feeding-time budget was most sensitive to changes in the probability of dolphins switching from traveling to feeding behavior and of maintaining feeding behavior. Thus, an increase in these probabilities would be associated with the largest reduction in the time dedicated to feeding. A reduction in the probability of changing from traveling to feeding would also be associated with the largest increases in the time it takes dolphins to resume feeding. To approach dolphins when they are traveling would not affect behavior less because presence of the boat may keep dolphins from returning to feeding. Our results may help operators of dolphin-watching vessels minimize negative effects on dolphins. ©2012 Society for Conservation Biology.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains.

PubMed

Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C

2010-11-30

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal. It consists of a plus-shaped maze with two open and two closed arms elevated 50cm from the floor. The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms. In this work, we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions: normal and under the effects of anxiogenic and anxiolytic drugs. The spatial structure of the elevated plus-maze is divided into squares, which are associated with states of a Markov chain. By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze, we constructed stochastic matrices for the three conditions studied. The stochastic matrices show specific patterns, which correspond to the observed behaviors of the rat under the three different conditions. For the control group, the stochastic matrix shows a clear preference for places in the closed arms. This preference is enhanced for the anxiogenic group. For the anxiolytic group, the stochastic matrix shows a pattern similar to a random walk. Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze. Copyright © 2010 Elsevier B.V. All rights reserved.

A Bivariate Mixed Distribution with a Heavy-tailed Component and its Application to Single-site Daily Rainfall Simulation

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

Li, Chao ..; Singh, Vijay P.; Mishra, Ashok K.

2013-02-06

This paper presents an improved brivariate mixed distribution, which is capable of modeling the dependence of daily rainfall from two distinct sources (e.g., rainfall from two stations, two consecutive days, or two instruments such as satellite and rain gauge). The distribution couples an existing framework for building a bivariate mixed distribution, the theory of copulae and a hybrid marginal distribution. Contributions of the improved distribution are twofold. One is the appropriate selection of the bivariate dependence structure from a wider admissible choice (10 candidate copula families). The other is the introduction of a marginal distribution capable of better representing lowmore » to moderate values as well as extremes of daily rainfall. Among several applications of the improved distribution, particularly presented here is its utility for single-site daily rainfall simulation. Rather than simulating rainfall occurrences and amounts separately, the developed generator unifies the two processes by generalizing daily rainfall as a Markov process with autocorrelation described by the improved bivariate mixed distribution. The generator is first tested on a sample station in Texas. Results reveal that the simulated and observed sequences are in good agreement with respect to essential characteristics. Then, extensive simulation experiments are carried out to compare the developed generator with three other alternative models: the conventional two-state Markov chain generator, the transition probability matrix model and the semi-parametric Markov chain model with kernel density estimation for rainfall amounts. Analyses establish that overall the developed generator is capable of reproducing characteristics of historical extreme rainfall events and is apt at extrapolating rare values beyond the upper range of available observed data. Moreover, it automatically captures the persistence of rainfall amounts on consecutive wet days in a relatively natural and easy way. Another interesting observation is that the recognized ‘overdispersion’ problem in daily rainfall simulation ascribes more to the loss of rainfall extremes than the under-representation of first-order persistence. The developed generator appears to be a sound option for daily rainfall simulation, especially in particular hydrologic planning situations when rare rainfall events are of great importance.« less

An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes

NASA Astrophysics Data System (ADS)

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.

Large deviations and mixing for dissipative PDEs with unbounded random kicks

NASA Astrophysics Data System (ADS)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

APOSTLE: 11 TRANSIT OBSERVATIONS OF TrES-3b

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

Kundurthy, P.; Becker, A. C.; Agol, E.

2013-02-10

The Apache Point Survey of Transit Lightcurves of Exoplanets (APOSTLE) observed 11 transits of TrES-3b over two years in order to constrain system parameters and look for transit timing and depth variations. We describe an updated analysis protocol for APOSTLE data, including the reduction pipeline, transit model, and Markov Chain Monte Carlo analyzer. Our estimates of the system parameters for TrES-3b are consistent with previous estimates to within the 2{sigma} confidence level. We improved the errors (by 10%-30%) on system parameters such as the orbital inclination (i {sub orb}), impact parameter (b), and stellar density ({rho}{sub *}) compared to previousmore » measurements. The near-grazing nature of the system, and incomplete sampling of some transits, limited our ability to place reliable uncertainties on individual transit depths and hence we do not report strong evidence for variability. Our analysis of the transit timing data shows no evidence for transit timing variations and our timing measurements are able to rule out super-Earth and gas giant companions in low-order mean motion resonance with TrES-3b.« less

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

Probabilistic Cellular Automata

PubMed Central

Agapie, Alexandru; Giuclea, Marius

2014-01-01

Abstract Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case—connecting the probability of a configuration in the stationary distribution to its number of zero-one borders—the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata. PMID:24999557

Probabilistic cellular automata.

PubMed

Agapie, Alexandru; Andreica, Anca; Giuclea, Marius

2014-09-01

Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.

