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

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.

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.

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.

Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets

NASA Astrophysics Data System (ADS)

Dharmaraja, Selvamuthu; Pasricha, Puneet; Tardelli, Paola

2017-11-01

This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed.

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.

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.

Fast-slow asymptotics for a Markov chain model of fast sodium current

NASA Astrophysics Data System (ADS)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

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.

Markov models in dentistry: application to resin-bonded bridges and review of the literature.

PubMed

Mahl, Dominik; Marinello, Carlo P; Sendi, Pedram

2012-10-01

Markov models are mathematical models that can be used to describe disease progression and evaluate the cost-effectiveness of medical interventions. Markov models allow projecting clinical and economic outcomes into the future and are therefore frequently used to estimate long-term outcomes of medical interventions. The purpose of this paper is to demonstrate its use in dentistry, using the example of resin-bonded bridges to replace missing teeth, and to review the literature. We used literature data and a four-state Markov model to project long-term outcomes of resin-bonded bridges over a time horizon of 60 years. In addition, the literature was searched in PubMed Medline for research articles on the application of Markov models in dentistry.

Three real-time architectures - A study using reward models

NASA Technical Reports Server (NTRS)

Sjogren, J. A.; Smith, R. M.

1990-01-01

Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the evolutionary behavior of the computer system by a continuous-time Markov chain, and a reward rate is associated with each state. In reliability/availability models, upstates have reward rate 1, and down states have reward rate zero associated with them. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Steady-state expected reward rate and expected instantaneous reward rate are clearly useful measures which can be extracted from the Markov reward model. The diversity of areas where Markov reward models may be used is illustrated with a comparative study of three examples of interest to the fault tolerant computing community.

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

A dynamic multi-scale Markov model based methodology for remaining life prediction

NASA Astrophysics Data System (ADS)

Yan, Jihong; Guo, Chaozhong; Wang, Xing

2011-05-01

The ability to accurately predict the remaining life of partially degraded components is crucial in prognostics. In this paper, a performance degradation index is designed using multi-feature fusion techniques to represent deterioration severities of facilities. Based on this indicator, an improved Markov model is proposed for remaining life prediction. Fuzzy C-Means (FCM) algorithm is employed to perform state division for Markov model in order to avoid the uncertainty of state division caused by the hard division approach. Considering the influence of both historical and real time data, a dynamic prediction method is introduced into Markov model by a weighted coefficient. Multi-scale theory is employed to solve the state division problem of multi-sample prediction. Consequently, a dynamic multi-scale Markov model is constructed. An experiment is designed based on a Bently-RK4 rotor testbed to validate the dynamic multi-scale Markov model, experimental results illustrate the effectiveness of the methodology.

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.

Technical manual for basic version of the Markov chain nest productivity model (MCnest)

EPA Science Inventory

The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...

User’s manual for basic version of MCnest Markov chain nest productivity model

EPA Science Inventory

The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...

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)

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.

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.

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.

Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

PubMed

Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

2010-09-01

Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.

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+) .

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.

[Application of Markov model in post-marketing pharmacoeconomic evaluation of traditional Chinese medicine].

PubMed

Wang, Xin; Su, Xia; Sun, Wentao; Xie, Yanming; Wang, Yongyan

2011-10-01

In post-marketing study of traditional Chinese medicine (TCM), pharmacoeconomic evaluation has an important applied significance. However, the economic literatures of TCM have been unable to fully and accurately reflect the unique overall outcomes of treatment with TCM. For the special nature of TCM itself, we recommend that Markov model could be introduced into post-marketing pharmacoeconomic evaluation of TCM, and also explore the feasibility of model application. Markov model can extrapolate the study time horizon, suit with effectiveness indicators of TCM, and provide measurable comprehensive outcome. In addition, Markov model can promote the development of TCM quality of life scale and the methodology of post-marketing pharmacoeconomic evaluation.

Markov stochasticity coordinates

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

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

Developing a Markov Model for Forecasting End Strength of Selected Marine Corps Reserve (SMCR) Officers

DTIC Science & Technology

2013-03-01

moving average ( ARIMA ) model because the data is not a times series. The best a manpower planner can do at this point is to make an educated assumption...MARKOV MODEL FOR FORECASTING END STRENGTH OF SELECTED MARINE CORPS RESERVE (SMCR) OFFICERS by Anthony D. Licari March 2013 Thesis Advisor...March 2013 3. REPORT TYPE AND DATES COVERED Master’s Thesis 4. TITLE AND SUBTITLE DEVELOPING A MARKOV MODEL FOR FORECASTING END STRENGTH OF

Sampling rare fluctuations of discrete-time Markov chains

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Sampling rare fluctuations of discrete-time Markov chains.

PubMed

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

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.

Identifying and correcting non-Markov states in peptide conformational dynamics

NASA Astrophysics Data System (ADS)

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

2010-02-01

Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ≈50 ps and longer. However, at the time scale of 30-40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

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…

Modelisation de l'historique d'operation de groupes turbine-alternateur

NASA Astrophysics Data System (ADS)

Szczota, Mickael

Because of their ageing fleet, the utility managers are increasingly in needs of tools that can help them to plan efficiently maintenance operations. Hydro-Quebec started a project that aim to foresee the degradation of their hydroelectric runner, and use that information to classify the generating unit. That classification will help to know which generating unit is more at risk to undergo a major failure. Cracks linked to the fatigue phenomenon are a predominant degradation mode and the loading sequences applied to the runner is a parameter impacting the crack growth. So, the aim of this memoir is to create a generator able to generate synthetic loading sequences that are statistically equivalent to the observed history. Those simulated sequences will be used as input in a life assessment model. At first, we describe how the generating units are operated by Hydro-Quebec and analyse the available data, the analysis shows that the data are non-stationnary. Then, we review modelisation and validation methods. In the following chapter a particular attention is given to a precise description of the validation and comparison procedure. Then, we present the comparison of three kind of model : Discrete Time Markov Chains, Discrete Time Semi-Markov Chains and the Moving Block Bootstrap. For the first two models, we describe how to take account for the non-stationnarity. Finally, we show that the Markov Chain is not adapted for our case, and that the Semi-Markov chains are better when they include the non-stationnarity. The final choice between Semi-Markov Chains and the Moving Block Bootstrap depends of the user. But, with a long term vision we recommend the use of Semi-Markov chains for their flexibility. Keywords: Stochastic models, Models validation, Reliability, Semi-Markov Chains, Markov Chains, Bootstrap

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.

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

zipHMMlib: a highly optimised HMM library exploiting repetitions in the input to speed up the forward algorithm.

PubMed

Sand, Andreas; Kristiansen, Martin; Pedersen, Christian N S; Mailund, Thomas

2013-11-22

Hidden Markov models are widely used for genome analysis as they combine ease of modelling with efficient analysis algorithms. Calculating the likelihood of a model using the forward algorithm has worst case time complexity linear in the length of the sequence and quadratic in the number of states in the model. For genome analysis, however, the length runs to millions or billions of observations, and when maximising the likelihood hundreds of evaluations are often needed. A time efficient forward algorithm is therefore a key ingredient in an efficient hidden Markov model library. We have built a software library for efficiently computing the likelihood of a hidden Markov model. The library exploits commonly occurring substrings in the input to reuse computations in the forward algorithm. In a pre-processing step our library identifies common substrings and builds a structure over the computations in the forward algorithm which can be reused. This analysis can be saved between uses of the library and is independent of concrete hidden Markov models so one preprocessing can be used to run a number of different models.Using this library, we achieve up to 78 times shorter wall-clock time for realistic whole-genome analyses with a real and reasonably complex hidden Markov model. In one particular case the analysis was performed in less than 8 minutes compared to 9.6 hours for the previously fastest library. We have implemented the preprocessing procedure and forward algorithm as a C++ library, zipHMM, with Python bindings for use in scripts. The library is available at http://birc.au.dk/software/ziphmm/.

Real-time antenna fault diagnosis experiments at DSS 13

NASA Technical Reports Server (NTRS)

Mellstrom, J.; Pierson, C.; Smyth, P.

1992-01-01

Experimental results obtained when a previously described fault diagnosis system was run online in real time at the 34-m beam waveguide antenna at Deep Space Station (DSS) 13 are described. Experimental conditions and the quality of results are described. A neural network model and a maximum-likelihood Gaussian classifier are compared with and without a Markov component to model temporal context. At the rate of a state update every 6.4 seconds, over a period of roughly 1 hour, the neural-Markov system had zero errors (incorrect state estimates) while monitoring both faulty and normal operations. The overall results indicate that the neural-Markov combination is the most accurate model and has significant practical potential.

Machine learning in sentiment reconstruction of the simulated stock market

NASA Astrophysics Data System (ADS)

Goykhman, Mikhail; Teimouri, Ali

2018-02-01

In this paper we continue the study of the simulated stock market framework defined by the driving sentiment processes. We focus on the market environment driven by the buy/sell trading sentiment process of the Markov chain type. We apply the methodology of the Hidden Markov Models and the Recurrent Neural Networks to reconstruct the transition probabilities matrix of the Markov sentiment process and recover the underlying sentiment states from the observed stock price behavior. We demonstrate that the Hidden Markov Model can successfully recover the transition probabilities matrix for the hidden sentiment process of the Markov Chain type. We also demonstrate that the Recurrent Neural Network can successfully recover the hidden sentiment states from the observed simulated stock price time series.

Zero-state Markov switching count-data models: an empirical assessment.

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2010-01-01

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the states is a zero-accident count state, which has accident probabilities that are so low that they cannot be statistically distinguished from zero, and the other state is a normal-count state, in which counts can be non-negative integers that are generated by some counting process, for example, a Poisson or negative binomial. While zero-inflated models have come under some criticism with regard to accident-frequency applications - one fact is undeniable - in many applications they provide a statistically superior fit to the data. The Markov switching approach we propose seeks to overcome some of the criticism associated with the zero-accident state of the zero-inflated model by allowing individual roadway segments to switch between zero and normal-count states over time. An important advantage of this Markov switching approach is that it allows for the direct statistical estimation of the specific roadway-segment state (i.e., zero-accident or normal-count state) whereas traditional zero-inflated models do not. To demonstrate the applicability of this approach, a two-state Markov switching negative binomial model (estimated with Bayesian inference) and standard zero-inflated negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. It is shown that the Markov switching model is a viable alternative and results in a superior statistical fit relative to the zero-inflated models.

Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series.

PubMed

Weber, Juliane; Zachow, Christopher; Witthaut, Dirk

2018-03-01

Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function. The two-state model is readily extended to stochastically reproduce the actual generation per period. To evaluate the additive binary Markov chain method, we introduce a coarse model of the electric power system to derive backup and storage needs. We find that the temporal correlations of wind power generation, the backup need as a function of the storage capacity, and the resting time distribution of high and low wind events for different shares of wind generation can be reconstructed.

Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

NASA Astrophysics Data System (ADS)

Weber, Juliane; Zachow, Christopher; Witthaut, Dirk

2018-03-01

Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function. The two-state model is readily extended to stochastically reproduce the actual generation per period. To evaluate the additive binary Markov chain method, we introduce a coarse model of the electric power system to derive backup and storage needs. We find that the temporal correlations of wind power generation, the backup need as a function of the storage capacity, and the resting time distribution of high and low wind events for different shares of wind generation can be reconstructed.

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

NASA Astrophysics Data System (ADS)

Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi

2017-11-01

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.

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.

The distribution of genome shared identical by descent for a pair of full sibs by means of the continuous time Markov chain

NASA Astrophysics Data System (ADS)

Julie, Hongki; Pasaribu, Udjianna S.; Pancoro, Adi

2015-12-01

This paper will allow Markov Chain's application in genome shared identical by descent by two individual at full sibs model. The full sibs model was a continuous time Markov Chain with three state. In the full sibs model, we look for the cumulative distribution function of the number of sub segment which have 2 IBD haplotypes from a segment of the chromosome which the length is t Morgan and the cumulative distribution function of the number of sub segment which have at least 1 IBD haplotypes from a segment of the chromosome which the length is t Morgan. This cumulative distribution function will be developed by the moment generating function.

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.

Monitoring volcano activity through Hidden Markov Model

NASA Astrophysics Data System (ADS)

Cassisi, C.; Montalto, P.; Prestifilippo, M.; Aliotta, M.; Cannata, A.; Patanè, D.

2013-12-01

During 2011-2013, Mt. Etna was mainly characterized by cyclic occurrences of lava fountains, totaling to 38 episodes. During this time interval Etna volcano's states (QUIET, PRE-FOUNTAIN, FOUNTAIN, POST-FOUNTAIN), whose automatic recognition is very useful for monitoring purposes, turned out to be strongly related to the trend of RMS (Root Mean Square) of the seismic signal recorded by stations close to the summit area. Since RMS time series behavior is considered to be stochastic, we can try to model the system generating its values, assuming to be a Markov process, by using Hidden Markov models (HMMs). HMMs are a powerful tool in modeling any time-varying series. HMMs analysis seeks to recover the sequence of hidden states from the observed emissions. In our framework, observed emissions are characters generated by the SAX (Symbolic Aggregate approXimation) technique, which maps RMS time series values with discrete literal emissions. The experiments show how it is possible to guess volcano states by means of HMMs and SAX.

Model-based Clustering of Categorical Time Series with Multinomial Logit Classification

NASA Astrophysics Data System (ADS)

Frühwirth-Schnatter, Sylvia; Pamminger, Christoph; Winter-Ebmer, Rudolf; Weber, Andrea

2010-09-01

A common problem in many areas of applied statistics is to identify groups of similar time series in a panel of time series. However, distance-based clustering methods cannot easily be extended to time series data, where an appropriate distance-measure is rather difficult to define, particularly for discrete-valued time series. Markov chain clustering, proposed by Pamminger and Frühwirth-Schnatter [6], is an approach for clustering discrete-valued time series obtained by observing a categorical variable with several states. This model-based clustering method is based on finite mixtures of first-order time-homogeneous Markov chain models. In order to further explain group membership we present an extension to the approach of Pamminger and Frühwirth-Schnatter [6] by formulating a probabilistic model for the latent group indicators within the Bayesian classification rule by using a multinomial logit model. The parameters are estimated for a fixed number of clusters within a Bayesian framework using an Markov chain Monte Carlo (MCMC) sampling scheme representing a (full) Gibbs-type sampler which involves only draws from standard distributions. Finally, an application to a panel of Austrian wage mobility data is presented which leads to an interesting segmentation of the Austrian labour market.

Estimation in a semi-Markov transformation model

PubMed Central

Dabrowska, Dorota M.

2012-01-01

Multi-state models provide a common tool for analysis of longitudinal failure time data. In biomedical applications, models of this kind are often used to describe evolution of a disease and assume that patient may move among a finite number of states representing different phases in the disease progression. Several authors developed extensions of the proportional hazard model for analysis of multi-state models in the presence of covariates. In this paper, we consider a general class of censored semi-Markov and modulated renewal processes and propose the use of transformation models for their analysis. Special cases include modulated renewal processes with interarrival times specified using transformation models, and semi-Markov processes with with one-step transition probabilities defined using copula-transformation models. We discuss estimation of finite and infinite dimensional parameters of the model, and develop an extension of the Gaussian multiplier method for setting confidence bands for transition probabilities. A transplant outcome data set from the Center for International Blood and Marrow Transplant Research is used for illustrative purposes. PMID:22740583

Reliability Analysis of the Electrical Control System of Subsea Blowout Preventers Using Markov Models

PubMed Central

Liu, Zengkai; Liu, Yonghong; Cai, Baoping

2014-01-01

Reliability analysis of the electrical control system of a subsea blowout preventer (BOP) stack is carried out based on Markov method. For the subsea BOP electrical control system used in the current work, the 3-2-1-0 and 3-2-0 input voting schemes are available. The effects of the voting schemes on system performance are evaluated based on Markov models. In addition, the effects of failure rates of the modules and repair time on system reliability indices are also investigated. PMID:25409010

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.

Utah State University Global Assimilation of Ionospheric Measurements Gauss-Markov Kalman filter model of the ionosphere: Model description and validation

NASA Astrophysics Data System (ADS)

Scherliess, L.; Schunk, R. W.; Sojka, J. J.; Thompson, D. C.; Zhu, L.

2006-11-01

The Utah State University Gauss-Markov Kalman Filter (GMKF) was developed as part of the Global Assimilation of Ionospheric Measurements (GAIM) program. The GMKF uses a physics-based model of the ionosphere and a Gauss-Markov Kalman filter as a basis for assimilating a diverse set of real-time (or near real-time) observations. The physics-based model is the Ionospheric Forecast Model (IFM), which accounts for five ion species and covers the E region, F region, and the topside from 90 to 1400 km altitude. Within the GMKF, the IFM derived ionospheric densities constitute a background density field on which perturbations are superimposed based on the available data and their errors. In the current configuration, the GMKF assimilates slant total electron content (TEC) from a variable number of global positioning satellite (GPS) ground sites, bottomside electron density (Ne) profiles from a variable number of ionosondes, in situ Ne from four Defense Meteorological Satellite Program (DMSP) satellites, and nighttime line-of-sight ultraviolet (UV) radiances measured by satellites. To test the GMKF for real-time operations and to validate its ionospheric density specifications, we have tested the model performance for a variety of geophysical conditions. During these model runs various combination of data types and data quantities were assimilated. To simulate real-time operations, the model ran continuously and automatically and produced three-dimensional global electron density distributions in 15 min increments. In this paper we will describe the Gauss-Markov Kalman filter model and present results of our validation study, with an emphasis on comparisons with independent observations.

CTPPL: A Continuous Time Probabilistic Programming Language

DTIC Science & Technology

2009-07-01

recent years there has been a flurry of interest in continuous time models, mostly focused on continuous time Bayesian networks ( CTBNs ) [Nodelman, 2007... CTBNs are built on homogenous Markov processes. A homogenous Markov pro- cess is a finite state, continuous time process, consisting of an initial...q1 : xn()] ... Some state transitions can produce emissions. In a CTBN , each variable has a conditional inten- sity matrix Qu for every combination of

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.

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.

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.

Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.

PubMed

Snipas, Mindaugas; Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Paulauskas, Nerijus; Bukauskas, Feliksas F

2015-01-01

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times.

Predicting hepatitis B monthly incidence rates using weighted Markov chains and time series methods.