State-and-transition simulation models: a framework for forecasting landscape change

USGS Publications Warehouse

Daniel, Colin; Frid, Leonardo; Sleeter, Benjamin M.; Fortin, Marie-Josée

2016-01-01

SummaryA wide range of spatially explicit simulation models have been developed to forecast landscape dynamics, including models for projecting changes in both vegetation and land use. While these models have generally been developed as separate applications, each with a separate purpose and audience, they share many common features.We present a general framework, called a state-and-transition simulation model (STSM), which captures a number of these common features, accompanied by a software product, called ST-Sim, to build and run such models. The STSM method divides a landscape into a set of discrete spatial units and simulates the discrete state of each cell forward as a discrete-time-inhomogeneous stochastic process. The method differs from a spatially interacting Markov chain in several important ways, including the ability to add discrete counters such as age and time-since-transition as state variables, to specify one-step transition rates as either probabilities or target areas, and to represent multiple types of transitions between pairs of states.We demonstrate the STSM method using a model of land-use/land-cover (LULC) change for the state of Hawai'i, USA. Processes represented in this example include expansion/contraction of agricultural lands, urbanization, wildfire, shrub encroachment into grassland and harvest of tree plantations; the model also projects shifts in moisture zones due to climate change. Key model output includes projections of the future spatial and temporal distribution of LULC classes and moisture zones across the landscape over the next 50 years.State-and-transition simulation models can be applied to a wide range of landscapes, including questions of both land-use change and vegetation dynamics. Because the method is inherently stochastic, it is well suited for characterizing uncertainty in model projections. When combined with the ST-Sim software, STSMs offer a simple yet powerful means for developing a wide range of models of landscape dynamics.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models

NASA Astrophysics Data System (ADS)

Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.

2012-12-01

In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by non-stationarity either of the system input (climatic variability) and/or the complexity of catchment storage characteristics. The statistical model is also capable of reproducing short (event) and longer-term (inter-event) and wet and dry dynamical "hydrological states". These reflect the non-linear transport mechanisms of flow pathways induced by transient climatic and hydrological variables and modified by catchment characteristics. We conclude that MSARMs are a powerful tool to analyze the temporal dynamics of hydrological data, allowing for explicit integration of non-stationary, non-linear and non-Normal characteristics.

Characterizing Giant Exoplanets through Multiwavelength Transit Observations: HAT-P-5 b

NASA Astrophysics Data System (ADS)

PeQueen, David Jeffrey; Cole, Jackson Lane; Gardner, Cristilyn N.; Garver, Bethany Ray; Jarka, Kyla L.; Kar, Aman; McGough, Aylin M.; Rivera, Daniel Ivan; Kasper, David; Jang-Condell, Hannah; Kobulnicky, Henry; Dale, Daniel

2018-01-01

During the summer of 2017, we observed hot Jupiter-type exoplanet transit events using the Wyoming Infrared Observatory’s 2.3 meter telescope. We observed 14 unique exoplanets during transit events; one such target was HAT-P-5 b. In total, we collected 53 usable science images in the Sloan filter set, particularly with the g’, r’, z’, and i’ band wavelength filters. This exoplanet transited approximately 40 minutes earlier than the currently published literature suggests. After reducing the data and running a Markov chain Monte Carlo analysis, we present results describing the planetary radius, semi-major axis, orbital period, and inclination of HAT-P-5 b. Characteristics of Rayleigh scattering are present in the atmosphere of this exoplanet. This work is supported by the National Science Foundation under REU grant AST 1560461.

Markov State Models Provide Insights into Dynamic Modulation of Protein Function

PubMed Central

2015-01-01

Conspectus Protein function is inextricably linked to protein dynamics. As we move from a static structural picture to a dynamic ensemble view of protein structure and function, novel computational paradigms are required for observing and understanding conformational dynamics of proteins and its functional implications. In principle, molecular dynamics simulations can provide the time evolution of atomistic models of proteins, but the long time scales associated with functional dynamics make it difficult to observe rare dynamical transitions. The issue of extracting essential functional components of protein dynamics from noisy simulation data presents another set of challenges in obtaining an unbiased understanding of protein motions. Therefore, a methodology that provides a statistical framework for efficient sampling and a human-readable view of the key aspects of functional dynamics from data analysis is required. The Markov state model (MSM), which has recently become popular worldwide for studying protein dynamics, is an example of such a framework. In this Account, we review the use of Markov state models for efficient sampling of the hierarchy of time scales associated with protein dynamics, automatic identification of key conformational states, and the degrees of freedom associated with slow dynamical processes. Applications of MSMs for studying long time scale phenomena such as activation mechanisms of cellular signaling proteins has yielded novel insights into protein function. In particular, from MSMs built using large-scale simulations of GPCRs and kinases, we have shown that complex conformational changes in proteins can be described in terms of structural changes in key structural motifs or “molecular switches” within the protein, the transitions between functionally active and inactive states of proteins proceed via multiple pathways, and ligand or substrate binding modulates the flux through these pathways. Finally, MSMs also provide a theoretical toolbox for studying the effect of nonequilibrium perturbations on conformational dynamics. Considering that protein dynamics in vivo occur under nonequilibrium conditions, MSMs coupled with nonequilibrium statistical mechanics provide a way to connect cellular components to their functional environments. Nonequilibrium perturbations of protein folding MSMs reveal the presence of dynamically frozen glass-like states in their conformational landscape. These frozen states are also observed to be rich in β-sheets, which indicates their possible role in the nucleation of β-sheet rich aggregates such as those observed in amyloid-fibril formation. Finally, we describe how MSMs have been used to understand the dynamical behavior of intrinsically disordered proteins such as amyloid-β, human islet amyloid polypeptide, and p53. While certainly not a panacea for studying functional dynamics, MSMs provide a rigorous theoretical foundation for understanding complex entropically dominated processes and a convenient lens for viewing protein motions. PMID:25625937

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1987-01-01

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay.

Stochastic charging of dust grains in planetary rings: Diffusion rates and their effects on Lorentz resonances

NASA Technical Reports Server (NTRS)

Schaffer, L.; Burns, J. A.

1995-01-01

Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.

Comparing clinical attachment level and pocket depth for predicting periodontal disease progression in healthy sites of patients with chronic periodontitis using multi-state Markov models.

PubMed

Mdala, Ibrahimu; Olsen, Ingar; Haffajee, Anne D; Socransky, Sigmund S; Thoresen, Magne; de Blasio, Birgitte Freiesleben

2014-09-01

To understand degeneration of healthy sites and identify factors associated with disease progression in patients with chronic periodontitis. Data on healthy sites from 163 American and Swedish subjects were analysed using two-three-state (health, gingivitis, chronic periodontitis) Markov models based on bleeding on probing (BOP), and either clinical attachment level (CAL) + BOP or pocket depth (PD) + BOP. In 2 years, 10% (CAL + BOP) and 3% (PD + BOP) of healthy sites developed chronic periodontitis. On average, healthy sites remained healthy for 32 months before transiting in both models. Most transitions (87-97%) from health were to the gingivitis state. The expected duration of the gingivitis lesion was 4-5 months and sites recovered with a high probability (96-98%). Disease severity as measured by number of sites with CAL/PD > 4 mm at baseline and smoking, were associated with fast progression from health to chronic periodontitis within 6 months as were gingival redness in the PD + BOP model only. With age, the rate of disease progression to gingivitis decreased. Transition probabilities for gingivitis and chronic periodontitis were higher with CAL + BOP than with PD + BOP. Smoking and disease severity were significant predictors for fast progression. © 2014 The Authors. Journal of Clinical Periodontology Published by John Wiley & Sons Ltd.

Markov Chains For Testing Redundant Software

NASA Technical Reports Server (NTRS)

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.

Heterogeneity-induced large deviations in activity and (in some cases) entropy production

NASA Astrophysics Data System (ADS)

Gingrich, Todd R.; Vaikuntanathan, Suriyanarayanan; Geissler, Phillip L.

2014-10-01

We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy production rates of the trajectories on a large ring with a single heterogeneous link. The corresponding joint rate function demonstrates two dynamical phases—one localized and the other delocalized, but the marginal rate functions do not always exhibit the underlying transition. Symmetries in dynamic order parameters influence the observation of a transition, such that distributions for certain dynamic order parameters need not reveal an underlying dynamical bistability. Solution of our model system furthermore yields the form of the effective Markov transition matrices that generate dynamics in which the two dynamical phases are at coexistence. We discuss the implications of the transition for the response of bacterial cells to antibiotic treatment, arguing that even simple models of a cell cycle lacking an explicit bistability in configuration space will exhibit a bistability of dynamical phases.

Optical character recognition of handwritten Arabic using hidden Markov models

NASA Astrophysics Data System (ADS)

Aulama, Mohannad M.; Natsheh, Asem M.; Abandah, Gheith A.; Olama, Mohammed M.

2011-04-01

The problem of optical character recognition (OCR) of handwritten Arabic has not received a satisfactory solution yet. In this paper, an Arabic OCR algorithm is developed based on Hidden Markov Models (HMMs) combined with the Viterbi algorithm, which results in an improved and more robust recognition of characters at the sub-word level. Integrating the HMMs represents another step of the overall OCR trends being currently researched in the literature. The proposed approach exploits the structure of characters in the Arabic language in addition to their extracted features to achieve improved recognition rates. Useful statistical information of the Arabic language is initially extracted and then used to estimate the probabilistic parameters of the mathematical HMM. A new custom implementation of the HMM is developed in this study, where the transition matrix is built based on the collected large corpus, and the emission matrix is built based on the results obtained via the extracted character features. The recognition process is triggered using the Viterbi algorithm which employs the most probable sequence of sub-words. The model was implemented to recognize the sub-word unit of Arabic text raising the recognition rate from being linked to the worst recognition rate for any character to the overall structure of the Arabic language. Numerical results show that there is a potentially large recognition improvement by using the proposed algorithms.