PubMed

Shahdoust, Maryam; Sadeghifar, Majid; Poorolajal, Jalal; Javanrooh, Niloofar; Amini, Payam

2015-01-01

Hepatitis B (HB) is a major global mortality. Accurately predicting the trend of the disease can provide an appropriate view to make health policy disease prevention. This paper aimed to apply three different to predict monthly incidence rates of HB. This historical cohort study was conducted on the HB incidence data of Hamadan Province, the west of Iran, from 2004 to 2012. Weighted Markov Chain (WMC) method based on Markov chain theory and two time series models including Holt Exponential Smoothing (HES) and SARIMA were applied on the data. The results of different applied methods were compared to correct percentages of predicted incidence rates. The monthly incidence rates were clustered into two clusters as state of Markov chain. The correct predicted percentage of the first and second clusters for WMC, HES and SARIMA methods was (100, 0), (84, 67) and (79, 47) respectively. The overall incidence rate of HBV is estimated to decrease over time. The comparison of results of the three models indicated that in respect to existing seasonality trend and non-stationarity, the HES had the most accurate prediction of the incidence rates.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times.

PubMed

Cator, E; van de Bovenkamp, R; Van Mieghem, P

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times

NASA Astrophysics Data System (ADS)

Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Dependability and performability analysis

NASA Technical Reports Server (NTRS)

Trivedi, Kishor S.; Ciardo, Gianfranco; Malhotra, Manish; Sahner, Robin A.

1993-01-01

Several practical issues regarding specifications and solution of dependability and performability models are discussed. Model types with and without rewards are compared. Continuous-time Markov chains (CTMC's) are compared with (continuous-time) Markov reward models (MRM's) and generalized stochastic Petri nets (GSPN's) are compared with stochastic reward nets (SRN's). It is shown that reward-based models could lead to more concise model specifications and solution of a variety of new measures. With respect to the solution of dependability and performability models, three practical issues were identified: largeness, stiffness, and non-exponentiality, and a variety of approaches are discussed to deal with them, including some of the latest research efforts.

Multidimensional Latent Markov Models in a Developmental Study of Inhibitory Control and Attentional Flexibility in Early Childhood

ERIC Educational Resources Information Center

Bartolucci, Francesco; Solis-Trapala, Ivonne L.

2010-01-01

We demonstrate the use of a multidimensional extension of the latent Markov model to analyse data from studies with repeated binary responses in developmental psychology. In particular, we consider an experiment based on a battery of tests which was administered to pre-school children, at three time periods, in order to measure their inhibitory…

Hidden Markov models for character recognition.

PubMed

Vlontzos, J A; Kung, S Y

1992-01-01

A hierarchical system for character recognition with hidden Markov model knowledge sources which solve both the context sensitivity problem and the character instantiation problem is presented. The system achieves 97-99% accuracy using a two-level architecture and has been implemented using a systolic array, thus permitting real-time (1 ms per character) multifont and multisize printed character recognition as well as handwriting recognition.

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.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Application of Stochastic Automata Networks for Creation of Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

PubMed Central

Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Bukauskas, Feliksas F.

2015-01-01

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times. PMID:25705700

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.

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.

An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes

ERIC Educational Resources Information Center

Kapland, David

2008-01-01

This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…

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.

Information-Theoretic Performance Analysis of Sensor Networks via Markov Modeling of Time Series Data.

PubMed

Li, Yue; Jha, Devesh K; Ray, Asok; Wettergren, Thomas A; Yue Li; Jha, Devesh K; Ray, Asok; Wettergren, Thomas A; Wettergren, Thomas A; Li, Yue; Ray, Asok; Jha, Devesh K

2018-06-01

This paper presents information-theoretic performance analysis of passive sensor networks for detection of moving targets. The proposed method falls largely under the category of data-level information fusion in sensor networks. To this end, a measure of information contribution for sensors is formulated in a symbolic dynamics framework. The network information state is approximately represented as the largest principal component of the time series collected across the network. To quantify each sensor's contribution for generation of the information content, Markov machine models as well as x-Markov (pronounced as cross-Markov) machine models, conditioned on the network information state, are constructed; the difference between the conditional entropies of these machines is then treated as an approximate measure of information contribution by the respective sensors. The x-Markov models represent the conditional temporal statistics given the network information state. The proposed method has been validated on experimental data collected from a local area network of passive sensors for target detection, where the statistical characteristics of environmental disturbances are similar to those of the target signal in the sense of time scale and texture. A distinctive feature of the proposed algorithm is that the network decisions are independent of the behavior and identity of the individual sensors, which is desirable from computational perspectives. Results are presented to demonstrate the proposed method's efficacy to correctly identify the presence of a target with very low false-alarm rates. The performance of the underlying algorithm is compared with that of a recent data-driven, feature-level information fusion algorithm. It is shown that the proposed algorithm outperforms the other algorithm.

Memetic Approaches for Optimizing Hidden Markov Models: A Case Study in Time Series Prediction

NASA Astrophysics Data System (ADS)

Bui, Lam Thu; Barlow, Michael

We propose a methodology for employing memetics (local search) within the framework of evolutionary algorithms to optimize parameters of hidden markov models. With this proposal, the rate and frequency of using local search are automatically changed over time either at a population or individual level. At the population level, we allow the rate of using local search to decay over time to zero (at the final generation). At the individual level, each individual is equipped with information of when it will do local search and for how long. This information evolves over time alongside the main elements of the chromosome representing the individual.

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

Forecasting land-cover growth using remotely sensed data: a case study of the Igneada protection area in Turkey.

PubMed

Bozkaya, A Gonca; Balcik, Filiz Bektas; Goksel, Cigdem; Esbah, Hayriye

2015-03-01

Human activities in many parts of the world have greatly affected natural areas. Therefore, monitoring and forecasting of land-cover changes are important components for sustainable utilization, conservation, and development of these areas. This research has been conducted on Igneada, a legally protected area on the northwest coast of Turkey, which is famous for its unique, mangrove forests. The main focus of this study was to apply a land use and cover model that could quantitatively and graphically present the changes and its impacts on Igneada landscapes in the future. In this study, a Markov chain-based, stochastic Markov model and cellular automata Markov model were used. These models were calibrated using a time series of developed areas derived from Landsat Thematic Mapper (TM) imagery between 1990 and 2010 that also projected future growth to 2030. The results showed that CA Markov yielded reliable information better than St. Markov model. The findings displayed constant but overall slight increase of settlement and forest cover, and slight decrease of agricultural lands. However, even the slightest unsustainable change can put a significant pressure on the sensitive ecosystems of Igneada. Therefore, the management of the protected area should not only focus on the landscape composition but also pay attention to landscape configuration.

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.

A method of hidden Markov model optimization for use with geophysical data sets

NASA Technical Reports Server (NTRS)

Granat, R. A.

2003-01-01

Geophysics research has been faced with a growing need for automated techniques with which to process large quantities of data. A successful tool must meet a number of requirements: it should be consistent, require minimal parameter tuning, and produce scientifically meaningful results in reasonable time. We introduce a hidden Markov model (HMM)-based method for analysis of geophysical data sets that attempts to address these issues.

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.

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

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 modulated Poisson process models incorporating covariates for rainfall intensity.

PubMed

Thayakaran, R; Ramesh, N I

2013-01-01

Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.

Application of Markov Models for Analysis of Development of Psychological Characteristics

ERIC Educational Resources Information Center

Kuravsky, Lev S.; Malykh, Sergey B.

2004-01-01

A technique to study combined influence of environmental and genetic factors on the base of changes in phenotype distributions is presented. Histograms are exploited as base analyzed characteristics. A continuous time, discrete state Markov process with piece-wise constant interstate transition rates is associated with evolution of each histogram.…

Detecting critical state before phase transition of complex systems by hidden Markov model

NASA Astrophysics Data System (ADS)

Liu, Rui; Chen, Pei; Li, Yongjun; Chen, Luonan

Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e., before-transition state, pre-transition state, and after-transition state, which can be considered as three different Markov processes. Thus, based on this dynamical feature, we present a novel computational method, i.e., hidden Markov model (HMM), to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e., the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin, and HCV-induced dysplasia and hepatocellular carcinoma.

Mixture Hidden Markov Models in Finance Research

NASA Astrophysics Data System (ADS)

Dias, José G.; Vermunt, Jeroen K.; Ramos, Sofia

Finite mixture models have proven to be a powerful framework whenever unobserved heterogeneity cannot be ignored. We introduce in finance research the Mixture Hidden Markov Model (MHMM) that takes into account time and space heterogeneity simultaneously. This approach is flexible in the sense that it can deal with the specific features of financial time series data, such as asymmetry, kurtosis, and unobserved heterogeneity. This methodology is applied to model simultaneously 12 time series of Asian stock markets indexes. Because we selected a heterogeneous sample of countries including both developed and emerging countries, we expect that heterogeneity in market returns due to country idiosyncrasies will show up in the results. The best fitting model was the one with two clusters at country level with different dynamics between the two regimes.

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.

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

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.

Hidden Markov Item Response Theory Models for Responses and Response Times.

PubMed

Molenaar, Dylan; Oberski, Daniel; Vermunt, Jeroen; De Boeck, Paul

2016-01-01

Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.

Analysis of single ion channel data incorporating time-interval omission and sampling

PubMed Central

The, Yu-Kai; Timmer, Jens

2005-01-01

Hidden Markov models are widely used to describe single channel currents from patch-clamp experiments. The inevitable anti-aliasing filter limits the time resolution of the measurements and therefore the standard hidden Markov model is not adequate anymore. The notion of time-interval omission has been introduced where brief events are not detected. The developed, exact solutions to this problem do not take into account that the measured intervals are limited by the sampling time. In this case the dead-time that specifies the minimal detectable interval length is not defined unambiguously. We show that a wrong choice of the dead-time leads to considerably biased estimates and present the appropriate equations to describe sampled data. PMID:16849220

A Modularized Efficient Framework for Non-Markov Time Series Estimation

NASA Astrophysics Data System (ADS)

Schamberg, Gabriel; Ba, Demba; Coleman, Todd P.

2018-06-01

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

[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.

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.

Optimized mixed Markov models for motif identification

PubMed Central

Huang, Weichun; Umbach, David M; Ohler, Uwe; Li, Leping

2006-01-01

Background Identifying functional elements, such as transcriptional factor binding sites, is a fundamental step in reconstructing gene regulatory networks and remains a challenging issue, largely due to limited availability of training samples. Results We introduce a novel and flexible model, the Optimized Mixture Markov model (OMiMa), and related methods to allow adjustment of model complexity for different motifs. In comparison with other leading methods, OMiMa can incorporate more than the NNSplice's pairwise dependencies; OMiMa avoids model over-fitting better than the Permuted Variable Length Markov Model (PVLMM); and OMiMa requires smaller training samples than the Maximum Entropy Model (MEM). Testing on both simulated and actual data (regulatory cis-elements and splice sites), we found OMiMa's performance superior to the other leading methods in terms of prediction accuracy, required size of training data or computational time. Our OMiMa system, to our knowledge, is the only motif finding tool that incorporates automatic selection of the best model. OMiMa is freely available at [1]. Conclusion Our optimized mixture of Markov models represents an alternative to the existing methods for modeling dependent structures within a biological motif. Our model is conceptually simple and effective, and can improve prediction accuracy and/or computational speed over other leading methods. PMID:16749929

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species.

PubMed

Wang, Xueying; Walton, Jay R; Parshad, Rana D

2016-01-01

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.

Detection method of financial crisis in Indonesia using MSGARCH models based on banking condition indicators

NASA Astrophysics Data System (ADS)

Sugiyanto; Zukhronah, E.; Sari, S. P.

2018-05-01

Financial crisis has hit Indonesia for several times resulting the needs for an early detection system to minimize the impact. One of many methods that can be used to detect the crisis is to model the crisis indicators using combination of volatility and Markov switching models [5]. There are some indicators that can be used to detect financial crisis. Three of them are the difference between interest rate on deposit and lending, the real interest rate on deposit, and the difference between real BI rate and real Fed rate which can be referred as banking condition indicators. Volatility model used to overcome the conditional variance that change over time. Combination of volatility and Markov switching models used to detect condition change on the data. The smoothed probability from the combined models can be used to detect the crisis. This research resulted that the best combined volatility and Markov switching models for the three indicators are MS-GARCH(3,1,1) models with three states assumption. Crises in mid of 1997 until 1998 has successfully detected with a certain range of smoothed probability value for the three indicators.

Semi-Markov models for interval censored transient cognitive states with back transitions and a competing risk

PubMed Central

Wei, Shaoceng; Kryscio, Richard J.

2015-01-01

Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk (Figure 1). Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript we apply a Semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants. PMID:24821001

Semi-Markov models for interval censored transient cognitive states with back transitions and a competing risk.

PubMed

Wei, Shaoceng; Kryscio, Richard J

2016-12-01

Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient cognitive states and death as a competing risk. Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript, we apply a semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants. © The Author(s) 2014.

Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant

NASA Astrophysics Data System (ADS)

Aggarwal, Anil Kr.; Kumar, Sanjeev; Singh, Vikram; Garg, Tarun Kr.

2015-12-01

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth-death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman-Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga-Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the urea synthesis system of the fertilizer plant.

Noise can speed convergence in Markov chains.

PubMed

Franzke, Brandon; Kosko, Bart

2011-10-01

A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.

The algebra of the general Markov model on phylogenetic trees and networks.

PubMed

Sumner, J G; Holland, B R; Jarvis, P D

2012-04-01

It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.

A novel grey-fuzzy-Markov and pattern recognition model for industrial accident forecasting

NASA Astrophysics Data System (ADS)

Edem, Inyeneobong Ekoi; Oke, Sunday Ayoola; Adebiyi, Kazeem Adekunle

2017-10-01

Industrial forecasting is a top-echelon research domain, which has over the past several years experienced highly provocative research discussions. The scope of this research domain continues to expand due to the continuous knowledge ignition motivated by scholars in the area. So, more intelligent and intellectual contributions on current research issues in the accident domain will potentially spark more lively academic, value-added discussions that will be of practical significance to members of the safety community. In this communication, a new grey-fuzzy-Markov time series model, developed from nondifferential grey interval analytical framework has been presented for the first time. This instrument forecasts future accident occurrences under time-invariance assumption. The actual contribution made in the article is to recognise accident occurrence patterns and decompose them into grey state principal pattern components. The architectural framework of the developed grey-fuzzy-Markov pattern recognition (GFMAPR) model has four stages: fuzzification, smoothening, defuzzification and whitenisation. The results of application of the developed novel model signify that forecasting could be effectively carried out under uncertain conditions and hence, positions the model as a distinctly superior tool for accident forecasting investigations. The novelty of the work lies in the capability of the model in making highly accurate predictions and forecasts based on the availability of small or incomplete accident data.

Distributions-per-level: a means of testing level detectors and models of patch-clamp data.

PubMed

Schröder, I; Huth, T; Suitchmezian, V; Jarosik, J; Schnell, S; Hansen, U P

2004-01-01

Level or jump detectors generate the reconstructed time series from a noisy record of patch-clamp current. The reconstructed time series is used to create dwell-time histograms for the kinetic analysis of the Markov model of the investigated ion channel. It is shown here that some additional lines in the software of such a detector can provide a powerful new means of patch-clamp analysis. For each current level that can be recognized by the detector, an array is declared. The new software assigns every data point of the original time series to the array that belongs to the actual state of the detector. From the data sets in these arrays distributions-per-level are generated. Simulated and experimental time series analyzed by Hinkley detectors are used to demonstrate the benefits of these distributions-per-level. First, they can serve as a test of the reliability of jump and level detectors. Second, they can reveal beta distributions as resulting from fast gating that would usually be hidden in the overall amplitude histogram. Probably the most valuable feature is that the malfunctions of the Hinkley detectors turn out to depend on the Markov model of the ion channel. Thus, the errors revealed by the distributions-per-level can be used to distinguish between different putative Markov models of the measured time series.

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

ModFossa: A library for modeling ion channels using Python.

PubMed

Ferneyhough, Gareth B; Thibealut, Corey M; Dascalu, Sergiu M; Harris, Frederick C

2016-06-01

The creation and simulation of ion channel models using continuous-time Markov processes is a powerful and well-used tool in the field of electrophysiology and ion channel research. While several software packages exist for the purpose of ion channel modeling, most are GUI based, and none are available as a Python library. In an attempt to provide an easy-to-use, yet powerful Markov model-based ion channel simulator, we have developed ModFossa, a Python library supporting easy model creation and stimulus definition, complete with a fast numerical solver, and attractive vector graphics plotting.

A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

NASA Technical Reports Server (NTRS)

Carpenter, Russell; Lee, Taesul

2008-01-01

Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population.

PubMed

Punzo, Antonio; Ingrassia, Salvatore; Maruotti, Antonello

2018-04-22

A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates are introduced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The hidden Markov regression models with random covariates class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data. Copyright © 2018 John Wiley & Sons, Ltd.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Modular techniques for dynamic fault-tree analysis

NASA Technical Reports Server (NTRS)

Patterson-Hine, F. A.; Dugan, Joanne B.

1992-01-01

It is noted that current approaches used to assess the dependability of complex systems such as Space Station Freedom and the Air Traffic Control System are incapable of handling the size and complexity of these highly integrated designs. A novel technique for modeling such systems which is built upon current techniques in Markov theory and combinatorial analysis is described. It enables the development of a hierarchical representation of system behavior which is more flexible than either technique alone. A solution strategy which is based on an object-oriented approach to model representation and evaluation is discussed. The technique is virtually transparent to the user since the fault tree models can be built graphically and the objects defined automatically. The tree modularization procedure allows the two model types, Markov and combinatoric, to coexist and does not require that the entire fault tree be translated to a Markov chain for evaluation. This effectively reduces the size of the Markov chain required and enables solutions with less truncation, making analysis of longer mission times possible. Using the fault-tolerant parallel processor as an example, a model is built and solved for a specific mission scenario and the solution approach is illustrated in detail.

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.

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 Mixed Effects Modeling Using Electronic Adherence Monitoring Records Identifies Influential Covariates to HIV Preexposure Prophylaxis.

PubMed

Madrasi, Kumpal; Chaturvedula, Ayyappa; Haberer, Jessica E; Sale, Mark; Fossler, Michael J; Bangsberg, David; Baeten, Jared M; Celum, Connie; Hendrix, Craig W

2017-05-01

Adherence is a major factor in the effectiveness of preexposure prophylaxis (PrEP) for HIV prevention. Modeling patterns of adherence helps to identify influential covariates of different types of adherence as well as to enable clinical trial simulation so that appropriate interventions can be developed. We developed a Markov mixed-effects model to understand the covariates influencing adherence patterns to daily oral PrEP. Electronic adherence records (date and time of medication bottle cap opening) from the Partners PrEP ancillary adherence study with a total of 1147 subjects were used. This study included once-daily dosing regimens of placebo, oral tenofovir disoproxil fumarate (TDF), and TDF in combination with emtricitabine (FTC), administered to HIV-uninfected members of serodiscordant couples. One-coin and first- to third-order Markov models were fit to the data using NONMEM ® 7.2. Model selection criteria included objective function value (OFV), Akaike information criterion (AIC), visual predictive checks, and posterior predictive checks. Covariates were included based on forward addition (α = 0.05) and backward elimination (α = 0.001). Markov models better described the data than 1-coin models. A third-order Markov model gave the lowest OFV and AIC, but the simpler first-order model was used for covariate model building because no additional benefit on prediction of target measures was observed for higher-order models. Female sex and older age had a positive impact on adherence, whereas Sundays, sexual abstinence, and sex with a partner other than the study partner had a negative impact on adherence. Our findings suggest adherence interventions should consider the role of these factors. © 2016, The American College of Clinical Pharmacology.