Optical character recognition of handwritten Arabic using hidden Markov models

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

Aulama, Mohannad M.; Natsheh, Asem M.; Abandah, Gheith A.

2011-01-01

The problem of optical character recognition (OCR) of handwritten Arabic has not received a satisfactory solution yet. In this paper, an Arabic OCR algorithm is developed based on Hidden Markov Models (HMMs) combined with the Viterbi algorithm, which results in an improved and more robust recognition of characters at the sub-word level. Integrating the HMMs represents another step of the overall OCR trends being currently researched in the literature. The proposed approach exploits the structure of characters in the Arabic language in addition to their extracted features to achieve improved recognition rates. Useful statistical information of the Arabic language ismore » initially extracted and then used to estimate the probabilistic parameters of the mathematical HMM. A new custom implementation of the HMM is developed in this study, where the transition matrix is built based on the collected large corpus, and the emission matrix is built based on the results obtained via the extracted character features. The recognition process is triggered using the Viterbi algorithm which employs the most probable sequence of sub-words. The model was implemented to recognize the sub-word unit of Arabic text raising the recognition rate from being linked to the worst recognition rate for any character to the overall structure of the Arabic language. Numerical results show that there is a potentially large recognition improvement by using the proposed algorithms.« less

Detecting seismic waves using a binary hidden Markov model classifier

NASA Astrophysics Data System (ADS)

Ray, J.; Lefantzi, S.; Brogan, R. A.; Forrest, R.; Hansen, C. W.; Young, C. J.

2016-12-01

We explore the use of Hidden Markov Models (HMM) to detect the arrival of seismic waves using data captured by a seismogram. HMMs define the state of a station as a binary variable based on whether the station is receiving a signal or not. HMMs are simple and fast, allowing them to monitor multiple datastreams arising from a large distributed network of seismographs. In this study we examine the efficacy of HMM-based detectors with respect to their false positive and negative rates as well as the accuracy of the signal onset time as compared to the value determined by an expert analyst. The study uses 3 component International Monitoring System (IMS) data from a carefully analyzed 2 week period from May, 2010, for which our analyst tried to identify every signal. Part of this interval is used for training the HMM to recognize the transition between state from noise to signal, while the other is used for evaluating the effectiveness of our new detection algorithm. We compare our results with the STA/LTA detection processing applied by the IDC to assess potential for operational use. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Spatio-Temporal Pattern Recognition Using Hidden Markov Models

DTIC Science & Technology

1994-06-01

Jersey, 1982. 5. H. B . Barlow and W. R. Levick . The mechanism of directionally selective units in rabbit’s retina. Journal of Physiology (London), 178:477...108 A.2.2 Re-estimate of .. .. ................... .110 A.2.3 Re-estimate of B ...... ................... 110 A.3 Logarithmic Form of the Baum-Welch...19 a0 Transition Probability from State i to State j ................ 19 B Observation Probability Matrix

Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating.

PubMed

Schmandt, Nicolaus T; Galán, Roberto F

2012-09-14

Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.

Markov Tracking for Agent Coordination

NASA Technical Reports Server (NTRS)

Washington, Richard; Lau, Sonie (Technical Monitor)

1998-01-01

Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

PubMed

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.

Prediction of beta-turns in proteins using the first-order Markov models.

PubMed

Lin, Thy-Hou; Wang, Ging-Ming; Wang, Yen-Tseng

2002-01-01

We present a method based on the first-order Markov models for predicting simple beta-turns and loops containing multiple turns in proteins. Sequences of 338 proteins in a database are divided using the published turn criteria into the following three regions, namely, the turn, the boundary, and the nonturn ones. A transition probability matrix is constructed for either the turn or the nonturn region using the weighted transition probabilities computed for dipeptides identified from each region. There are two such matrices constructed for the boundary region since the transition probabilities for dipeptides immediately preceding or following a turn are different. The window used for scanning a protein sequence from amino (N-) to carboxyl (C-) terminal is a hexapeptide since the transition probability computed for a turn tetrapeptide is capped at both the N- and C- termini with a boundary transition probability indexed respectively from the two boundary transition matrices. A sum of the averaged product of the transition probabilities of all the hexapeptides involving each residue is computed. This is then weighted with a probability computed from assuming that all the hexapeptides are from the nonturn region to give the final prediction quantity. Both simple beta-turns and loops containing multiple turns in a protein are then identified by the rising of the prediction quantity computed. The performance of the prediction scheme or the percentage (%) of correct prediction is evaluated through computation of Matthews correlation coefficients for each protein predicted. It is found that the prediction method is capable of giving prediction results with better correlation between the percent of correct prediction and the Matthews correlation coefficients for a group of test proteins as compared with those predicted using some secondary structural prediction methods. The prediction accuracy for about 40% of proteins in the database or 50% of proteins in the test set is better than 70%. Such a percentage for the test set is reduced to 30 if the structures of all the proteins in the set are treated as unknown.