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.

Sensitivity Study for Long Term Reliability

NASA Technical Reports Server (NTRS)

White, Allan L.

2008-01-01

This paper illustrates using Markov models to establish system and maintenance requirements for small electronic controllers where the goal is a high probability of continuous service for a long period of time. The system and maintenance items considered are quality of components, various degrees of simple redundancy, redundancy with reconfiguration, diagnostic levels, periodic maintenance, and preventive maintenance. Markov models permit a quantitative investigation with comparison and contrast. An element of special interest is the use of conditional probability to study the combination of imperfect diagnostics and periodic maintenance.

Significance testing of clinical data using virus dynamics models with a Markov chain Monte Carlo method: application to emergence of lamivudine-resistant hepatitis B virus.

PubMed Central

Burroughs, N J; Pillay, D; Mutimer, D

1999-01-01

Bayesian analysis using a virus dynamics model is demonstrated to facilitate hypothesis testing of patterns in clinical time-series. Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy, chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non-parametric tests. We show that lamivudine-resistant mutants grow faster in transplant patients than in chronic carriers, which probably explains the differences in emergence times and failure rates between these two sets of patients. Incorporation of dynamic models into Bayesian parameter analysis is of general applicability in medical statistics. PMID:10643081

The application of a Grey Markov Model to forecasting annual maximum water levels at hydrological stations

NASA Astrophysics Data System (ADS)

Dong, Sheng; Chi, Kun; Zhang, Qiyi; Zhang, Xiangdong

2012-03-01

Compared with traditional real-time forecasting, this paper proposes a Grey Markov Model (GMM) to forecast the maximum water levels at hydrological stations in the estuary area. The GMM combines the Grey System and Markov theory into a higher precision model. The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation values, and thus gives forecast results involving two aspects of information. The procedure for forecasting annul maximum water levels with the GMM contains five main steps: 1) establish the GM (1, 1) model based on the data series; 2) estimate the trend values; 3) establish a Markov Model based on relative error series; 4) modify the relative errors caused in step 2, and then obtain the relative errors of the second order estimation; 5) compare the results with measured data and estimate the accuracy. The historical water level records (from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of the Haihe River near Tianjin, China are utilized to calibrate and verify the proposed model according to the above steps. Every 25 years' data are regarded as a hydro-sequence. Eight groups of simulated results show reasonable agreement between the predicted values and the measured data. The GMM is also applied to the 10 other hydrological stations in the same estuary. The forecast results for all of the hydrological stations are good or acceptable. The feasibility and effectiveness of this new forecasting model have been proved in this paper.

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.

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.

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

Bykova, Nadezda A; Favorov, Alexander V; Mironov, Andrey A

2013-01-01

The problem of reconstruction of ancestral states given a phylogeny and data from extant species arises in a wide range of biological studies. The continuous-time Markov model for the discrete states evolution is generally used for the reconstruction of ancestral states. We modify this model to account for a case when the states of the extant species are uncertain. This situation appears, for example, if the states for extant species are predicted by some program and thus are known only with some level of reliability; it is common for bioinformatics field. The main idea is formulation of the problem as a hidden Markov model on a tree (tree HMM, tHMM), where the basic continuous-time Markov model is expanded with the introduction of emission probabilities of observed data (e.g. prediction scores) for each underlying discrete state. Our tHMM decoding algorithm allows us to predict states at the ancestral nodes as well as to refine states at the leaves on the basis of quantitative comparative genomics. The test on the simulated data shows that the tHMM approach applied to the continuous variable reflecting the probabilities of the states (i.e. prediction score) appears to be more accurate then the reconstruction from the discrete states assignment defined by the best score threshold. We provide examples of applying our model to the evolutionary analysis of N-terminal signal peptides and transcription factor binding sites in bacteria. The program is freely available at http://bioinf.fbb.msu.ru/~nadya/tHMM and via web-service at http://bioinf.fbb.msu.ru/treehmmweb.

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.

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.

A tutorial on the CARE III approach to reliability modeling. [of fault tolerant avionics and control systems

NASA Technical Reports Server (NTRS)

Trivedi, K. S.; Geist, R. M.

1981-01-01

The CARE 3 reliability model for aircraft avionics and control systems is described by utilizing a number of examples which frequently use state-of-the-art mathematical modeling techniques as a basis for their exposition. Behavioral decomposition followed by aggregration were used in an attempt to deal with reliability models with a large number of states. A comprehensive set of models of the fault-handling processes in a typical fault-tolerant system was used. These models were semi-Markov in nature, thus removing the usual restrictions of exponential holding times within the coverage model. The aggregate model is a non-homogeneous Markov chain, thus allowing the times to failure to posses Weibull-like distributions. Because of the departures from traditional models, the solution method employed is that of Kolmogorov integral equations, which are evaluated numerically.

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

NASA Technical Reports Server (NTRS)

Liu, K.; Skelton, R. E.; Sharkey, J. P.

1992-01-01

A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Towards early software reliability prediction for computer forensic tools (case study).

PubMed

Abu Talib, Manar

2016-01-01

Versatility, flexibility and robustness are essential requirements for software forensic tools. Researchers and practitioners need to put more effort into assessing this type of tool. A Markov model is a robust means for analyzing and anticipating the functioning of an advanced component based system. It is used, for instance, to analyze the reliability of the state machines of real time reactive systems. This research extends the architecture-based software reliability prediction model for computer forensic tools, which is based on Markov chains and COSMIC-FFP. Basically, every part of the computer forensic tool is linked to a discrete time Markov chain. If this can be done, then a probabilistic analysis by Markov chains can be performed to analyze the reliability of the components and of the whole tool. The purposes of the proposed reliability assessment method are to evaluate the tool's reliability in the early phases of its development, to improve the reliability assessment process for large computer forensic tools over time, and to compare alternative tool designs. The reliability analysis can assist designers in choosing the most reliable topology for the components, which can maximize the reliability of the tool and meet the expected reliability level specified by the end-user. The approach of assessing component-based tool reliability in the COSMIC-FFP context is illustrated with the Forensic Toolkit Imager case study.

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.

A Hidden Markov Model for Analysis of Frontline Veterinary Data for Emerging Zoonotic Disease Surveillance

PubMed Central

Robertson, Colin; Sawford, Kate; Gunawardana, Walimunige S. N.; Nelson, Trisalyn A.; Nathoo, Farouk; Stephen, Craig

2011-01-01

Surveillance systems tracking health patterns in animals have potential for early warning of infectious disease in humans, yet there are many challenges that remain before this can be realized. Specifically, there remains the challenge of detecting early warning signals for diseases that are not known or are not part of routine surveillance for named diseases. This paper reports on the development of a hidden Markov model for analysis of frontline veterinary sentinel surveillance data from Sri Lanka. Field veterinarians collected data on syndromes and diagnoses using mobile phones. A model for submission patterns accounts for both sentinel-related and disease-related variability. Models for commonly reported cattle diagnoses were estimated separately. Region-specific weekly average prevalence was estimated for each diagnoses and partitioned into normal and abnormal periods. Visualization of state probabilities was used to indicate areas and times of unusual disease prevalence. The analysis suggests that hidden Markov modelling is a useful approach for surveillance datasets from novel populations and/or having little historical baselines. PMID:21949763

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

Monitoring Farmland Loss Caused by Urbanization in Beijing from Modis Time Series Using Hierarchical Hidden Markov Model

NASA Astrophysics Data System (ADS)

Yuan, Y.; Meng, Y.; Chen, Y. X.; Jiang, C.; Yue, A. Z.

2018-04-01

In this study, we proposed a method to map urban encroachment onto farmland using satellite image time series (SITS) based on the hierarchical hidden Markov model (HHMM). In this method, the farmland change process is decomposed into three hierarchical levels, i.e., the land cover level, the vegetation phenology level, and the SITS level. Then a three-level HHMM is constructed to model the multi-level semantic structure of farmland change process. Once the HHMM is established, a change from farmland to built-up could be detected by inferring the underlying state sequence that is most likely to generate the input time series. The performance of the method is evaluated on MODIS time series in Beijing. Results on both simulated and real datasets demonstrate that our method improves the change detection accuracy compared with the HMM-based method.

A discrete Markov metapopulation model for persistence and extinction of species.

PubMed

Thompson, Colin J; Shtilerman, Elad; Stone, Lewi

2016-09-07

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

[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.

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1995-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) (vertical bar)/x), 1 less than or equal to i isless than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1993-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) perpendicular to x), 1 less than or equal to i is less than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Hierarchical modeling for reliability analysis using Markov models. B.S./M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Fagundo, Arturo

1994-01-01

Markov models represent an extremely attractive tool for the reliability analysis of many systems. However, Markov model state space grows exponentially with the number of components in a given system. Thus, for very large systems Markov modeling techniques alone become intractable in both memory and CPU time. Often a particular subsystem can be found within some larger system where the dependence of the larger system on the subsystem is of a particularly simple form. This simple dependence can be used to decompose such a system into one or more subsystems. A hierarchical technique is presented which can be used to evaluate these subsystems in such a way that their reliabilities can be combined to obtain the reliability for the full system. This hierarchical approach is unique in that it allows the subsystem model to pass multiple aggregate state information to the higher level model, allowing more general systems to be evaluated. Guidelines are developed to assist in the system decomposition. An appropriate method for determining subsystem reliability is also developed. This method gives rise to some interesting numerical issues. Numerical error due to roundoff and integration are discussed at length. Once a decomposition is chosen, the remaining analysis is straightforward but tedious. However, an approach is developed for simplifying the recombination of subsystem reliabilities. Finally, a real world system is used to illustrate the use of this technique in a more practical context.

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.

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.

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.

Exact Markov chains versus diffusion theory for haploid random mating.

PubMed

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

NASA Astrophysics Data System (ADS)

Formentin, M.; Külske, C.; Reichenbachs, A.

2012-01-01

We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

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.

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.

Markov switching of the electricity supply curve and power prices dynamics

NASA Astrophysics Data System (ADS)

Mari, Carlo; Cananà, Lucianna

2012-02-01

Regime-switching models seem to well capture the main features of power prices behavior in deregulated markets. In a recent paper, we have proposed an equilibrium methodology to derive electricity prices dynamics from the interplay between supply and demand in a stochastic environment. In particular, assuming that the supply function is described by a power law where the exponent is a two-state strictly positive Markov process, we derived a regime switching dynamics of power prices in which regime switches are induced by transitions between Markov states. In this paper, we provide a dynamical model to describe the random behavior of power prices where the only non-Brownian component of the motion is endogenously introduced by Markov transitions in the exponent of the electricity supply curve. In this context, the stochastic process driving the switching mechanism becomes observable, and we will show that the non-Brownian component of the dynamics induced by transitions from Markov states is responsible for jumps and spikes of very high magnitude. The empirical analysis performed on three Australian markets confirms that the proposed approach seems quite flexible and capable of incorporating the main features of power prices time-series, thus reproducing the first four moments of log-returns empirical distributions in a satisfactory way.

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,...

Under-reported data analysis with INAR-hidden Markov chains.

PubMed

Fernández-Fontelo, Amanda; Cabaña, Alejandra; Puig, Pedro; Moriña, David

2016-11-20

In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Multivariate Markov chain modeling for stock markets

NASA Astrophysics Data System (ADS)

Maskawa, Jun-ichi

2003-06-01

We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.

Estimation of customer lifetime value of a health insurance with interest rates obeying uniform distribution

NASA Astrophysics Data System (ADS)

Widyawan, A.; Pasaribu, U. S.; Henintyas, Permana, D.

2015-12-01

Nowadays some firms, including insurer firms, think that customer-centric services are better than product-centric ones in terms of marketing. Insurance firms will try to attract as many new customer as possible while maintaining existing customer. This causes the Customer Lifetime Value (CLV) becomes a very important thing. CLV are able to put customer into different segments and calculate the present value of a firm's relationship with its customer. Insurance customer will depend on the last service he or she can get. So if the service is bad now, then customer will not renew his contract though the service is very good at an erlier time. Because of this situation one suitable mathematical model for modeling customer's relationships and calculating their lifetime value is Markov Chain. In addition, the advantages of using Markov Chain Modeling is its high degree of flexibility. In 2000, Pfeifer and Carraway states that Markov Chain Modeling can be used for customer retention situation. In this situation, Markov Chain Modeling requires only two states, which are present customer and former ones. This paper calculates customer lifetime value in an insurance firm with two distinctive interest rates; the constant interest rate and uniform distribution of interest rates. The result shows that loyal customer and the customer who increase their contract value have the highest CLV.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

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

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

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

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.

Traffic Video Image Segmentation Model Based on Bayesian and Spatio-Temporal Markov Random Field

NASA Astrophysics Data System (ADS)

Zhou, Jun; Bao, Xu; Li, Dawei; Yin, Yongwen

2017-10-01

Traffic video image is a kind of dynamic image and its background and foreground is changed at any time, which results in the occlusion. In this case, using the general method is more difficult to get accurate image segmentation. A segmentation algorithm based on Bayesian and Spatio-Temporal Markov Random Field is put forward, which respectively build the energy function model of observation field and label field to motion sequence image with Markov property, then according to Bayesian' rule, use the interaction of label field and observation field, that is the relationship of label field’s prior probability and observation field’s likelihood probability, get the maximum posterior probability of label field’s estimation parameter, use the ICM model to extract the motion object, consequently the process of segmentation is finished. Finally, the segmentation methods of ST - MRF and the Bayesian combined with ST - MRF were analyzed. Experimental results: the segmentation time in Bayesian combined with ST-MRF algorithm is shorter than in ST-MRF, and the computing workload is small, especially in the heavy traffic dynamic scenes the method also can achieve better segmentation effect.

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

NASA Astrophysics Data System (ADS)

Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes

2018-03-01

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

How old is this bird? The age distribution under some phase sampling schemes.

PubMed

Hautphenne, Sophie; Massaro, Melanie; Taylor, Peter

2017-12-01

In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.

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.

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

PubMed

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

2016-12-28

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

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

Assessing the Deterrence Value of Carrier Presence Against Adversary Aggression in a Coalition Environment

DTIC Science & Technology

2017-09-01

seeks to quantify the deterrence value of a CSG using a game - theoretic framework. Consider a region with several nations, where two major players stand...develop a Markov game to model the interactions between the two players and these other nations over a period of time. The game starts in Notional...establishing diplomatic advantage are equally important in deterring aggression. 14. SUBJECT TERMS carrier strike group, CSG, deterrence, Markov game

The cutoff phenomenon in finite Markov chains.

PubMed Central

Diaconis, P

1996-01-01

Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists. PMID:11607633

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

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

Intelligent data analysis to model and understand live cell time-lapse sequences.

PubMed

Paterson, Allan; Ashtari, M; Ribé, D; Stenbeck, G; Tucker, A

2012-01-01

One important aspect of cellular function, which is at the basis of tissue homeostasis, is the delivery of proteins to their correct destinations. Significant advances in live cell microscopy have allowed tracking of these pathways by following the dynamics of fluorescently labelled proteins in living cells. This paper explores intelligent data analysis techniques to model the dynamic behavior of proteins in living cells as well as to classify different experimental conditions. We use a combination of decision tree classification and hidden Markov models. In particular, we introduce a novel approach to "align" hidden Markov models so that hidden states from different models can be cross-compared. Our models capture the dynamics of two experimental conditions accurately with a stable hidden state for control data and multiple (less stable) states for the experimental data recapitulating the behaviour of particle trajectories within live cell time-lapse data. In addition to having successfully developed an automated framework for the classification of protein transport dynamics from live cell time-lapse data our model allows us to understand the dynamics of a complex trafficking pathway in living cells in culture.

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.

Markov models of genome segmentation

NASA Astrophysics Data System (ADS)

Thakur, Vivek; Azad, Rajeev K.; Ramaswamy, Ram

2007-01-01

We introduce Markov models for segmentation of symbolic sequences, extending a segmentation procedure based on the Jensen-Shannon divergence that has been introduced earlier. Higher-order Markov models are more sensitive to the details of local patterns and in application to genome analysis, this makes it possible to segment a sequence at positions that are biologically meaningful. We show the advantage of higher-order Markov-model-based segmentation procedures in detecting compositional inhomogeneity in chimeric DNA sequences constructed from genomes of diverse species, and in application to the E. coli K12 genome, boundaries of genomic islands, cryptic prophages, and horizontally acquired regions are accurately identified.

Error modeling for differential GPS. M.S. Thesis - MIT, 12 May 1995

NASA Technical Reports Server (NTRS)

Blerman, Gregory S.

1995-01-01

Differential Global Positioning System (DGPS) positioning is used to accurately locate a GPS receiver based upon the well-known position of a reference site. In utilizing this technique, several error sources contribute to position inaccuracy. This thesis investigates the error in DGPS operation and attempts to develop a statistical model for the behavior of this error. The model for DGPS error is developed using GPS data collected by Draper Laboratory. The Marquardt method for nonlinear curve-fitting is used to find the parameters of a first order Markov process that models the average errors from the collected data. The results show that a first order Markov process can be used to model the DGPS error as a function of baseline distance and time delay. The model's time correlation constant is 3847.1 seconds (1.07 hours) for the mean square error. The distance correlation constant is 122.8 kilometers. The total process variance for the DGPS model is 3.73 sq meters.

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.

Modeling haplotype block variation using Markov chains.

PubMed

Greenspan, G; Geiger, D

2006-04-01

Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity.

Modeling Haplotype Block Variation Using Markov Chains

PubMed Central

Greenspan, G.; Geiger, D.

2006-01-01

Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity. PMID:16361244

Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes

PubMed Central

Nakamura, Tomoaki; Nagai, Takayuki; Mochihashi, Daichi; Kobayashi, Ichiro; Asoh, Hideki; Kaneko, Masahide

2017-01-01

Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM) that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM), the emission distributions of which are Gaussian processes (GPs). Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods. PMID:29311889

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.

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.

Probabilistic Reasoning Over Seismic Time Series: Volcano Monitoring by Hidden Markov Models at Mt. Etna

NASA Astrophysics Data System (ADS)

Cassisi, Carmelo; Prestifilippo, Michele; Cannata, Andrea; Montalto, Placido; Patanè, Domenico; Privitera, Eugenio

2016-07-01

From January 2011 to December 2015, Mt. Etna was mainly characterized by a cyclic eruptive behavior with more than 40 lava fountains from New South-East Crater. Using the RMS (Root Mean Square) of the seismic signal recorded by stations close to the summit area, an automatic recognition of the different states of volcanic activity (QUIET, PRE-FOUNTAIN, FOUNTAIN, POST-FOUNTAIN) has been applied for monitoring purposes. Since values of the RMS time series calculated on the seismic signal are generated from a stochastic process, we can try to model the system generating its sampled values, assumed to be a Markov process, using Hidden Markov Models (HMMs). HMMs analysis seeks to recover the sequence of hidden states from the observations. In our framework, observations are characters generated by the Symbolic Aggregate approXimation (SAX) technique, which maps RMS time series values with symbols of a pre-defined alphabet. The main advantages of the proposed framework, based on HMMs and SAX, with respect to other automatic systems applied on seismic signals at Mt. Etna, are the use of multiple stations and static thresholds to well characterize the volcano states. Its application on a wide seismic dataset of Etna volcano shows the possibility to guess the volcano states. The experimental results show that, in most of the cases, we detected lava fountains in advance.

Inference for finite-sample trajectories in dynamic multi-state site-occupancy models using hidden Markov model smoothing

USGS Publications Warehouse

Fiske, Ian J.; Royle, J. Andrew; Gross, Kevin

2014-01-01

Ecologists and wildlife biologists increasingly use latent variable models to study patterns of species occurrence when detection is imperfect. These models have recently been generalized to accommodate both a more expansive description of state than simple presence or absence, and Markovian dynamics in the latent state over successive sampling seasons. In this paper, we write these multi-season, multi-state models as hidden Markov models to find both maximum likelihood estimates of model parameters and finite-sample estimators of the trajectory of the latent state over time. These estimators are especially useful for characterizing population trends in species of conservation concern. We also develop parametric bootstrap procedures that allow formal inference about latent trend. We examine model behavior through simulation, and we apply the model to data from the North American Amphibian Monitoring Program.

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.

Modeling treatment of ischemic heart disease with partially observable Markov decision processes.

PubMed

Hauskrecht, M; Fraser, H

1998-01-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead they are very often dependent and interleaved over time, mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of Partially observable Markov decision processes (POMDPs) developed and used in operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In the paper, we show how the POMDP framework could be used to model and solve the problem of the management of patients with ischemic heart disease, and point out modeling advantages of the framework over standard decision formalisms.

[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.

Time Ordering in Frontal Lobe Patients: A Stochastic Model Approach

ERIC Educational Resources Information Center

Magherini, Anna; Saetti, Maria Cristina; Berta, Emilia; Botti, Claudio; Faglioni, Pietro

2005-01-01

Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared…

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.

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.

IEEE 802.15.4 MAC with GTS transmission for heterogeneous devices with application to wheelchair body-area sensor networks.

PubMed

Shrestha, Bharat; Hossain, Ekram; Camorlinga, Sergio

2011-09-01

In wireless personal area networks, such as wireless body-area sensor networks, stations or devices have different bandwidth requirements and, thus, create heterogeneous traffics. For such networks, the IEEE 802.15.4 medium access control (MAC) can be used in the beacon-enabled mode, which supports guaranteed time slot (GTS) allocation for time-critical data transmissions. This paper presents a general discrete-time Markov chain model for the IEEE 802.15.4-based networks taking into account the slotted carrier sense multiple access with collision avoidance and GTS transmission phenomena together in the heterogeneous traffic scenario and under nonsaturated condition. For this purpose, the standard GTS allocation scheme is modified. For each non-identical device, the Markov model is solved and the average service time and the service utilization factor are analyzed in the non-saturated mode. The analysis is validated by simulations using network simulator version 2.33. Also, the model is enhanced with a wireless propagation model and the performance of the MAC is evaluated in a wheelchair body-area sensor network scenario.

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.

Cost effectiveness of adding clostridial collagenase ointment to selective debridement in individuals with stage IV pressure ulcers.

PubMed

Carter, Marissa J; Gilligan, Adrienne M; Waycaster, Curtis R; Schaum, Kathleen; Fife, Caroline E

2017-03-01

The purpose of this study was to determine the cost effectiveness (from a payer's perspective) of adding clostridial collagenase ointment (CCO) to selective debridement compared with selective debridement alone (non-CCO) in the treatment of stage IV pressure ulcers among patients identified from the US Wound Registry. A 3-state Markov model was developed to determine costs and outcomes between the CCO and non-CCO groups over a 2-year time horizon. Outcome data were derived from a retrospective clinical study and included the proportion of pressure ulcers that were closed (epithelialized) over 2 years and the time to wound closure. Transition probabilities for the Markov states were estimated from the clinical study. In the Markov model, the clinical outcome is presented as ulcer-free weeks, which represents the time the wound is in the epithelialized state. Costs for each 4-week cycle were based on frequencies of clinic visits, debridement, and CCO application rates from the clinical study. The final model outputs were cumulative costs (in US dollars), clinical outcome (ulcer-free weeks), and incremental cost-effectiveness ratio (ICER) at 2 years. Compared with the non-CCO group, the CCO group incurred lower costs ($11,151 vs $17,596) and greater benefits (33.9 vs 16.8 ulcer-free weeks), resulting in an economically dominant ICER of -$375 per ulcer. Thus, for each additional ulcer-free week that can be gained, there is a concurrent cost savings of $375 if CCO treatment is selected. Over a 2-year period, an additional 17.2 ulcer-free weeks can be gained with concurrent cost savings of $6,445 for each patient. In this Markov model based on real-world data from the US Wound Registry, the addition of CCO to selective debridement in the treatment of pressure ulcers was economically dominant over selective debridement alone, resulting in greater benefit to the patient at lower cost.

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

Unifying Model-Based and Reactive Programming within a Model-Based Executive

NASA Technical Reports Server (NTRS)

Williams, Brian C.; Gupta, Vineet; Norvig, Peter (Technical Monitor)

1999-01-01

Real-time, model-based, deduction has recently emerged as a vital component in AI's tool box for developing highly autonomous reactive systems. Yet one of the current hurdles towards developing model-based reactive systems is the number of methods simultaneously employed, and their corresponding melange of programming and modeling languages. This paper offers an important step towards unification. We introduce RMPL, a rich modeling language that combines probabilistic, constraint-based modeling with reactive programming constructs, while offering a simple semantics in terms of hidden state Markov processes. We introduce probabilistic, hierarchical constraint automata (PHCA), which allow Markov processes to be expressed in a compact representation that preserves the modularity of RMPL programs. Finally, a model-based executive, called Reactive Burton is described that exploits this compact encoding to perform efficIent simulation, belief state update and control sequence generation.

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…

Autoregressive-moving-average hidden Markov model for vision-based fall prediction-An application for walker robot.

PubMed

Taghvaei, Sajjad; Jahanandish, Mohammad Hasan; Kosuge, Kazuhiro

2017-01-01

Population aging of the societies requires providing the elderly with safe and dependable assistive technologies in daily life activities. Improving the fall detection algorithms can play a major role in achieving this goal. This article proposes a real-time fall prediction algorithm based on the acquired visual data of a user with walking assistive system from a depth sensor. In the lack of a coupled dynamic model of the human and the assistive walker a hybrid "system identification-machine learning" approach is used. An autoregressive-moving-average (ARMA) model is fitted on the time-series walking data to forecast the upcoming states, and a hidden Markov model (HMM) based classifier is built on the top of the ARMA model to predict falling in the upcoming time frames. The performance of the algorithm is evaluated through experiments with four subjects including an experienced physiotherapist while using a walker robot in five different falling scenarios; namely, fall forward, fall down, fall back, fall left, and fall right. The algorithm successfully predicts the fall with a rate of 84.72%.

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

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.

Markov-chain model of classified atomistic transition states for discrete kinetic Monte Carlo simulations.

PubMed

Numazawa, Satoshi; Smith, Roger

2011-10-01

Classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The scheme is then used to determine transitions that can be applied in a lattice-based kinetic Monte Carlo (KMC) atomistic simulation model. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multidimensional Boolean valued functions in three-dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology-dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. Excellent agreement with observed experimental results is obtained.

Hidden Semi-Markov Models and Their Application

NASA Astrophysics Data System (ADS)

Beyreuther, M.; Wassermann, J.

2008-12-01

In the framework of detection and classification of seismic signals there are several different approaches. Our choice for a more robust detection and classification algorithm is to adopt Hidden Markov Models (HMM), a technique showing major success in speech recognition. HMM provide a powerful tool to describe highly variable time series based on a double stochastic model and therefore allow for a broader class description than e.g. template based pattern matching techniques. Being a fully probabilistic model, HMM directly provide a confidence measure of an estimated classification. Furthermore and in contrast to classic artificial neuronal networks or support vector machines, HMM are incorporating the time dependence explicitly in the models thus providing a adequate representation of the seismic signal. As the majority of detection algorithms, HMM are not based on the time and amplitude dependent seismogram itself but on features estimated from the seismogram which characterize the different classes. Features, or in other words characteristic functions, are e.g. the sonogram bands, instantaneous frequency, instantaneous bandwidth or centroid time. In this study we apply continuous Hidden Semi-Markov Models (HSMM), an extension of continuous HMM. The duration probability of a HMM is an exponentially decaying function of the time, which is not a realistic representation of the duration of an earthquake. In contrast HSMM use Gaussians as duration probabilities, which results in an more adequate model. The HSMM detection and classification system is running online as an EARTHWORM module at the Bavarian Earthquake Service. Here the signals that are to be classified simply differ in epicentral distance. This makes it possible to easily decide whether a classification is correct or wrong and thus allows to better evaluate the advantages and disadvantages of the proposed algorithm. The evaluation is based on several month long continuous data and the results are additionally compared to the previously published discrete HMM, continuous HMM and a classic STA/LTA. The intermediate evaluation results are very promising.

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).

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

NASA Astrophysics Data System (ADS)

Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben

2017-08-01

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.

Damage evaluation by a guided wave-hidden Markov model based method

NASA Astrophysics Data System (ADS)

Mei, Hanfei; Yuan, Shenfang; Qiu, Lei; Zhang, Jinjin

2016-02-01

Guided wave based structural health monitoring has shown great potential in aerospace applications. However, one of the key challenges of practical engineering applications is the accurate interpretation of the guided wave signals under time-varying environmental and operational conditions. This paper presents a guided wave-hidden Markov model based method to improve the damage evaluation reliability of real aircraft structures under time-varying conditions. In the proposed approach, an HMM based unweighted moving average trend estimation method, which can capture the trend of damage propagation from the posterior probability obtained by HMM modeling is used to achieve a probabilistic evaluation of the structural damage. To validate the developed method, experiments are performed on a hole-edge crack specimen under fatigue loading condition and a real aircraft wing spar under changing structural boundary conditions. Experimental results show the advantage of the proposed method.

Accelerometry-based classification of human activities using Markov modeling.

PubMed

Mannini, Andrea; Sabatini, Angelo Maria

2011-01-01

Accelerometers are a popular choice as body-motion sensors: the reason is partly in their capability of extracting information that is useful for automatically inferring the physical activity in which the human subject is involved, beside their role in feeding biomechanical parameters estimators. Automatic classification of human physical activities is highly attractive for pervasive computing systems, whereas contextual awareness may ease the human-machine interaction, and in biomedicine, whereas wearable sensor systems are proposed for long-term monitoring. This paper is concerned with the machine learning algorithms needed to perform the classification task. Hidden Markov Model (HMM) classifiers are studied by contrasting them with Gaussian Mixture Model (GMM) classifiers. HMMs incorporate the statistical information available on movement dynamics into the classification process, without discarding the time history of previous outcomes as GMMs do. An example of the benefits of the obtained statistical leverage is illustrated and discussed by analyzing two datasets of accelerometer time series.

Irreversible Markov chains in spin models: Topological excitations

NASA Astrophysics Data System (ADS)

Lei, Ze; Krauth, Werner

2018-01-01

We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.

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.

Reciprocal Markov Modeling of Feedback Mechanisms Between Emotion and Dietary Choice Using Experience-Sampling Data.

PubMed

Lu, Ji; Pan, Junhao; Zhang, Qiang; Dubé, Laurette; Ip, Edward H

2015-01-01

With intensively collected longitudinal data, recent advances in the experience-sampling method (ESM) benefit social science empirical research, but also pose important methodological challenges. As traditional statistical models are not generally well equipped to analyze a system of variables that contain feedback loops, this paper proposes the utility of an extended hidden Markov model to model reciprocal the relationship between momentary emotion and eating behavior. This paper revisited an ESM data set (Lu, Huet, & Dube, 2011) that observed 160 participants' food consumption and momentary emotions 6 times per day in 10 days. Focusing on the analyses on feedback loop between mood and meal-healthiness decision, the proposed reciprocal Markov model (RMM) can accommodate both hidden ("general" emotional states: positive vs. negative state) and observed states (meal: healthier, same or less healthy than usual) without presuming independence between observations and smooth trajectories of mood or behavior changes. The results of RMM analyses illustrated the reciprocal chains of meal consumption and mood as well as the effect of contextual factors that moderate the interrelationship between eating and emotion. A simulation experiment that generated data consistent with the empirical study further demonstrated that the procedure is promising in terms of recovering the parameters.

Modelling past land use using archaeological and pollen data

NASA Astrophysics Data System (ADS)

Pirzamanbein, Behnaz; Lindström, johan; Poska, Anneli; Gaillard-Lemdahl, Marie-José

2016-04-01

Accurate maps of past land use are necessary for studying the impact of anthropogenic land-cover changes on climate and biodiversity. We develop a Bayesian hierarchical model to reconstruct the land use using Gaussian Markov random fields. The model uses two observations sets: 1) archaeological data, representing human settlements, urbanization and agricultural findings; and 2) pollen-based land estimates of the three land-cover types Coniferous forest, Broadleaved forest and Unforested/Open land. The pollen based estimates are obtained from the REVEALS model, based on pollen counts from lakes and bogs. Our developed model uses the sparse pollen-based estimations to reconstruct the spatial continuous cover of three land cover types. Using the open-land component and the archaeological data, the extent of land-use is reconstructed. The model is applied on three time periods - centred around 1900 CE, 1000 and, 4000 BCE over Sweden for which both pollen-based estimates and archaeological data are available. To estimate the model parameters and land use, a block updated Markov chain Monte Carlo (MCMC) algorithm is applied. Using the MCMC posterior samples uncertainties in land-use predictions are computed. Due to lack of good historic land use data, model results are evaluated by cross-validation. Keywords. Spatial reconstruction, Gaussian Markov random field, Fossil pollen records, Archaeological data, Human land-use, Prediction uncertainty

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.

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.

Semantic Context Detection Using Audio Event Fusion

NASA Astrophysics Data System (ADS)

Chu, Wei-Ta; Cheng, Wen-Huang; Wu, Ja-Ling

2006-12-01

Semantic-level content analysis is a crucial issue in achieving efficient content retrieval and management. We propose a hierarchical approach that models audio events over a time series in order to accomplish semantic context detection. Two levels of modeling, audio event and semantic context modeling, are devised to bridge the gap between physical audio features and semantic concepts. In this work, hidden Markov models (HMMs) are used to model four representative audio events, that is, gunshot, explosion, engine, and car braking, in action movies. At the semantic context level, generative (ergodic hidden Markov model) and discriminative (support vector machine (SVM)) approaches are investigated to fuse the characteristics and correlations among audio events, which provide cues for detecting gunplay and car-chasing scenes. The experimental results demonstrate the effectiveness of the proposed approaches and provide a preliminary framework for information mining by using audio characteristics.

Inferring phenomenological models of Markov processes from data

NASA Astrophysics Data System (ADS)

Rivera, Catalina; Nemenman, Ilya

Microscopically accurate modeling of stochastic dynamics of biochemical networks is hard due to the extremely high dimensionality of the state space of such networks. Here we propose an algorithm for inference of phenomenological, coarse-grained models of Markov processes describing the network dynamics directly from data, without the intermediate step of microscopically accurate modeling. The approach relies on the linear nature of the Chemical Master Equation and uses Bayesian Model Selection for identification of parsimonious models that fit the data. When applied to synthetic data from the Kinetic Proofreading process (KPR), a common mechanism used by cells for increasing specificity of molecular assembly, the algorithm successfully uncovers the known coarse-grained description of the process. This phenomenological description has been notice previously, but this time it is derived in an automated manner by the algorithm. James S. McDonnell Foundation Grant No. 220020321.

Comparison of INAR(1)-Poisson model and Markov prediction model in forecasting the number of DHF patients in west java Indonesia

NASA Astrophysics Data System (ADS)

Ahdika, Atina; Lusiyana, Novyan

2017-02-01

World Health Organization (WHO) noted Indonesia as the country with the highest dengue (DHF) cases in Southeast Asia. There are no vaccine and specific treatment for DHF. One of the efforts which can be done by both government and resident is doing a prevention action. In statistics, there are some methods to predict the number of DHF cases to be used as the reference to prevent the DHF cases. In this paper, a discrete time series model, INAR(1)-Poisson model in specific, and Markov prediction model are used to predict the number of DHF patients in West Java Indonesia. The result shows that MPM is the best model since it has the smallest value of MAE (mean absolute error) and MAPE (mean absolute percentage error).

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.

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

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

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

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

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Piunovskiy, A. B., E-mail: piunov@liv.ac.uk

2016-08-15

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures ofmore » the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.« less

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.

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.

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.

An approximation formula for a class of Markov reliability models

NASA Technical Reports Server (NTRS)

White, A. L.

1984-01-01

A way of considering a small but often used class of reliability model and approximating algebraically the systems reliability is shown. The models considered are appropriate for redundant reconfigurable digital control systems that operate for a short period of time without maintenance, and for such systems the method gives a formula in terms of component fault rates, system recovery rates, and system operating time.

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.

Time series segmentation: a new approach based on Genetic Algorithm and Hidden Markov Model

NASA Astrophysics Data System (ADS)

Toreti, A.; Kuglitsch, F. G.; Xoplaki, E.; Luterbacher, J.