A Langevin equation for the rates of currency exchange based on the Markov analysis

NASA Astrophysics Data System (ADS)

Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G. R.; Ghasemi, F.; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2007-11-01

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D and D, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

Mathematical model of the loan portfolio dynamics in the form of Markov chain considering the process of new customers attraction

NASA Astrophysics Data System (ADS)

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.

A Bayesian model for visual space perception

NASA Technical Reports Server (NTRS)

Curry, R. E.

1972-01-01

A model for visual space perception is proposed that contains desirable features in the theories of Gibson and Brunswik. This model is a Bayesian processor of proximal stimuli which contains three important elements: an internal model of the Markov process describing the knowledge of the distal world, the a priori distribution of the state of the Markov process, and an internal model relating state to proximal stimuli. The universality of the model is discussed and it is compared with signal detection theory models. Experimental results of Kinchla are used as a special case.

On spatial mutation-selection models

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

Kondratiev, Yuri, E-mail: kondrat@math.uni-bielefeld.de; Kutoviy, Oleksandr, E-mail: kutoviy@math.uni-bielefeld.de, E-mail: kutovyi@mit.edu; Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

2013-11-15

We discuss the selection procedure in the framework of mutation models. We study the regulation for stochastically developing systems based on a transformation of the initial Markov process which includes a cost functional. The transformation of initial Markov process by cost functional has an analytic realization in terms of a Kimura-Maruyama type equation for the time evolution of states or in terms of the corresponding Feynman-Kac formula on the path space. The state evolution of the system including the limiting behavior is studied for two types of mutation-selection models.

Modeling Dyadic Processes Using Hidden Markov Models: A Time Series Approach to Mother-Infant Interactions during Infant Immunization

ERIC Educational Resources Information Center

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…

Learning models of Human-Robot Interaction from small data

PubMed Central

Zehfroosh, Ashkan; Kokkoni, Elena; Tanner, Herbert G.; Heinz, Jeffrey

2018-01-01

This paper offers a new approach to learning discrete models for human-robot interaction (HRI) from small data. In the motivating application, HRI is an integral part of a pediatric rehabilitation paradigm that involves a play-based, social environment aiming at improving mobility for infants with mobility impairments. Designing interfaces in this setting is challenging, because in order to harness, and eventually automate, the social interaction between children and robots, a behavioral model capturing the causality between robot actions and child reactions is needed. The paper adopts a Markov decision process (MDP) as such a model, and selects the transition probabilities through an empirical approximation procedure called smoothing. Smoothing has been successfully applied in natural language processing (NLP) and identification where, similarly to the current paradigm, learning from small data sets is crucial. The goal of this paper is two-fold: (i) to describe our application of HRI, and (ii) to provide evidence that supports the application of smoothing for small data sets. PMID:29492408

Learning models of Human-Robot Interaction from small data.

PubMed

Zehfroosh, Ashkan; Kokkoni, Elena; Tanner, Herbert G; Heinz, Jeffrey

2017-07-01

This paper offers a new approach to learning discrete models for human-robot interaction (HRI) from small data. In the motivating application, HRI is an integral part of a pediatric rehabilitation paradigm that involves a play-based, social environment aiming at improving mobility for infants with mobility impairments. Designing interfaces in this setting is challenging, because in order to harness, and eventually automate, the social interaction between children and robots, a behavioral model capturing the causality between robot actions and child reactions is needed. The paper adopts a Markov decision process (MDP) as such a model, and selects the transition probabilities through an empirical approximation procedure called smoothing. Smoothing has been successfully applied in natural language processing (NLP) and identification where, similarly to the current paradigm, learning from small data sets is crucial. The goal of this paper is two-fold: (i) to describe our application of HRI, and (ii) to provide evidence that supports the application of smoothing for small data sets.

The Building Game: From Enumerative Combinatorics to Conformational Diffusion

NASA Astrophysics Data System (ADS)

Johnson-Chyzhykov, Daniel; Menon, Govind

2016-08-01

We study a discrete attachment model for the self-assembly of polyhedra called the building game. We investigate two distinct aspects of the model: (i) enumerative combinatorics of the intermediate states and (ii) a notion of Brownian motion for the polyhedral linkage defined by each intermediate that we term conformational diffusion. The combinatorial configuration space of the model is computed for the Platonic, Archimedean, and Catalan solids of up to 30 faces, and several novel enumerative results are generated. These represent the most exhaustive computations of this nature to date. We further extend the building game to include geometric information. The combinatorial structure of each intermediate yields a systems of constraints specifying a polyhedral linkage and its moduli space. We use a random walk to simulate a reflected Brownian motion in each moduli space. Empirical statistics of the random walk may be used to define the rates of transition for a Markov process modeling the process of self-assembly.