2009-04-01

The subdivision of a time series into homogeneous segments has been performed using various methods applied to different disciplines. In climatology, for example, it is accompanied by the well-known homogenization problem and the detection of artificial change points. In this context, we present a new method (GAMM) based on Hidden Markov Model (HMM) and Genetic Algorithm (GA), applicable to series of independent observations (and easily adaptable to autoregressive processes). A left-to-right hidden Markov model, estimating the parameters and the best-state sequence, respectively, with the Baum-Welch and Viterbi algorithms, was applied. In order to avoid the well-known dependence of the Baum-Welch algorithm on the initial condition, a Genetic Algorithm was developed. This algorithm is characterized by mutation, elitism and a crossover procedure implemented with some restrictive rules. Moreover the function to be minimized was derived following the approach of Kehagias (2004), i.e. it is the so-called complete log-likelihood. The number of states was determined applying a two-fold cross-validation procedure (Celeux and Durand, 2008). Being aware that the last issue is complex, and it influences all the analysis, a Multi Response Permutation Procedure (MRPP; Mielke et al., 1981) was inserted. It tests the model with K+1 states (where K is the state number of the best model) if its likelihood is close to K-state model. Finally, an evaluation of the GAMM performances, applied as a break detection method in the field of climate time series homogenization, is shown. 1. G. Celeux and J.B. Durand, Comput Stat 2008. 2. A. Kehagias, Stoch Envir Res 2004. 3. P.W. Mielke, K.J. Berry, G.W. Brier, Monthly Wea Rev 1981.

Analysis of mean time to data loss of fault-tolerant disk arrays RAID-6 based on specialized Markov chain

NASA Astrophysics Data System (ADS)

Rahman, P. A.; D'K Novikova Freyre Shavier, G.

2018-03-01

This scientific paper is devoted to the analysis of the mean time to data loss of redundant disk arrays RAID-6 with alternation of data considering different failure rates of disks both in normal state of the disk array and in degraded and rebuild states, and also nonzero time of the disk replacement. The reliability model developed by the authors on the basis of the Markov chain and obtained calculation formula for estimation of the mean time to data loss (MTTDL) of the RAID-6 disk arrays are also presented. At last, the technique of estimation of the initial reliability parameters and examples of calculation of the MTTDL of the RAID-6 disk arrays for the different numbers of disks are also given.

Using Markov state models to study self-assembly

NASA Astrophysics Data System (ADS)

Perkett, Matthew R.; Hagan, Michael F.

2014-06-01

Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.

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

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.

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.

Sub-seasonal-to-seasonal Reservoir Inflow Forecast using Bayesian Hierarchical Hidden Markov Model

NASA Astrophysics Data System (ADS)

Mukhopadhyay, S.; Arumugam, S.

2017-12-01

Sub-seasonal-to-seasonal (S2S) (15-90 days) streamflow forecasting is an emerging area of research that provides seamless information for reservoir operation from weather time scales to seasonal time scales. From an operational perspective, sub-seasonal inflow forecasts are highly valuable as these enable water managers to decide short-term releases (15-30 days), while holding water for seasonal needs (e.g., irrigation and municipal supply) and to meet end-of-the-season target storage at a desired level. We propose a Bayesian Hierarchical Hidden Markov Model (BHHMM) to develop S2S inflow forecasts for the Tennessee Valley Area (TVA) reservoir system. Here, the hidden states are predicted by relevant indices that influence the inflows at S2S time scale. The hidden Markov model also captures the both spatial and temporal hierarchy in predictors that operate at S2S time scale with model parameters being estimated as a posterior distribution using a Bayesian framework. We present our work in two steps, namely single site model and multi-site model. For proof of concept, we consider inflows to Douglas Dam, Tennessee, in the single site model. For multisite model we consider reservoirs in the upper Tennessee valley. Streamflow forecasts are issued and updated continuously every day at S2S time scale. We considered precipitation forecasts obtained from NOAA Climate Forecast System (CFSv2) GCM as predictors for developing S2S streamflow forecasts along with relevant indices for predicting hidden states. Spatial dependence of the inflow series of reservoirs are also preserved in the multi-site model. To circumvent the non-normality of the data, we consider the HMM in a Generalized Linear Model setting. Skill of the proposed approach is tested using split sample validation against a traditional multi-site canonical correlation model developed using the same set of predictors. From the posterior distribution of the inflow forecasts, we also highlight different system behavior under varied global and local scale climatic influences from the developed BHMM.

[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.

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.

Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains

NASA Astrophysics Data System (ADS)

Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.

2018-01-01

We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.

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.

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.

Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.

PubMed

Chattopadhyay, Ishanu; Ray, Asok

2009-12-01

This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.

Predicting Loss-of-Control Boundaries Toward a Piloting Aid

NASA Technical Reports Server (NTRS)

Barlow, Jonathan; Stepanyan, Vahram; Krishnakumar, Kalmanje

2012-01-01

This work presents an approach to predicting loss-of-control with the goal of providing the pilot a decision aid focused on maintaining the pilot's control action within predicted loss-of-control boundaries. The predictive architecture combines quantitative loss-of-control boundaries, a data-based predictive control boundary estimation algorithm and an adaptive prediction method to estimate Markov model parameters in real-time. The data-based loss-of-control boundary estimation algorithm estimates the boundary of a safe set of control inputs that will keep the aircraft within the loss-of-control boundaries for a specified time horizon. The adaptive prediction model generates estimates of the system Markov Parameters, which are used by the data-based loss-of-control boundary estimation algorithm. The combined algorithm is applied to a nonlinear generic transport aircraft to illustrate the features of the architecture.

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

On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis.

PubMed

Yamazaki, Keisuke

2012-07-01

Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

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.

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Markov chains for testing redundant software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1988-01-01

A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.

Free flowing and cohesive powders agitation in a cylindrical convective blender- kinetics experiments and Markov chain modelling

NASA Astrophysics Data System (ADS)

Legoix, Léonard; Milhé, Mathieu; Gatumel, Cendrine; Berthiaux, Henri

2017-06-01

An original methodology for studying powder flow in a cylindrical convective blender has been developed. A free-flowing and a cohesive powder were studied, at a fixed stirring speed, in rolling regime. For both powders, three apparent flow mechanisms were evidenced: convection in the volume swept by the blades, diffusion/shearing between the agitated zone and the stagnant one, as well as in the stagnant zone itself, and avalanches at the powder bed surface between agitated and stagnant zones. After defining six zones in the blender, tracing experiments were carried out by placing appropriate tracers in different starting zones and sampling the whole bed at different stirring times, which lead to mixing kinetics of the powders into themselves. A Markov chains model of the blender allowed the quantification of the three mechanisms respective magnitude by fitting the experimental data. This simple model has a good agreement with the free-flowing powder data, but is not able to represent well the observations for the cohesive powder. Bed consolidation should probably be taken into account for this kind of powders and thus a linear Markov model is not sufficient.

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.

A hidden Markov model for decoding and the analysis of replay in spike trains.

PubMed

Box, Marc; Jones, Matt W; Whiteley, Nick

2016-12-01

We present a hidden Markov model that describes variation in an animal's position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of position, which we find to be a more parsimonious description of the system than other models. We use a sequential Monte Carlo algorithm for Bayesian inference of model parameters, including the state space dimension, and we explain how to estimate position from spike train observations (decoding). We obtain greater accuracy over other methods in the conditions of high temporal resolution and small neuronal sample size. We also present a novel, model-based approach to the study of replay: the expression of spike train activity related to behaviour during times of motionlessness or sleep, thought to be integral to the consolidation of long-term memories. We demonstrate how we can detect the time, information content and compression rate of replay events in simulated and real hippocampal data recorded from rats in two different environments, and verify the correlation between the times of detected replay events and of sharp wave/ripples in the local field potential.

Convergence yet Continued Complexity: A Systematic Review and Critique of Health Economic Models of Relapsing-Remitting Multiple Sclerosis in the United Kingdom.

PubMed

Allen, Felicity; Montgomery, Stephen; Maruszczak, Maciej; Kusel, Jeanette; Adlard, Nicholas

2015-09-01

Several disease-modifying therapies have marketing authorizations for the treatment of relapsing-remitting multiple sclerosis (RRMS). Given their appraisal by the National Institute for Health and Care Excellence, the objective was to systematically identify and critically evaluate the structures and assumptions used in health economic models of disease-modifying therapies for RRMS in the United Kingdom. Embase, MEDLINE, The Cochrane Library, and the National Institute for Health and Care Excellence Web site were searched systematically on March 3, 2014, to identify articles relating to health economic models in RRMS with a UK perspective. Data sources, techniques, and assumptions of the included models were extracted, compared, and critically evaluated. Of 386 results, 26 full texts were evaluated, leading to the inclusion of 18 articles (relating to 12 models). Early models varied considerably in method and structure, but convergence over time toward a Markov model with states based on disability score, a 1-year cycle length, and a lifetime time horizon was apparent. Recent models also allowed for disability improvement within the natural history of the condition. Considerable variety remains, with increasing numbers of comparators, the need for treatment sequencing, and different assumptions around efficacy waning and treatment withdrawal. Despite convergence over time to a similar Markov structure, there are still significant discrepancies between health economic models of RRMS in the United Kingdom. Differing methods, assumptions, and data sources render the comparison of model implementation and results problematic. The commonly used Markov structure leads to problems such as incapability to deal with heterogeneous populations and multiplying complexity with the addition of treatment sequences; these would best be solved by using alternative models such as discrete event simulations. Copyright © 2015 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

An accurate computational method for an order parameter with a Markov state model constructed using a manifold-learning technique

NASA Astrophysics Data System (ADS)

Ito, Reika; Yoshidome, Takashi

2018-01-01

Markov state models (MSMs) are a powerful approach for analyzing the long-time behaviors of protein motion using molecular dynamics simulation data. However, their quantitative performance with respect to the physical quantities is poor. We believe that this poor performance is caused by the failure to appropriately classify protein conformations into states when constructing MSMs. Herein, we show that the quantitative performance of an order parameter is improved when a manifold-learning technique is employed for the classification in the MSM. The MSM construction using the K-center method, which has been previously used for classification, has a poor quantitative performance.

Neyman, Markov processes and survival analysis.

PubMed

Yang, Grace

2013-07-01

J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.

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.

Markov modeling of peptide folding in the presence of protein crowders

NASA Astrophysics Data System (ADS)

Nilsson, Daniel; Mohanty, Sandipan; Irbäck, Anders

2018-02-01

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data

PubMed Central

Takayasu, Hideki; Takayasu, Misako

2017-01-01

We extend the concept of statistical symmetry as the invariance of a probability distribution under transformation to analyze binary sign time series data of price difference from the foreign exchange market. We model segments of the sign time series as Markov sequences and apply a local hypothesis test to evaluate the symmetries of independence and time reversion in different periods of the market. For the test, we derive the probability of a binary Markov process to generate a given set of number of symbol pairs. Using such analysis, we could not only segment the time series according the different behaviors but also characterize the segments in terms of statistical symmetries. As a particular result, we find that the foreign exchange market is essentially time reversible but this symmetry is broken when there is a strong external influence. PMID:28542208

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.

Markov Chain Estimation of Avian Seasonal Fecundity

EPA Science Inventory

To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...

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.

A Hybrid Secure Scheme for Wireless Sensor Networks against Timing Attacks Using Continuous-Time Markov Chain and Queueing Model.

PubMed

Meng, Tianhui; Li, Xiaofan; Zhang, Sha; Zhao, Yubin

2016-09-28

Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained.

A Hybrid Secure Scheme for Wireless Sensor Networks against Timing Attacks Using Continuous-Time Markov Chain and Queueing Model

PubMed Central

Meng, Tianhui; Li, Xiaofan; Zhang, Sha; Zhao, Yubin

2016-01-01

Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained. PMID:27690042

Using Markov state models to study self-assembly

PubMed Central

Perkett, Matthew R.; Hagan, Michael F.

2014-01-01

Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude. PMID:24907984

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Bayesian Analysis of Biogeography when the Number of Areas is Large

PubMed Central

Landis, Michael J.; Matzke, Nicholas J.; Moore, Brian R.; Huelsenbeck, John P.

2013-01-01

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a “data-augmentation” approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea. [ancestral area analysis; Bayesian biogeographic inference; data augmentation; historical biogeography; Markov chain Monte Carlo.] PMID:23736102

A semi-Markov model for mitosis segmentation in time-lapse phase contrast microscopy image sequences of stem cell populations.

PubMed

Liu, An-An; Li, Kang; Kanade, Takeo

2012-02-01

We propose a semi-Markov model trained in a max-margin learning framework for mitosis event segmentation in large-scale time-lapse phase contrast microscopy image sequences of stem cell populations. Our method consists of three steps. First, we apply a constrained optimization based microscopy image segmentation method that exploits phase contrast optics to extract candidate subsequences in the input image sequence that contains mitosis events. Then, we apply a max-margin hidden conditional random field (MM-HCRF) classifier learned from human-annotated mitotic and nonmitotic sequences to classify each candidate subsequence as a mitosis or not. Finally, a max-margin semi-Markov model (MM-SMM) trained on manually-segmented mitotic sequences is utilized to reinforce the mitosis classification results, and to further segment each mitosis into four predefined temporal stages. The proposed method outperforms the event-detection CRF model recently reported by Huh as well as several other competing methods in very challenging image sequences of multipolar-shaped C3H10T1/2 mesenchymal stem cells. For mitosis detection, an overall precision of 95.8% and a recall of 88.1% were achieved. For mitosis segmentation, the mean and standard deviation for the localization errors of the start and end points of all mitosis stages were well below 1 and 2 frames, respectively. In particular, an overall temporal location error of 0.73 ± 1.29 frames was achieved for locating daughter cell birth events.

Reciprocal Markov modeling of feedback mechanisms between emotion and dietary choice using experience sampling data

PubMed Central

Lu, Ji; Pan, Junhao; Zhang, Qiang; Dubé, Laurette; Ip, Edward H.

2015-01-01

With intensively collected longitudinal data, recent advances in Experience Sampling Method (ESM) benefit social science empirical research, but also pose important methodological challenges. As traditional statistical models are not generally well-equipped to analyze a system of variables that contain feedback loops, this paper proposes the utility of an extended hidden Markov model to model reciprocal relationship between momentary emotion and eating behavior. This paper revisited an ESM data set (Lu, Huet & Dube, 2011) that observed 160 participants’ food consumption and momentary emotions six times per day in 10 days. Focusing on the analyses on feedback loop between mood and meal healthiness decision, the proposed Reciprocal Markov Model (RMM) can accommodate both hidden (“general” emotional states: positive vs. negative state) and observed states (meal: healthier, same or less healthy than usual) without presuming independence between observations and smooth trajectories of mood or behavior changes. The results of RMM analyses illustrated the reciprocal chains of meal consumption and mood as well as the effect of contextual factors that moderate the interrelationship between eating and emotion. A simulation experiment that generated data consistent to the empirical study further demonstrated that the procedure is promising in terms of recovering the parameters. PMID:26717120

The detection of financial crisis using combination of volatility and markov switching models based on real output, domestic credit per GDP, and ICI indicators

NASA Astrophysics Data System (ADS)

Sugiyanto; Zukhronah, Etik; Setianingrum, Meganisa

2018-05-01

Open economic system has not only provided ease for every country to interact with each other, but also make it easier to transmitted the crisis. Financial crisis that hit Indonesia in 1997-1998 and 2008 severely impacted the economy, thus a method to detect crisis is required. According to Kamisky et al. [6], crisis can be detected based on several financial indicators such as real output, domestic credit per Gross Domestic Product (GDP), and Indonesia Composite Index (ICI). This research aims to determine the appropriate combination of volatility and Markov switching model to detect financial crisis in Indonesia based on the indicators. Volatility model used for modeling the unconstant-variance of ARMA. Markov switching is an alternative model of time series data with changed conditions in the data, or called state. In this research, we are using three assumption of states namely low volatility state, medium volatility state and high volatility state. The data of each indicator were taken from 1990 until 2016. The result of the study show that MS-ARCH(3,1) can be used to detect the financial crisis that hit Indonesia in 1997-1998 and 2008 based on real output, domestic credit per GDP, and ICI indicators.

Planning treatment of ischemic heart disease with partially observable Markov decision processes.

PubMed

Hauskrecht, M; Fraser, H

2000-03-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead, they are very often dependent and interleaved over time. This is mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of partially observable Markov decision processes (POMDPs) developed and used in the operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In this paper, we show how the POMDP framework can be used to model and solve the problem of the management of patients with ischemic heart disease (IHD), and demonstrate the modeling advantages of the framework over standard decision formalisms.

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

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

Xu, Zuwei; Zhao, Haibo, E-mail: klinsmannzhb@163.com; Zheng, Chuguang

2015-01-15

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule providesmore » a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.« less

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

NASA Astrophysics Data System (ADS)

Naseri Kouzehgarani, Asal

2009-12-01

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms---that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers. We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs.

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.

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.

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

NASA Astrophysics Data System (ADS)

Sun, L.; Melatos, A.; Suvorova, S.; Moran, W.; Evans, R. J.

2018-02-01

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semicoherent search based on a hidden Markov model tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the F statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semicoherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by 2 to 3 orders of magnitude.

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.

Validation of the SURE Program, phase 1

NASA Technical Reports Server (NTRS)

Dotson, Kelly J.

1987-01-01

Presented are the results of the first phase in the validation of the SURE (Semi-Markov Unreliability Range Evaluator) program. The SURE program gives lower and upper bounds on the death-state probabilities of a semi-Markov model. With these bounds, the reliability of a semi-Markov model of a fault-tolerant computer system can be analyzed. For the first phase in the validation, fifteen semi-Markov models were solved analytically for the exact death-state probabilities and these solutions compared to the corresponding bounds given by SURE. In every case, the SURE bounds covered the exact solution. The bounds, however, had a tendency to separate in cases where the recovery rate was slow or the fault arrival rate was fast.

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.

Discrete Latent Markov Models for Normally Distributed Response Data

ERIC Educational Resources Information Center

Schmittmann, Verena D.; Dolan, Conor V.; van der Maas, Han L. J.; Neale, Michael C.

2005-01-01

Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These…

A simplified parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.

Economic evaluation of nivolumab for the treatment of second-line advanced squamous NSCLC in Canada: a comparison of modeling approaches to estimate and extrapolate survival outcomes.

PubMed

Goeree, Ron; Villeneuve, Julie; Goeree, Jeff; Penrod, John R; Orsini, Lucinda; Tahami Monfared, Amir Abbas

2016-06-01

Background Lung cancer is the most common type of cancer in the world and is associated with significant mortality. Nivolumab demonstrated statistically significant improvements in progression-free survival (PFS) and overall survival (OS) for patients with advanced squamous non-small cell lung cancer (NSCLC) who were previously treated. The cost-effectiveness of nivolumab has not been assessed in Canada. A contentious component of projecting long-term cost and outcomes in cancer relates to the modeling approach adopted, with the two most common approaches being partitioned survival (PS) and Markov models. The objectives of this analysis were to estimate the cost-utility of nivolumab and to compare the results using these alternative modeling approaches. Methods Both PS and Markov models were developed using docetaxel and erlotinib as comparators. A three-health state model was used consisting of progression-free, progressed disease, and death. Disease progression and time to progression were estimated by identifying best-fitting survival curves from the clinical trial data for PFS and OS. Expected costs and health outcomes were calculated by combining health-state occupancy with medical resource use and quality-of-life assigned to each of the three health states. The health outcomes included in the model were survival and quality-adjusted-life-years (QALYs). Results Nivolumab was found to have the highest expected per-patient cost, but also improved per-patient life years (LYs) and QALYs. Nivolumab cost an additional $151,560 and $140,601 per QALY gained compared to docetaxel and erlotinib, respectively, using a PS model approach. The cost-utility estimates using a Markov model were very similar ($152,229 and $141,838, respectively, per QALY gained). Conclusions Nivolumab was found to involve a trade-off between improved patient survival and QALYs, and increased cost. It was found that the use of a PS or Markov model produced very similar estimates of expected cost, outcomes, and incremental cost-utility.

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

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.

Validating the Modeling and Simulation of a Generic Tracking Radar

DTIC Science & Technology

2009-07-28

order Gauss-Markov time series with CTGM = 250 units and rGM = 10 s is shown in the top panel of Figure 1. The time series, ifr , can represent any...are shared among the sensors. The total position and velocity estimation errors valid at time index k are given by < fr *|fc = rk\\k - rk and

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.

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

A tridiagonal parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.

Hideen Markov Models and Neural Networks for Fault Detection in Dynamic Systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic

1994-01-01

None given. (From conclusion): Neural networks plus Hidden Markov Models(HMM)can provide excellene detection and false alarm rate performance in fault detection applications. Modified models allow for novelty detection. Also covers some key contributions of neural network model, and application status.

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.

H2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

NASA Astrophysics Data System (ADS)

Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle

2017-10-01

This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space ?. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space ? considering the infinite time horizon case.

Adaptive control based on retrospective cost optimization

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S. (Inventor); Santillo, Mario A. (Inventor)

2012-01-01

A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.

Uncertainty in a Markov state model with missing states and rates: Application to a room temperature kinetic model obtained using high temperature molecular dynamics.

PubMed

Chatterjee, Abhijit; Bhattacharya, Swati

2015-09-21

Several studies in the past have generated Markov State Models (MSMs), i.e., kinetic models, of biomolecular systems by post-analyzing long standard molecular dynamics (MD) calculations at the temperature of interest and focusing on the maximally ergodic subset of states. Questions related to goodness of these models, namely, importance of the missing states and kinetic pathways, and the time for which the kinetic model is valid, are generally left unanswered. We show that similar questions arise when we generate a room-temperature MSM (denoted MSM-A) for solvated alanine dipeptide using state-constrained MD calculations at higher temperatures and Arrhenius relation — the main advantage of such a procedure being a speed-up of several thousand times over standard MD-based MSM building procedures. Bounds for rate constants calculated using probability theory from state-constrained MD at room temperature help validate MSM-A. However, bounds for pathways possibly missing in MSM-A show that alternate kinetic models exist that produce the same dynamical behaviour at short time scales as MSM-A but diverge later. Even in the worst case scenario, MSM-A is found to be valid longer than the time required to generate it. Concepts introduced here can be straightforwardly extended to other MSM building techniques.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

Studies of regional-scale climate variability and change. Hidden Markov models and coupled ocean-atmosphere modes

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

Ghil, M.; Kravtsov, S.; Robertson, A. W.

2008-10-14

This project was a continuation of previous work under DOE CCPP funding, in which we had developed a twin approach of probabilistic network (PN) models (sometimes called dynamic Bayesian networks) and intermediate-complexity coupled ocean-atmosphere models (ICMs) to identify the predictable modes of climate variability and to investigate their impacts on the regional scale. We had developed a family of PNs (similar to Hidden Markov Models) to simulate historical records of daily rainfall, and used them to downscale GCM seasonal predictions. Using an idealized atmospheric model, we had established a novel mechanism through which ocean-induced sea-surface temperature (SST) anomalies might influencemore » large-scale atmospheric circulation patterns on interannual and longer time scales; we had found similar patterns in a hybrid coupled ocean-atmosphere-sea-ice model. The goal of the this continuation project was to build on these ICM results and PN model development to address prediction of rainfall and temperature statistics at the local scale, associated with global climate variability and change, and to investigate the impact of the latter on coupled ocean-atmosphere modes. Our main results from the grant consist of extensive further development of the hidden Markov models for rainfall simulation and downscaling together with the development of associated software; new intermediate coupled models; a new methodology of inverse modeling for linking ICMs with observations and GCM results; and, observational studies of decadal and multi-decadal natural climate results, informed by ICM results.« less

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

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…

Probabilistic reasoning over seismic RMS time series: volcano monitoring through HMMs and SAX technique

NASA Astrophysics Data System (ADS)

Aliotta, M. A.; Cassisi, C.; Prestifilippo, M.; Cannata, A.; Montalto, P.; Patanè, D.

2014-12-01

During the last years, volcanic activity at Mt. Etna was often characterized by cyclic occurrences of fountains. In the period between January 2011 and June 2013, 38 episodes of lava fountains has been observed. Automatic recognition of the volcano's states related to lava fountain episodes (Quiet, Pre-Fountaining, Fountaining, Post-Fountaining) is very useful for monitoring purposes. We discovered that such states are strongly related to the trend of RMS (Root Mean Square) of the seismic signal recorded in the summit area. In the framework of the project PON SIGMA (Integrated Cloud-Sensor System for Advanced Multirisk Management) work, we tried to model the system generating its sampled values (assuming to be a Markov process and assuming that RMS time series is a stochastic process), by using Hidden Markov models (HMMs), that are a powerful tool for modeling any time-varying series. HMMs analysis seeks to discover the sequence of hidden states from the observed emissions. In our framework, observed emissions are characters generated by SAX (Symbolic Aggregate approXimation) technique. SAX is able to map RMS time series values with discrete literal emissions. Our experiments showed how to predict volcano states by means of SAX and HMMs.

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.

Short-term droughts forecast using Markov chain model in Victoria, Australia

NASA Astrophysics Data System (ADS)

Rahmat, Siti Nazahiyah; Jayasuriya, Niranjali; Bhuiyan, Muhammed A.

2017-07-01

A comprehensive risk management strategy for dealing with drought should include both short-term and long-term planning. The objective of this paper is to present an early warning method to forecast drought using the Standardised Precipitation Index (SPI) and a non-homogeneous Markov chain model. A model such as this is useful for short-term planning. The developed method has been used to forecast droughts at a number of meteorological monitoring stations that have been regionalised into six (6) homogenous clusters with similar drought characteristics based on SPI. The non-homogeneous Markov chain model was used to estimate drought probabilities and drought predictions up to 3 months ahead. The drought severity classes defined using the SPI were computed at a 12-month time scale. The drought probabilities and the predictions were computed for six clusters that depict similar drought characteristics in Victoria, Australia. Overall, the drought severity class predicted was quite similar for all the clusters, with the non-drought class probabilities ranging from 49 to 57 %. For all clusters, the near normal class had a probability of occurrence varying from 27 to 38 %. For the more moderate and severe classes, the probabilities ranged from 2 to 13 % and 3 to 1 %, respectively. The developed model predicted drought situations 1 month ahead reasonably well. However, 2 and 3 months ahead predictions should be used with caution until the models are developed further.

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 ) .

Markov chain aggregation and its applications to combinatorial reaction networks.

PubMed

Ganguly, Arnab; Petrov, Tatjana; Koeppl, Heinz

2014-09-01

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

PubMed Central

Li, Degui; Li, Runze

2016-01-01

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory. PMID:27667894

Two Aspects of the Simplex Model: Goodness of Fit to Linear Growth Curve Structures and the Analysis of Mean Trends.

ERIC Educational Resources Information Center

Mandys, Frantisek; Dolan, Conor V.; Molenaar, Peter C. M.

1994-01-01

Studied the conditions under which the quasi-Markov simplex model fits a linear growth curve covariance structure and determined when the model is rejected. Presents a quasi-Markov simplex model with structured means and gives an example. (SLD)

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.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses.

PubMed

Guerrier, Claire; Holcman, David

2016-10-18

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

Challenges in economic modeling of anticancer therapies: an example of modeling the survival benefit of olaparib maintenance therapy for patients with BRCA-mutated platinum-sensitive relapsed ovarian cancer.

PubMed

Hettle, Robert; Posnett, John; Borrill, John

2015-01-01

The aim of this paper is to describe a four health-state, semi-Markov model structure with health states defined by initiation of subsequent treatment, designed to make best possible use of the data available from a phase 2 clinical trial. The approach is illustrated using data from a sub-group of patients enrolled in a phase 2 clinical trial of olaparib maintenance therapy in patients with platinum-sensitive relapsed ovarian cancer and a BRCA mutation (NCT00753545). A semi-Markov model was developed with four health states: progression-free survival (PFS), first subsequent treatment (FST), second subsequent treatment (SST), and death. Transition probabilities were estimated by fitting survival curves to trial data for time from randomization to FST, time from FST to SST, and time from SST to death. Survival projections generated by the model are broadly consistent with the outcomes observed in the clinical trial. However, limitations of the trial data (small sample size, immaturity of the PFS and overall survival [OS] end-points, and treatment switching) create uncertainty in estimates of survival. The model framework offers a promising approach to evaluating cost-effectiveness of a maintenance therapy for patients with cancer, which may be generalizable to other chronic diseases.

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.

Integrating hidden Markov model and PRAAT: a toolbox for robust automatic speech transcription

NASA Astrophysics Data System (ADS)

Kabir, A.; Barker, J.; Giurgiu, M.

2010-09-01

An automatic time-aligned phone transcription toolbox of English speech corpora has been developed. Especially the toolbox would be very useful to generate robust automatic transcription and able to produce phone level transcription using speaker independent models as well as speaker dependent models without manual intervention. The system is based on standard Hidden Markov Models (HMM) approach and it was successfully experimented over a large audiovisual speech corpus namely GRID corpus. One of the most powerful features of the toolbox is the increased flexibility in speech processing where the speech community would be able to import the automatic transcription generated by HMM Toolkit (HTK) into a popular transcription software, PRAAT, and vice-versa. The toolbox has been evaluated through statistical analysis on GRID data which shows that automatic transcription deviates by an average of 20 ms with respect to manual transcription.

Predicting airborne particle deposition by a modified Markov chain model for fast estimation of potential contaminant spread

NASA Astrophysics Data System (ADS)

Mei, Xiong; Gong, Guangcai

2018-07-01

As potential carriers of hazardous pollutants, airborne particles may deposit onto surfaces due to gravitational settling. A modified Markov chain model to predict gravity induced particle dispersion and deposition is proposed in the paper. The gravity force is considered as a dominant weighting factor to adjust the State Transfer Matrix, which represents the probabilities of the change of particle spatial distributions between consecutive time steps within an enclosure. The model performance has been further validated by particle deposition in a ventilation chamber and a horizontal turbulent duct flow in pre-existing literatures. Both the proportion of deposited particles and the dimensionless deposition velocity are adopted to characterize the validation results. Comparisons between our simulated results and the experimental data from literatures show reasonable accuracy. Moreover, it is also found that the dimensionless deposition velocity can be remarkably influenced by particle size and stream-wise velocity in a typical horizontal flow. This study indicates that the proposed model can predict the gravity-dominated airborne particle deposition with reasonable accuracy and acceptable computing time.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Probability-based constrained MPC for structured uncertain systems with state and random input delays

NASA Astrophysics Data System (ADS)

Lu, Jianbo; Li, Dewei; Xi, Yugeng

2013-07-01

This article is concerned with probability-based constrained model predictive control (MPC) for systems with both structured uncertainties and time delays, where a random input delay and multiple fixed state delays are included. The process of input delay is governed by a discrete-time finite-state Markov chain. By invoking an appropriate augmented state, the system is transformed into a standard structured uncertain time-delay Markov jump linear system (MJLS). For the resulting system, a multi-step feedback control law is utilised to minimise an upper bound on the expected value of performance objective. The proposed design has been proved to stabilise the closed-loop system in the mean square sense and to guarantee constraints on control inputs and system states. Finally, a numerical example is given to illustrate the proposed results.

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.

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.

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 new class of enhanced kinetic sampling methods for building Markov state models

NASA Astrophysics Data System (ADS)

Bhoutekar, Arti; Ghosh, Susmita; Bhattacharya, Swati; Chatterjee, Abhijit

2017-10-01

Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

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.

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Nonpoint Source Solute Transport Normal to Aquifer Bedding in Heterogeneous, Markov Chain Random Fields

NASA Astrophysics Data System (ADS)

Zhang, H.; Harter, T.; Sivakumar, B.

2005-12-01

Facies-based geostatistical models have become important tools for the stochastic analysis of flow and transport processes in heterogeneous aquifers. However, little is known about the dependency of these processes on the parameters of facies- based geostatistical models. This study examines the nonpoint source solute transport normal to the major bedding plane in the presence of interconnected high conductivity (coarse- textured) facies in the aquifer medium and the dependence of the transport behavior upon the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute travel time probability distribution functions (pdfs) for solute flux from the water table to the bottom boundary (production horizon) of the aquifer. The cases examined include, two-, three-, and four-facies models with horizontal to vertical facies mean length anisotropy ratios, ek, from 25:1 to 300:1, and with a wide range of facies volume proportions (e.g, from 5% to 95% coarse textured facies). Predictions of travel time pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer, the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and - to a lesser degree - the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, travel time pdfs are not log- normally distributed as is often assumed. Also, macrodispersive behavior (variance of the travel time pdf) was found to not be a unique function of the conductivity variance. The skewness of the travel time pdf varied from negatively skewed to strongly positively skewed within the parameter range examined. We also show that the Markov chain approach may give significantly different travel time pdfs when compared to the more commonly used Gaussian random field approach even though the first and second order moments in the geostatistical distribution of the lnK field are identical. The choice of the appropriate geostatistical model is therefore critical in the assessment of nonpoint source transport.

Probabilistic Model and Analysis of Conventional Preinstalled Mine Field Defense.

DTIC Science & Technology

1980-09-01

process to model the one or two positions of mines in the mine field. The duel between the anti-tank weapon and offensive tanks crossing the field is...mine field. The duel between the anti-tank weapon and offensive tanks crossing the field is modeled with a con- tinuous time Markov chain. Some...11 B. DUEL ------------------------------------------- 15 IV. DUEL

Building Higher-Order Markov Chain Models with EXCEL

ERIC Educational Resources Information Center

Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K.

2004-01-01

Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…

Policy Transfer via Markov Logic Networks

NASA Astrophysics Data System (ADS)

Torrey, Lisa; Shavlik, Jude

We propose using a statistical-relational model, the Markov Logic Network, for knowledge transfer in reinforcement learning. Our goal is to extract relational knowledge from a source task and use it to speed up learning in a related target task. We show that Markov Logic Networks are effective models for capturing both source-task Q-functions and source-task policies. We apply them via demonstration, which involves using them for decision making in an initial stage of the target task before continuing to learn. Through experiments in the RoboCup simulated-soccer domain, we show that transfer via Markov Logic Networks can significantly improve early performance in complex tasks, and that transferring policies is more effective than transferring Q-functions.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-01-01

We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.

Rice crop mapping and change prediction using multi-temporal satellite images in the Mekong Delta, Vietnam

NASA Astrophysics Data System (ADS)

Chen, C. R.; Chen, C. F.; Nguyen, S. T.

2014-12-01

The rice cropping systems in the Vietnamese Mekong Delta (VMD) has been undergoing major changes to cope with developing agro-economics, increasing population and changing climate. Information on rice cropping practices and changes in cropping systems is critical for policymakers to devise successful strategies to ensure food security and rice grain exports for the country. The primary objective of this research is to map rice cropping systems and predict future dynamics of rice cropping systems using the MODIS time-series data of 2002, 2006, and 2010. First, a phenology-based classification approach was applied for the classification and assessment of rice cropping systems in study region. Second, the Cellular Automata-Markov (CA-Markov) models was used to simulate the rice-cropping system map of VMD for 2010. The comparisons between the classification maps and the ground reference data indicated satisfactory results with overall accuracies and Kappa coefficients, respectively, of 81.4% and 0.75 for 2002, 80.6% and 0.74 for 2006 and 85.5% and 0.81 for 2010. The simulated map of rice cropping system for 2010 was extrapolated by CA-Markov model based on the trend of rice cropping systems during 2002~2006. The comparison between predicted scenario and classification map for 2010 presents a reasonably closer agreement. In conclusion, the CA-Markov model performs a powerful tool for the dynamic modeling of changes in rice cropping systems, and the results obtained demonstrate that the approach produces satisfactory results in terms of accuracy, quantitative forecast and spatial pattern changes. Meanwhile, the projections of the future changes would provide useful inputs to the agricultural policy for effective management of the rice cropping practices in VMD.

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.

The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carlo estimation for multilevel models with applications to discrete time survival models.

PubMed

Browne, William J; Steele, Fiona; Golalizadeh, Mousa; Green, Martin J

2009-06-01

We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.

Markov chain-incorporated and synthetic data-supported conditional artificial neural network models for forecasting monthly precipitation in arid regions

NASA Astrophysics Data System (ADS)

Aksoy, Hafzullah; Dahamsheh, Ahmad

2018-07-01

For forecasting monthly precipitation in an arid region, the feed forward back-propagation, radial basis function and generalized regression artificial neural networks (ANNs) are used in this study. The ANN models are improved after incorporation of a Markov chain-based algorithm (MC-ANNs) with which the percentage of dry months is forecasted perfectly, thus generation of any non-physical negative precipitation is eliminated. Due to the fact that recorded precipitation time series are usually shorter than the length needed for a proper calibration of ANN models, synthetic monthly precipitation data are generated by Thomas-Fiering model to further improve the performance of forecasting. For case studies from Jordan, it is seen that only a slightly better performance is achieved with the use of MC and synthetic data. A conditional statement is, therefore, established and imbedded into the ANN models after the incorporation of MC and support of synthetic data, to substantially improve the ability of the models for forecasting monthly precipitation in arid regions.