Current fluctuations in periodically driven systems

NASA Astrophysics Data System (ADS)

Barato, Andre C.; Chetrite, Raphael

2018-05-01

Small nonequelibrium systems driven by an external periodic protocol can be described by Markov processes with time-periodic transition rates. In general, current fluctuations in such small systems are large and may play a crucial role. We develop a theoretical formalism to evaluate the rate of such large deviations in periodically driven systems. We show that the scaled cumulant generating function that characterizes current fluctuations is given by a maximal Floquet exponent. Comparing deterministic protocols with stochastic protocols, we show that, with respect to large deviations, systems driven by a stochastic protocol with an infinitely large number of jumps are equivalent to systems driven by deterministic protocols. Our results are illustrated with three case studies: a two-state model for a heat engine, a three-state model for a molecular pump, and a biased random walk with a time-periodic affinity.

Utilization of two web-based continuing education courses evaluated by Markov chain model.

PubMed

Tian, Hao; Lin, Jin-Mann S; Reeves, William C

2012-01-01

To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Markov chain models were built from 2008 web usage data to evaluate the courses' web structure and navigation patterns. The web site was then modified to resolve identified design issues and the improvement in user activity over the subsequent 12 months was quantitatively evaluated. Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. The continuing education courses' sequential structure design was clearly reflected in the resulting actual web usage models, and none of the skip transitions provided was heavily used. The web navigation patterns of the two different continuing education courses were similar. Two possible design flaws were identified and fixed in only one of the two courses. Over the following 12 months, the drop-out rate in the modified course significantly decreased from 41% to 35%, but remained unchanged in the unmodified course. The web improvement effects were further verified via a second-order Markov chain model. The results imply that differences in web content have less impact than web structure design on how learners navigate through continuing education courses. Evaluation of user navigation can help identify web design flaws and guide modifications. This study showed that Markov chain models provide a valuable tool to evaluate web-based education courses. Both the results and techniques in this study would be very useful for public health education and research specialists.

Utilization of two web-based continuing education courses evaluated by Markov chain model

PubMed Central

Lin, Jin-Mann S; Reeves, William C

2011-01-01

Objectives To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Design Markov chain models were built from 2008 web usage data to evaluate the courses' web structure and navigation patterns. The web site was then modified to resolve identified design issues and the improvement in user activity over the subsequent 12 months was quantitatively evaluated. Measurements Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. Results The continuing education courses' sequential structure design was clearly reflected in the resulting actual web usage models, and none of the skip transitions provided was heavily used. The web navigation patterns of the two different continuing education courses were similar. Two possible design flaws were identified and fixed in only one of the two courses. Over the following 12 months, the drop-out rate in the modified course significantly decreased from 41% to 35%, but remained unchanged in the unmodified course. The web improvement effects were further verified via a second-order Markov chain model. Conclusions The results imply that differences in web content have less impact than web structure design on how learners navigate through continuing education courses. Evaluation of user navigation can help identify web design flaws and guide modifications. This study showed that Markov chain models provide a valuable tool to evaluate web-based education courses. Both the results and techniques in this study would be very useful for public health education and research specialists. PMID:21976027

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

Adaptation of hidden Markov models for recognizing speech of reduced frame rate.

PubMed

Lee, Lee-Min; Jean, Fu-Rong

2013-12-01

The frame rate of the observation sequence in distributed speech recognition applications may be reduced to suit a resource-limited front-end device. In order to use models trained using full-frame-rate data in the recognition of reduced frame-rate (RFR) data, we propose a method for adapting the transition probabilities of hidden Markov models (HMMs) to match the frame rate of the observation. Experiments on the recognition of clean and noisy connected digits are conducted to evaluate the proposed method. Experimental results show that the proposed method can effectively compensate for the frame-rate mismatch between the training and the test data. Using our adapted model to recognize the RFR speech data, one can significantly reduce the computation time and achieve the same level of accuracy as that of a method, which restores the frame rate using data interpolation.

Study of behavior and determination of customer lifetime value(CLV) using Markov chain model

NASA Astrophysics Data System (ADS)

Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.

2014-03-01

Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.

Adaptive Markov Random Fields for Example-Based Super-resolution of Faces

NASA Astrophysics Data System (ADS)

Stephenson, Todd A.; Chen, Tsuhan

2006-12-01

Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution). For example, hallucination and Markov random field (MRF) methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.

Hidden Markov model-derived structural alphabet for proteins: the learning of protein local shapes captures sequence specificity.

PubMed

Camproux, A C; Tufféry, P

2005-08-05

Understanding and predicting protein structures depend on the complexity and the accuracy of the models used to represent them. We have recently set up a Hidden Markov Model to optimally compress protein three-dimensional conformations into a one-dimensional series of letters of a structural alphabet. Such a model learns simultaneously the shape of representative structural letters describing the local conformation and the logic of their connections, i.e. the transition matrix between the letters. Here, we move one step further and report some evidence that such a model of protein local architecture also captures some accurate amino acid features. All the letters have specific and distinct amino acid distributions. Moreover, we show that words of amino acids can have significant propensities for some letters. Perspectives point towards the prediction of the series of letters describing the structure of a protein from its amino acid sequence.

Study of behavior and determination of customer lifetime value(CLV) using Markov chain model

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

Permana, Dony, E-mail: donypermana@students.itb.ac.id; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.

Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by addingmore » the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.« less

Motion of kinesin in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Knoops, Gert; Vanderzande, Carlo

2018-05-01

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

PubMed Central

Irvine, L A; Jafri, M S; Winslow, R L

1999-01-01

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening. PMID:10096885

Global-constrained hidden Markov model applied on wireless capsule endoscopy video segmentation

NASA Astrophysics Data System (ADS)

Wan, Yiwen; Duraisamy, Prakash; Alam, Mohammad S.; Buckles, Bill

2012-06-01

Accurate analysis of wireless capsule endoscopy (WCE) videos is vital but tedious. Automatic image analysis can expedite this task. Video segmentation of WCE into the four parts of the gastrointestinal tract is one way to assist a physician. The segmentation approach described in this paper integrates pattern recognition with statiscal analysis. Iniatially, a support vector machine is applied to classify video frames into four classes using a combination of multiple color and texture features as the feature vector. A Poisson cumulative distribution, for which the parameter depends on the length of segments, models a prior knowledge. A priori knowledge together with inter-frame difference serves as the global constraints driven by the underlying observation of each WCE video, which is fitted by Gaussian distribution to constrain the transition probability of hidden Markov model.Experimental results demonstrated effectiveness of the approach.

A Markovian model of evolving world input-output network

PubMed Central

Isacchini, Giulio

2017-01-01

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money. PMID:29065145

Automatic conversational scene analysis in children with Asperger syndrome/high-functioning autism and typically developing peers.

PubMed

Tavano, Alessandro; Pesarin, Anna; Murino, Vittorio; Cristani, Marco

2014-01-01

Individuals with Asperger syndrome/High Functioning Autism fail to spontaneously attribute mental states to the self and others, a life-long phenotypic characteristic known as mindblindness. We hypothesized that mindblindness would affect the dynamics of conversational interaction. Using generative models, in particular Gaussian mixture models and observed influence models, conversations were coded as interacting Markov processes, operating on novel speech/silence patterns, termed Steady Conversational Periods (SCPs). SCPs assume that whenever an agent's process changes state (e.g., from silence to speech), it causes a general transition of the entire conversational process, forcing inter-actant synchronization. SCPs fed into observed influence models, which captured the conversational dynamics of children and adolescents with Asperger syndrome/High Functioning Autism, and age-matched typically developing participants. Analyzing the parameters of the models by means of discriminative classifiers, the dialogs of patients were successfully distinguished from those of control participants. We conclude that meaning-free speech/silence sequences, reflecting inter-actant synchronization, at least partially encode typical and atypical conversational dynamics. This suggests a direct influence of theory of mind abilities onto basic speech initiative behavior.

Cuntz-Krieger algebras representations from orbits of interval maps

NASA Astrophysics Data System (ADS)

Correia Ramos, C.; Martins, Nuno; Pinto, Paulo R.; Sousa Ramos, J.

2008-05-01

Let f be an expansive Markov interval map with finite transition matrix Af. Then for every point, we yield an irreducible representation of the Cuntz-Krieger algebra and show that two such representations are unitarily equivalent if and only if the points belong to the same generalized orbit. The restriction of each representation to the gauge part of is decomposed into irreducible representations, according to the decomposition of the orbit.

Site 765: Sedimentology

USGS Publications Warehouse

,

1990-01-01

Various techniques were used to decipher the sedimentation history of Site 765, including Markov chain analysis of facies transitions, XRD analysis of clay and other minerals, and multivariate analysis of smear-slide data, in addition to the standard descriptive procedures employed by the shipboard sedimentologist. This chapter presents brief summaries of methodology and major findings of these three techniques, a summary of the sedimentation history, and a discussion of trends in sedimentation through time.

Hidden Markov models reveal complexity in the diving behaviour of short-finned pilot whales

PubMed Central

Quick, Nicola J.; Isojunno, Saana; Sadykova, Dina; Bowers, Matthew; Nowacek, Douglas P.; Read, Andrew J.

2017-01-01

Diving behaviour of short-finned pilot whales is often described by two states; deep foraging and shallow, non-foraging dives. However, this simple classification system ignores much of the variation that occurs during subsurface periods. We used multi-state hidden Markov models (HMM) to characterize states of diving behaviour and the transitions between states in short-finned pilot whales. We used three parameters (number of buzzes, maximum dive depth and duration) measured in 259 dives by digital acoustic recording tags (DTAGs) deployed on 20 individual whales off Cape Hatteras, North Carolina, USA. The HMM identified a four-state model as the best descriptor of diving behaviour. The state-dependent distributions for the diving parameters showed variation between states, indicative of different diving behaviours. Transition probabilities were considerably higher for state persistence than state switching, indicating that dive types occurred in bouts. Our results indicate that subsurface behaviour in short-finned pilot whales is more complex than a simple dichotomy of deep and shallow diving states, and labelling all subsurface behaviour as deep dives or shallow dives discounts a significant amount of important variation. We discuss potential drivers of these patterns, including variation in foraging success, prey availability and selection, bathymetry, physiological constraints and socially mediated behaviour. PMID:28361954

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models.