Zero velocity interval detection based on a continuous hidden Markov model in micro inertial pedestrian navigation

NASA Astrophysics Data System (ADS)

Sun, Wei; Ding, Wei; Yan, Huifang; Duan, Shunli

2018-06-01

Shoe-mounted pedestrian navigation systems based on micro inertial sensors rely on zero velocity updates to correct their positioning errors in time, which effectively makes determining the zero velocity interval play a key role during normal walking. However, as walking gaits are complicated, and vary from person to person, it is difficult to detect walking gaits with a fixed threshold method. This paper proposes a pedestrian gait classification method based on a hidden Markov model. Pedestrian gait data are collected with a micro inertial measurement unit installed at the instep. On the basis of analyzing the characteristics of the pedestrian walk, a single direction angular rate gyro output is used to classify gait features. The angular rate data are modeled into a univariate Gaussian mixture model with three components, and a four-state left–right continuous hidden Markov model (CHMM) is designed to classify the normal walking gait. The model parameters are trained and optimized using the Baum–Welch algorithm and then the sliding window Viterbi algorithm is used to decode the gait. Walking data are collected through eight subjects walking along the same route at three different speeds; the leave-one-subject-out cross validation method is conducted to test the model. Experimental results show that the proposed algorithm can accurately detect different walking gaits of zero velocity interval. The location experiment shows that the precision of CHMM-based pedestrian navigation improved by 40% when compared to the angular rate threshold method.

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.

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.

Hidden Markov models and other machine learning approaches in computational molecular biology

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

Baldi, P.

1995-12-31

This tutorial was one of eight tutorials selected to be presented at the Third International Conference on Intelligent Systems for Molecular Biology which was held in the United Kingdom from July 16 to 19, 1995. Computational tools are increasingly needed to process the massive amounts of data, to organize and classify sequences, to detect weak similarities, to separate coding from non-coding regions, and reconstruct the underlying evolutionary history. The fundamental problem in machine learning is the same as in scientific reasoning in general, as well as statistical modeling: to come up with a good model for the data. In thismore » tutorial four classes of models are reviewed. They are: Hidden Markov models; artificial Neural Networks; Belief Networks; and Stochastic Grammars. When dealing with DNA and protein primary sequences, Hidden Markov models are one of the most flexible and powerful alignments and data base searches. In this tutorial, attention is focused on the theory of Hidden Markov Models, and how to apply them to problems in molecular biology.« less

Deep Space Network Antenna Monitoring Using Adaptive Time Series Methods and Hidden Markov Models

NASA Technical Reports Server (NTRS)

Smyth, Padhraic; Mellstrom, Jeff

1993-01-01

The Deep Space Network (DSN)(designed and operated by the Jet Propulsion Laboratory for the National Aeronautics and Space Administration (NASA) provides end-to-end telecommunication capabilities between earth and various interplanetary spacecraft throughout the solar system.

LECTURES ON GAME THEORY, MARKOV CHAINS, AND RELATED TOPICS

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

Thompson, G L

1958-03-01

Notes on nine lectures delivered at Sandin Corporation in August 1957 are given. Part one contains the manuscript of a paper concerning a judging problem. Part two is concerned with finite Markov-chain theory amd discusses regular Markov chains, absorbing Markov chains, the classification of states, application to the Leontief input-output model, and semimartingales. Part three contains notes on game theory and covers matrix games, the effect of psychological attitudes on the outcomes of games, extensive games, amd matrix theory applied to mathematical economics. (auth)

Attention Switching during Scene Perception: How Goals Influence the Time Course of Eye Movements across Advertisements

ERIC Educational Resources Information Center

Wedel, Michel; Pieters, Rik; Liechty, John

2008-01-01

Eye movements across advertisements express a temporal pattern of bursts of respectively relatively short and long saccades, and this pattern is systematically influenced by activated scene perception goals. This was revealed by a continuous-time hidden Markov model applied to eye movements of 220 participants exposed to 17 ads under a…

[Analysis and modelling of safety culture in a Mexican hospital by Markov chains].

PubMed

Velázquez-Martínez, J D; Cruz-Suárez, H; Santos-Reyes, J

2016-01-01

The objective of this study was to analyse and model the safety culture with Markov chains, as well as predicting and/or prioritizing over time the evolutionary behaviour of the safety culture of the health's staff in one Mexican hospital. The Markov chain theory has been employed in the analysis, and the input data has been obtained from a previous study based on the Safety Attitude Questionnaire (CAS-MX-II), by considering the following 6 dimensions: safety climate, teamwork, job satisfaction, recognition of stress, perception of management, and work environment. The results highlighted the predictions and/or prioritisation of the approximate time for the possible integration into the evolutionary behaviour of the safety culture as regards the "slightly agree" (Likert scale) for: safety climate (in 12 years; 24.13%); teamwork (8 years; 34.61%); job satisfaction (11 years; 52.41%); recognition of the level of stress (8 years; 19.35%); and perception of the direction (22 years; 27.87%). The work environment dimension was unable to determine the behaviour of staff information, i.e. no information cultural roots were obtained. In general, it has been shown that there are weaknesses in the safety culture of the hospital, which is an opportunity to suggest changes to the mandatory policies in order to strengthen it. Copyright © 2016 SECA. Publicado por Elsevier España, S.L.U. All rights reserved.

An Illustration of the Use of Markov Decision Processes to Represent Student Growth (Learning). Research Report. ETS RR-07-40

ERIC Educational Resources Information Center

Almond, Russell G.

2007-01-01

Over the course of instruction, instructors generally collect a great deal of information about each student. Integrating that information intelligently requires models for how a student's proficiency changes over time. Armed with such models, instructors can "filter" the data--more accurately estimate the student's current proficiency…

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.

Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains.

PubMed

Tataru, Paula; Hobolth, Asger

2011-12-05

Continuous time Markov chains (CTMCs) is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes) are unaccessible and the past must be inferred from DNA sequence data observed in the present. We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD), the second on uniformization (UNI), and the third on integrals of matrix exponentials (EXPM). The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

NASA Astrophysics Data System (ADS)

Dibak, Manuel; del Razo, Mauricio J.; De Sancho, David; Schütte, Christof; Noé, Frank

2018-06-01

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

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

Multi-site Stochastic Simulation of Daily Streamflow with Markov Chain and KNN Algorithm

NASA Astrophysics Data System (ADS)

Mathai, J.; Mujumdar, P.

2017-12-01

A key focus of this study is to develop a method which is physically consistent with the hydrologic processes that can capture short-term characteristics of daily hydrograph as well as the correlation of streamflow in temporal and spatial domains. In complex water resource systems, flow fluctuations at small time intervals require that discretisation be done at small time scales such as daily scales. Also, simultaneous generation of synthetic flows at different sites in the same basin are required. We propose a method to equip water managers with a streamflow generator within a stochastic streamflow simulation framework. The motivation for the proposed method is to generate sequences that extend beyond the variability represented in the historical record of streamflow time series. The method has two steps: In step 1, daily flow is generated independently at each station by a two-state Markov chain, with rising limb increments randomly sampled from a Gamma distribution and the falling limb modelled as exponential recession and in step 2, the streamflow generated in step 1 is input to a nonparametric K-nearest neighbor (KNN) time series bootstrap resampler. The KNN model, being data driven, does not require assumptions on the dependence structure of the time series. A major limitation of KNN based streamflow generators is that they do not produce new values, but merely reshuffle the historical data to generate realistic streamflow sequences. However, daily flow generated using the Markov chain approach is capable of generating a rich variety of streamflow sequences. Furthermore, the rising and falling limbs of daily hydrograph represent different physical processes, and hence they need to be modelled individually. Thus, our method combines the strengths of the two approaches. We show the utility of the method and improvement over the traditional KNN by simulating daily streamflow sequences at 7 locations in the Godavari River basin in India.

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.

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.

Markov state models and molecular alchemy

NASA Astrophysics Data System (ADS)

Schütte, Christof; Nielsen, Adam; Weber, Marcus

2015-01-01

In recent years, Markov state models (MSMs) have attracted a considerable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g. for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article, a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under consideration. The performance of the reweighting scheme is illustrated for simple test cases, including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.

Auxiliary Parameter MCMC for Exponential Random Graph Models

NASA Astrophysics Data System (ADS)

Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro

2016-11-01

Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.

Nested Interrupt Analysis of Low Cost and High Performance Embedded Systems Using GSPN Framework

NASA Astrophysics Data System (ADS)

Lin, Cheng-Min

Interrupt service routines are a key technology for embedded systems. In this paper, we introduce the standard approach for using Generalized Stochastic Petri Nets (GSPNs) as a high-level model for generating CTMC Continuous-Time Markov Chains (CTMCs) and then use Markov Reward Models (MRMs) to compute the performance for embedded systems. This framework is employed to analyze two embedded controllers with low cost and high performance, ARM7 and Cortex-M3. Cortex-M3 is designed with a tail-chaining mechanism to improve the performance of ARM7 when a nested interrupt occurs on an embedded controller. The Platform Independent Petri net Editor 2 (PIPE2) tool is used to model and evaluate the controllers in terms of power consumption and interrupt overhead performance. Using numerical results, in spite of the power consumption or interrupt overhead, Cortex-M3 performs better than ARM7.

Statistical Inference in Hidden Markov Models Using k-Segment Constraints

PubMed Central

Titsias, Michalis K.; Holmes, Christopher C.; Yau, Christopher

2016-01-01

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. PMID:27226674

Analyzing Single-Molecule Protein Transportation Experiments via Hierarchical Hidden Markov Models

PubMed Central

Chen, Yang; Shen, Kuang

2017-01-01

To maintain proper cellular functions, over 50% of proteins encoded in the genome need to be transported to cellular membranes. The molecular mechanism behind such a process, often referred to as protein targeting, is not well understood. Single-molecule experiments are designed to unveil the detailed mechanisms and reveal the functions of different molecular machineries involved in the process. The experimental data consist of hundreds of stochastic time traces from the fluorescence recordings of the experimental system. We introduce a Bayesian hierarchical model on top of hidden Markov models (HMMs) to analyze these data and use the statistical results to answer the biological questions. In addition to resolving the biological puzzles and delineating the regulating roles of different molecular complexes, our statistical results enable us to propose a more detailed mechanism for the late stages of the protein targeting process. PMID:28943680

How well-connected is the surface of the global ocean?

PubMed

Froyland, Gary; Stuart, Robyn M; van Sebille, Erik

2014-09-01

The Ekman dynamics of the ocean surface circulation is known to contain attracting regions such as the great oceanic gyres and the associated garbage patches. Less well-known are the extents of the basins of attractions of these regions and how strongly attracting they are. Understanding the shape and extent of the basins of attraction sheds light on the question of the strength of connectivity of different regions of the ocean, which helps in understanding the flow of buoyant material like plastic litter. Using short flow time trajectory data from a global ocean model, we create a Markov chain model of the surface ocean dynamics. The surface ocean is not a conservative dynamical system as water in the ocean follows three-dimensional pathways, with upwelling and downwelling in certain regions. Using our Markov chain model, we easily compute net surface upwelling and downwelling, and verify that it matches observed patterns of upwelling and downwelling in the real ocean. We analyze the Markov chain to determine multiple attracting regions. Finally, using an eigenvector approach, we (i) identify the five major ocean garbage patches, (ii) partition the ocean into basins of attraction for each of the garbage patches, and (iii) partition the ocean into regions that demonstrate transient dynamics modulo the attracting garbage patches.

The introduction of hydrogen bond and hydrophobicity effects into the rotational isomeric states model for conformational analysis of unfolded peptides.

PubMed

Engin, Ozge; Sayar, Mehmet; Erman, Burak

2009-01-13

Relative contributions of local and non-local interactions to the unfolded conformations of peptides are examined by using the rotational isomeric states model which is a Markov model based on pairwise interactions of torsion angles. The isomeric states of a residue are well described by the Ramachandran map of backbone torsion angles. The statistical weight matrices for the states are determined by molecular dynamics simulations applied to monopeptides and dipeptides. Conformational properties of tripeptides formed from combinations of alanine, valine, tyrosine and tryptophan are investigated based on the Markov model. Comparison with molecular dynamics simulation results on these tripeptides identifies the sequence-distant long-range interactions that are missing in the Markov model. These are essentially the hydrogen bond and hydrophobic interactions that are obtained between the first and the third residue of a tripeptide. A systematic correction is proposed for incorporating these long-range interactions into the rotational isomeric states model. Preliminary results suggest that the Markov assumption can be improved significantly by renormalizing the statistical weight matrices to include the effects of the long-range correlations.

The introduction of hydrogen bond and hydrophobicity effects into the rotational isomeric states model for conformational analysis of unfolded peptides

NASA Astrophysics Data System (ADS)

Engin, Ozge; Sayar, Mehmet; Erman, Burak

2009-03-01

Relative contributions of local and non-local interactions to the unfolded conformations of peptides are examined by using the rotational isomeric states model which is a Markov model based on pairwise interactions of torsion angles. The isomeric states of a residue are well described by the Ramachandran map of backbone torsion angles. The statistical weight matrices for the states are determined by molecular dynamics simulations applied to monopeptides and dipeptides. Conformational properties of tripeptides formed from combinations of alanine, valine, tyrosine and tryptophan are investigated based on the Markov model. Comparison with molecular dynamics simulation results on these tripeptides identifies the sequence-distant long-range interactions that are missing in the Markov model. These are essentially the hydrogen bond and hydrophobic interactions that are obtained between the first and the third residue of a tripeptide. A systematic correction is proposed for incorporating these long-range interactions into the rotational isomeric states model. Preliminary results suggest that the Markov assumption can be improved significantly by renormalizing the statistical weight matrices to include the effects of the long-range correlations.

Upscaling transport of a reacting solute through a peridocially converging-diverging channel at pre-asymptotic times

NASA Astrophysics Data System (ADS)

Sund, Nicole L.; Bolster, Diogo; Dawson, Clint

2015-11-01

In this study we extend the Spatial Markov model, which has been successfully used to upscale conservative transport across a diverse range of porous media flows, to test if it can accurately upscale reactive transport, defined by a spatially heterogeneous first order degradation rate. We test the model in a well known highly simplified geometry, commonly considered as an idealized pore or fracture structure, a periodic channel with wavy boundaries. The edges of the flow domain have a layer through which there is no flow, but in which diffusion of a solute still occurs. Reactions are confined to this region. We demonstrate that the Spatial Markov model, an upscaled random walk model that enforces correlation between successive jumps, can reproduce breakthrough curves measured from microscale simulations that explicitly resolve all pertinent processes. We also demonstrate that a similar random walk model that does not enforce successive correlations is unable to reproduce all features of the measured breakthrough curves.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

PubMed

Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

2014-12-01

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysing grouping of nucleotides in DNA sequences using lumped processes constructed from Markov chains.

PubMed

Guédon, Yann; d'Aubenton-Carafa, Yves; Thermes, Claude

2006-03-01

The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is therefore addressed. In the classical approach to lumpability, this problem can be formulated as the determination of an appropriate state space (smaller than the original state space) such that the lumped chain defined on this state space retains the Markov property. We propose a different perspective on lumpability where the state space is fixed and the partitioning of this state space is represented by a one-to-many probabilistic function within a two-level stochastic process. Three nested classes of lumped processes can be defined in this way as sub-classes of first-order Markov chains. These lumped processes enable parsimonious reparameterizations of Markov chains that help to reveal relevant partitions of the state space. Characterizations of the lumped processes on the original transition probability matrix are derived. Different model selection methods relying either on hypothesis testing or on penalized log-likelihood criteria are presented as well as extensions to lumped processes constructed from high-order Markov chains. The relevance of the proposed approach to lumpability is illustrated by the analysis of DNA sequences. In particular, the use of lumped processes enables to highlight differences between intronic sequences and gene untranslated region sequences.

Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms

PubMed Central

Rechner, Steffen; Berger, Annabell

2016-01-01

We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442

Joint coverage probability in a simulation study on Continuous-Time Markov Chain parameter estimation.

PubMed

Benoit, Julia S; Chan, Wenyaw; Doody, Rachelle S

2015-01-01

Parameter dependency within data sets in simulation studies is common, especially in models such as Continuous-Time Markov Chains (CTMC). Additionally, the literature lacks a comprehensive examination of estimation performance for the likelihood-based general multi-state CTMC. Among studies attempting to assess the estimation, none have accounted for dependency among parameter estimates. The purpose of this research is twofold: 1) to develop a multivariate approach for assessing accuracy and precision for simulation studies 2) to add to the literature a comprehensive examination of the estimation of a general 3-state CTMC model. Simulation studies are conducted to analyze longitudinal data with a trinomial outcome using a CTMC with and without covariates. Measures of performance including bias, component-wise coverage probabilities, and joint coverage probabilities are calculated. An application is presented using Alzheimer's disease caregiver stress levels. Comparisons of joint and component-wise parameter estimates yield conflicting inferential results in simulations from models with and without covariates. In conclusion, caution should be taken when conducting simulation studies aiming to assess performance and choice of inference should properly reflect the purpose of the simulation.

Set-free Markov state model building

NASA Astrophysics Data System (ADS)

Weber, Marcus; Fackeldey, Konstantin; Schütte, Christof

2017-03-01

Molecular dynamics (MD) simulations face challenging problems since the time scales of interest often are much longer than what is possible to simulate; and even if sufficiently long simulations are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant time scales accessible via coarse grained representations that also allow for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows us to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.

Comparison of RF spectrum prediction methods for dynamic spectrum access

NASA Astrophysics Data System (ADS)

Kovarskiy, Jacob A.; Martone, Anthony F.; Gallagher, Kyle A.; Sherbondy, Kelly D.; Narayanan, Ram M.

2017-05-01

Dynamic spectrum access (DSA) refers to the adaptive utilization of today's busy electromagnetic spectrum. Cognitive radio/radar technologies require DSA to intelligently transmit and receive information in changing environments. Predicting radio frequency (RF) activity reduces sensing time and energy consumption for identifying usable spectrum. Typical spectrum prediction methods involve modeling spectral statistics with Hidden Markov Models (HMM) or various neural network structures. HMMs describe the time-varying state probabilities of Markov processes as a dynamic Bayesian network. Neural Networks model biological brain neuron connections to perform a wide range of complex and often non-linear computations. This work compares HMM, Multilayer Perceptron (MLP), and Recurrent Neural Network (RNN) algorithms and their ability to perform RF channel state prediction. Monte Carlo simulations on both measured and simulated spectrum data evaluate the performance of these algorithms. Generalizing spectrum occupancy as an alternating renewal process allows Poisson random variables to generate simulated data while energy detection determines the occupancy state of measured RF spectrum data for testing. The results suggest that neural networks achieve better prediction accuracy and prove more adaptable to changing spectral statistics than HMMs given sufficient training data.

Estimating HIV incidence and detection rates from surveillance data.