PubMed

Brouwer, Andrew F; Meza, Rafael; Eisenberg, Marisa C

2017-07-01

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous-time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous-time Markov processes. © 2016 Society for Risk Analysis.

Modeling dyadic processes using Hidden Markov Models: A time series approach to mother-infant interactions during infant immunization.

PubMed

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.

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

Modeling dyadic processes using Hidden Markov Models: A time series approach to mother-infant interactions during infant immunization

PubMed Central

Stifter, Cynthia A.; Rovine, Michael

2016-01-01

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. PMID:27284272

Multiscale hidden Markov models for photon-limited imaging

NASA Astrophysics Data System (ADS)

Nowak, Robert D.

1999-06-01

Photon-limited image analysis is often hindered by low signal-to-noise ratios. A novel Bayesian multiscale modeling and analysis method is developed in this paper to assist in these challenging situations. In addition to providing a very natural and useful framework for modeling an d processing images, Bayesian multiscale analysis is often much less computationally demanding compared to classical Markov random field models. This paper focuses on a probabilistic graph model called the multiscale hidden Markov model (MHMM), which captures the key inter-scale dependencies present in natural image intensities. The MHMM framework presented here is specifically designed for photon-limited imagin applications involving Poisson statistics, and applications to image intensity analysis are examined.

Computer modeling of lung cancer diagnosis-to-treatment process

PubMed Central

Ju, Feng; Lee, Hyo Kyung; Osarogiagbon, Raymond U.; Yu, Xinhua; Faris, Nick

2015-01-01

We introduce an example of a rigorous, quantitative method for quality improvement in lung cancer care-delivery. Computer process modeling methods are introduced for lung cancer diagnosis, staging and treatment selection process. Two types of process modeling techniques, discrete event simulation (DES) and analytical models, are briefly reviewed. Recent developments in DES are outlined and the necessary data and procedures to develop a DES model for lung cancer diagnosis, leading up to surgical treatment process are summarized. The analytical models include both Markov chain model and closed formulas. The Markov chain models with its application in healthcare are introduced and the approach to derive a lung cancer diagnosis process model is presented. Similarly, the procedure to derive closed formulas evaluating the diagnosis process performance is outlined. Finally, the pros and cons of these methods are discussed. PMID:26380181

Conformational transition in signal transduction: metastable states and transition pathways in the activation of a signaling protein.

PubMed

Banerjee, Rahul; Yan, Honggao; Cukier, Robert I

2015-06-04

Signal transduction is of vital importance to the growth and adaptation of living organisms. The key to understand mechanisms of biological signal transduction is elucidation of the conformational dynamics of its signaling proteins, as the activation of a signaling protein is fundamentally a process of conformational transition from an inactive to an active state. A predominant form of signal transduction for bacterial sensing of environmental changes in the wild or inside their hosts is a variety of two-component systems, in which the conformational transition of a response regulator (RR) from an inactive to an active state initiates responses to the environmental changes. Here, RR activation has been investigated using RR468 as a model system by extensive unbiased all-atom molecular dynamics (MD) simulations in explicit solvent, starting from snapshots along a targeted MD trajectory that covers the conformational transition. Markov state modeling, transition path theory, and geometric analyses of the wealth of the MD data have provided a comprehensive description of the RR activation. It involves a network of metastable states, with one metastable state essentially the same as the inactive state and another very similar to the active state that are connected via a small set of intermediates. Five major pathways account for >75% of the fluxes of the conformational transition from the inactive to the active-like state. The thermodynamic stability of the states and the activation barriers between states are found, to identify rate-limiting steps. The conformal transition is initiated predominantly by movements of the β3α3 loop, followed by movements of the β4α4-loop and neighboring α4 helix region, and capped by additional movements of the β3α3 loop. A number of transient hydrophobic and hydrogen bond interactions are revealed, and they may be important for the conformational transition.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

On the Limiting Markov Process of Energy Exchanges in a Rarely Interacting Ball-Piston Gas

NASA Astrophysics Data System (ADS)

Bálint, Péter; Gilbert, Thomas; Nándori, Péter; Szász, Domokos; Tóth, Imre Péter

2017-02-01

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.

Theory and Applications of Weakly Interacting Markov Processes

DTIC Science & Technology

2018-02-03

Moderate deviation principles for stochastic dynamical systems. Boston University, Math Colloquium, March 27, 2015. • Moderate Deviation Principles for...Markov chain approximation method. Submitted. [8] E. Bayraktar and M. Ludkovski. Optimal trade execution in illiquid markets. Math . Finance, 21(4):681...701, 2011. [9] E. Bayraktar and M. Ludkovski. Liquidation in limit order books with controlled intensity. Math . Finance, 24(4):627–650, 2014. [10] P.D