PubMed

Posner, Stephanie J; Myers, Leann; Hassig, Susan E; Rice, Janet C; Kissinger, Patricia; Farley, Thomas A

2004-03-01

Markov models that incorporate HIV test information can increase precision in estimates of new infections and permit the estimation of detection rates. The purpose of this study was to assess the functioning of a Markov model for estimating new HIV infections and HIV detection rates in Louisiana using surveillance data. We expanded a discrete-time Markov model by accounting for the change in AIDS case definition made by the Centers for Disease Control and Prevention in 1993. The model was applied to quarterly HIV/AIDS surveillance data reported in Louisiana from 1981 to 1996 for various exposure and demographic subgroups. When modeling subgroups defined by exposure categories, we adjusted for the high proportion of missing exposure information among recent cases. We ascertained sensitivity to changes in various model assumptions. The model was able to produce results consistent with other sources of information in the state. Estimates of new infections indicated a transition of the HIV epidemic in Louisiana from (1) predominantly white men and men who have sex with men to (2) women, blacks, and high-risk heterosexuals. The model estimated that 61% of all HIV/AIDS cases were detected and reported by 1996, yet half of all HIV/non-AIDS cases were yet to be detected. Sensitivity analyses demonstrated that the model was robust to several uncertainties. In general, the methodology provided a useful and flexible alternative for estimating infection and detection trends using data from a U.S. surveillance program. Its use for estimating current infection will need further exploration to address assumptions related to newer treatments.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

PubMed Central

Ito, Sosuke

2016-01-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics. PMID:27833120

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

NASA Astrophysics Data System (ADS)

Ito, Sosuke

2016-11-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.

Variable Star Signature Classification using Slotted Symbolic Markov Modeling

NASA Astrophysics Data System (ADS)

Johnston, K. B.; Peter, A. M.

2017-01-01

With the advent of digital astronomy, new benefits and new challenges have been presented to the modern day astronomer. No longer can the astronomer rely on manual processing, instead the profession as a whole has begun to adopt more advanced computational means. This paper focuses on the construction and application of a novel time-domain signature extraction methodology and the development of a supporting supervised pattern classification algorithm for the identification of variable stars. A methodology for the reduction of stellar variable observations (time-domain data) into a novel feature space representation is introduced. The methodology presented will be referred to as Slotted Symbolic Markov Modeling (SSMM) and has a number of advantages which will be demonstrated to be beneficial; specifically to the supervised classification of stellar variables. It will be shown that the methodology outperformed a baseline standard methodology on a standardized set of stellar light curve data. The performance on a set of data derived from the LINEAR dataset will also be shown.

Variable Star Signature Classification using Slotted Symbolic Markov Modeling

NASA Astrophysics Data System (ADS)

Johnston, Kyle B.; Peter, Adrian M.

2016-01-01

With the advent of digital astronomy, new benefits and new challenges have been presented to the modern day astronomer. No longer can the astronomer rely on manual processing, instead the profession as a whole has begun to adopt more advanced computational means. Our research focuses on the construction and application of a novel time-domain signature extraction methodology and the development of a supporting supervised pattern classification algorithm for the identification of variable stars. A methodology for the reduction of stellar variable observations (time-domain data) into a novel feature space representation is introduced. The methodology presented will be referred to as Slotted Symbolic Markov Modeling (SSMM) and has a number of advantages which will be demonstrated to be beneficial; specifically to the supervised classification of stellar variables. It will be shown that the methodology outperformed a baseline standard methodology on a standardized set of stellar light curve data. The performance on a set of data derived from the LINEAR dataset will also be shown.

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.

A simplified parsimonious higher order multivariate Markov chain model with new convergence condition

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a simplified parsimonious higher-order multivariate Markov chain model with new convergence condition. (TPHOMMCM-NCC). Moreover, estimation method of the parameters in TPHOMMCM-NCC is give. Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC.

Techniques for modeling the reliability of fault-tolerant systems with the Markov state-space approach

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Johnson, Sally C.

1995-01-01

This paper presents a step-by-step tutorial of the methods and the tools that were used for the reliability analysis of fault-tolerant systems. The approach used in this paper is the Markov (or semi-Markov) state-space method. The paper is intended for design engineers with a basic understanding of computer architecture and fault tolerance, but little knowledge of reliability modeling. The representation of architectural features in mathematical models is emphasized. This paper does not present details of the mathematical solution of complex reliability models. Instead, it describes the use of several recently developed computer programs SURE, ASSIST, STEM, and PAWS that automate the generation and the solution of these models.

Hidden Markov induced Dynamic Bayesian Network for recovering time evolving gene regulatory networks

NASA Astrophysics Data System (ADS)

Zhu, Shijia; Wang, Yadong

2015-12-01

Dynamic Bayesian Networks (DBN) have been widely used to recover gene regulatory relationships from time-series data in computational systems biology. Its standard assumption is ‘stationarity’, and therefore, several research efforts have been recently proposed to relax this restriction. However, those methods suffer from three challenges: long running time, low accuracy and reliance on parameter settings. To address these problems, we propose a novel non-stationary DBN model by extending each hidden node of Hidden Markov Model into a DBN (called HMDBN), which properly handles the underlying time-evolving networks. Correspondingly, an improved structural EM algorithm is proposed to learn the HMDBN. It dramatically reduces searching space, thereby substantially improving computational efficiency. Additionally, we derived a novel generalized Bayesian Information Criterion under the non-stationary assumption (called BWBIC), which can help significantly improve the reconstruction accuracy and largely reduce over-fitting. Moreover, the re-estimation formulas for all parameters of our model are derived, enabling us to avoid reliance on parameter settings. Compared to the state-of-the-art methods, the experimental evaluation of our proposed method on both synthetic and real biological data demonstrates more stably high prediction accuracy and significantly improved computation efficiency, even with no prior knowledge and parameter settings.

Housing Value Projection Model Related to Educational Planning: The Feasibility of a New Methodology. Final Report.

ERIC Educational Resources Information Center

Helbock, Richard W.; Marker, Gordon

This study concerns the feasibility of a Markov chain model for projecting housing values and racial mixes. Such projections could be used in planning the layout of school districts to achieve desired levels of socioeconomic heterogeneity. Based upon the concepts and assumptions underlying a Markov chain model, it is concluded that such a model is…

A coupled duration-focused architecture for real-time music-to-score alignment.

PubMed

Cont, Arshia

2010-06-01

The capacity for real-time synchronization and coordination is a common ability among trained musicians performing a music score that presents an interesting challenge for machine intelligence. Compared to speech recognition, which has influenced many music information retrieval systems, music's temporal dynamics and complexity pose challenging problems to common approximations regarding time modeling of data streams. In this paper, we propose a design for a real-time music-to-score alignment system. Given a live recording of a musician playing a music score, the system is capable of following the musician in real time within the score and decoding the tempo (or pace) of its performance. The proposed design features two coupled audio and tempo agents within a unique probabilistic inference framework that adaptively updates its parameters based on the real-time context. Online decoding is achieved through the collaboration of the coupled agents in a Hidden Hybrid Markov/semi-Markov framework, where prediction feedback of one agent affects the behavior of the other. We perform evaluations for both real-time alignment and the proposed temporal model. An implementation of the presented system has been widely used in real concert situations worldwide and the readers are encouraged to access the actual system and experiment the results.

Study on statistical models for land mobile satellite channel

NASA Astrophysics Data System (ADS)

Wang, Ying; Hu, Xiulin

2005-11-01

Mobile terminals in a mobile satellite communication system cause the radio propagation channel to vary with time. So it is necessary to study the channel models in order to estimate the behavior of satellite signal propagation. A lot of research work have been done on the L- and S- bands. With the development of gigabit data transmissions and multimedia applications in recent years, the Ka-band studies gain much attention. Non-geostationary satellites are also in research because of its low propagation delay and low path loss. The future satellite mobile communication systems would be integrated into the other terrestrial networks in order to enable global, seamless and ubiquitous communications. At the same time QoS-technologies are studied to satisfy users' different service classes, such as mobility and resource managements. All the above make a suitable efficient channel model face new challenges. This paper firstly introduces existed channel models and analyzes their respective characteristics. Then we focus on a general model presented by Xie YongJun, which is popular under any environment and describes difference through different parameter values. However we believe that it is better to take multi-state Markov model as category in order to adapt to different environments. So a general model based on Markov process is presented and necessary simulation is carried out.

An Enhanced MEMS Error Modeling Approach Based on Nu-Support Vector Regression

PubMed Central

Bhatt, Deepak; Aggarwal, Priyanka; Bhattacharya, Prabir; Devabhaktuni, Vijay

2012-01-01

Micro Electro Mechanical System (MEMS)-based inertial sensors have made possible the development of a civilian land vehicle navigation system by offering a low-cost solution. However, the accurate modeling of the MEMS sensor errors is one of the most challenging tasks in the design of low-cost navigation systems. These sensors exhibit significant errors like biases, drift, noises; which are negligible for higher grade units. Different conventional techniques utilizing the Gauss Markov model and neural network method have been previously utilized to model the errors. However, Gauss Markov model works unsatisfactorily in the case of MEMS units due to the presence of high inherent sensor errors. On the other hand, modeling the random drift utilizing Neural Network (NN) is time consuming, thereby affecting its real-time implementation. We overcome these existing drawbacks by developing an enhanced Support Vector Machine (SVM) based error model. Unlike NN, SVMs do not suffer from local minimisation or over-fitting problems and delivers a reliable global solution. Experimental results proved that the proposed SVM approach reduced the noise standard deviation by 10–35% for gyroscopes and 61–76% for accelerometers. Further, positional error drifts under static conditions improved by 41% and 80% in comparison to NN and GM approaches. PMID:23012552

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.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

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.

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.

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.

Using Markov Models of Fault Growth Physics and Environmental Stresses to Optimize Control Actions

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.

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.

User's Manual MCnest - Markov Chain Nest Productivity Model Version 2.0

EPA Science Inventory

The Markov chain nest productivity model, or MCnest, is a set of algorithms for integrating the results of avian toxicity tests with reproductive life-history data to project the relative magnitude of chemical effects on avian reproduction. The mathematical foundation of MCnest i...

Improving Localization Accuracy: Successive Measurements Error Modeling

PubMed Central

Abu Ali, Najah; Abu-Elkheir, Mervat

2015-01-01

Vehicle self-localization is an essential requirement for many of the safety applications envisioned for vehicular networks. The mathematical models used in current vehicular localization schemes focus on modeling the localization error itself, and overlook the potential correlation between successive localization measurement errors. In this paper, we first investigate the existence of correlation between successive positioning measurements, and then incorporate this correlation into the modeling positioning error. We use the Yule Walker equations to determine the degree of correlation between a vehicle’s future position and its past positions, and then propose a p-order Gauss–Markov model to predict the future position of a vehicle from its past p positions. We investigate the existence of correlation for two datasets representing the mobility traces of two vehicles over a period of time. We prove the existence of correlation between successive measurements in the two datasets, and show that the time correlation between measurements can have a value up to four minutes. Through simulations, we validate the robustness of our model and show that it is possible to use the first-order Gauss–Markov model, which has the least complexity, and still maintain an accurate estimation of a vehicle’s future location over time using only its current position. Our model can assist in providing better modeling of positioning errors and can be used as a prediction tool to improve the performance of classical localization algorithms such as the Kalman filter. PMID:26140345

Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire.

PubMed

Bacaër, Nicolas

2016-10-01

The stochastic SIS epidemic model in a random environment. In a random environment that is a two-state continuous-time Markov chain, the mean time to extinction of the stochastic SIS epidemic model grows in the supercritical case exponentially with respect to the population size if the two states are favorable, and like a power law if one state is favorable while the other is unfavorable.

Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

ERIC Educational Resources Information Center

Kieftenbeld, Vincent; Natesan, Prathiba

2012-01-01

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

Markov Model of Accident Progression at Fukushima Daiichi

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

Cuadra A.; Bari R.; Cheng, L-Y

2012-11-11

On March 11, 2011, a magnitude 9.0 earthquake followed by a tsunami caused loss of offsite power and disabled the emergency diesel generators, leading to a prolonged station blackout at the Fukushima Daiichi site. After successful reactor trip for all operating reactors, the inability to remove decay heat over an extended period led to boil-off of the water inventory and fuel uncovery in Units 1-3. A significant amount of metal-water reaction occurred, as evidenced by the quantities of hydrogen generated that led to hydrogen explosions in the auxiliary buildings of the Units 1 & 3, and in the de-fuelled Unitmore » 4. Although it was assumed that extensive fuel damage, including fuel melting, slumping, and relocation was likely to have occurred in the core of the affected reactors, the status of the fuel, vessel, and drywell was uncertain. To understand the possible evolution of the accident conditions at Fukushima Daiichi, a Markov model of the likely state of one of the reactors was constructed and executed under different assumptions regarding system performance and reliability. The Markov approach was selected for several reasons: It is a probabilistic model that provides flexibility in scenario construction and incorporates time dependence of different model states. It also readily allows for sensitivity and uncertainty analyses of different failure and repair rates of cooling systems. While the analysis was motivated by a need to gain insight on the course of events for the damaged units at Fukushima Daiichi, the work reported here provides a more general analytical basis for studying and evaluating severe accident evolution over extended periods of time. This work was performed at the request of the U.S. Department of Energy to explore 'what-if' scenarios in the immediate aftermath of the accidents.« less

Estimating the ratios of the stationary distribution values for Markov chains modeling evolutionary algorithms.

PubMed

Mitavskiy, Boris; Cannings, Chris

2009-01-01

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When the mutation rate is positive, the Markov chain modeling of an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution. Rather little is known about the stationary distribution. In fact, the only quantitative facts established so far tell us that the stationary distributions of Markov chains modeling evolutionary algorithms concentrate on uniform populations (i.e., those populations consisting of a repeated copy of the same individual). At the same time, knowing the stationary distribution may provide some information about the expected time it takes for the algorithm to reach a certain solution, assessment of the biases due to recombination and selection, and is of importance in population genetics to assess what is called a "genetic load" (see the introduction for more details). In the recent joint works of the first author, some bounds have been established on the rates at which the stationary distribution concentrates on the uniform populations. The primary tool used in these papers is the "quotient construction" method. It turns out that the quotient construction method can be exploited to derive much more informative bounds on ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the three main stages of an evolutionary algorithm: namely, selection, recombination, and mutation.

Surgical motion characterization in simulated needle insertion procedures

NASA Astrophysics Data System (ADS)

Holden, Matthew S.; Ungi, Tamas; Sargent, Derek; McGraw, Robert C.; Fichtinger, Gabor

2012-02-01

PURPOSE: Evaluation of surgical performance in image-guided needle insertions is of emerging interest, to both promote patient safety and improve the efficiency and effectiveness of training. The purpose of this study was to determine if a Markov model-based algorithm can more accurately segment a needle-based surgical procedure into its five constituent tasks than a simple threshold-based algorithm. METHODS: Simulated needle trajectories were generated with known ground truth segmentation by a synthetic procedural data generator, with random noise added to each degree of freedom of motion. The respective learning algorithms were trained, and then tested on different procedures to determine task segmentation accuracy. In the threshold-based algorithm, a change in tasks was detected when the needle crossed a position/velocity threshold. In the Markov model-based algorithm, task segmentation was performed by identifying the sequence of Markov models most likely to have produced the series of observations. RESULTS: For amplitudes of translational noise greater than 0.01mm, the Markov model-based algorithm was significantly more accurate in task segmentation than the threshold-based algorithm (82.3% vs. 49.9%, p<0.001 for amplitude 10.0mm). For amplitudes less than 0.01mm, the two algorithms produced insignificantly different results. CONCLUSION: Task segmentation of simulated needle insertion procedures was improved by using a Markov model-based algorithm as opposed to a threshold-based algorithm for procedures involving translational noise.

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

Clustering Multivariate Time Series Using Hidden Markov Models

PubMed Central

Ghassempour, Shima; Girosi, Federico; Maeder, Anthony

2014-01-01

In this paper we describe an algorithm for clustering multivariate time series with variables taking both categorical and continuous values. Time series of this type are frequent in health care, where they represent the health trajectories of individuals. The problem is challenging because categorical variables make it difficult to define a meaningful distance between trajectories. We propose an approach based on Hidden Markov Models (HMMs), where we first map each trajectory into an HMM, then define a suitable distance between HMMs and finally proceed to cluster the HMMs with a method based on a distance matrix. We test our approach on a simulated, but realistic, data set of 1,255 trajectories of individuals of age 45 and over, on a synthetic validation set with known clustering structure, and on a smaller set of 268 trajectories extracted from the longitudinal Health and Retirement Survey. The proposed method can be implemented quite simply using standard packages in R and Matlab and may be a good candidate for solving the difficult problem of clustering multivariate time series with categorical variables using tools that do not require advanced statistic knowledge, and therefore are accessible to a wide range of researchers. PMID:24662996

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.

Search for gravitational waves from Scorpius X-1 in the first Advanced LIGO observing run with a hidden Markov model

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Afrough, M.; Agarwal, B.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allen, G.; Allocca, A.; Almoubayyed, H.; Altin, P. A.; Amato, A.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Antier, S.; Appert, S.; Arai, K.; Araya, M. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; AultONeal, K.; Avila-Alvarez, A.; Babak, S.; Bacon, P.; Bader, M. K. M.; Bae, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Banagiri, S.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bawaj, M.; Bazzan, M.; Bécsy, B.; Beer, C.; Bejger, M.; Belahcene, I.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Etienne, Z. B.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Billman, C. R.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blackman, J.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bode, N.; Boer, M.; Bogaert, G.; Bohe, A.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T. A.; Calloni, E.; Camp, J. B.; Canepa, M.; Canizares, P.; Cannon, K. C.; Cao, H.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Carney, M. F.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chatterjee, D.; Cheeseboro, B. D.; Chen, H. Y.; Chen, Y.; Cheng, H.-P.; Chincarini, A.; Chiummo, A.; Chmiel, T.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, A. J. K.; Chua, S.; Chung, A. K. W.; Chung, S.; Ciani, G.; Ciolfi, R.; Cirelli, C. E.; Cirone, A.; Clara, F.; Clark, J. A.; Cleva, F.; Cocchieri, C.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L. R.; Constancio, M.; Conti, L.; Cooper, S. J.; Corban, P.; Corbitt, T. R.; Corley, K. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Covas, P. B.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Creighton, J. D. E.; Creighton, T. D.; Cripe, J.; Crowder, S. G.; Cullen, T. J.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davies, G. S.; Davis, D.; Daw, E. J.; Day, B.; De, S.; DeBra, D.; Deelman, E.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Devenson, J.; Devine, R. C.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Renzo, F.; Doctor, Z.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dorrington, I.; Douglas, R.; Dovale Álvarez, M.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Duncan, J.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favata, M.; Fays, M.; Fehrmann, H.; Feicht, J.; Fejer, M. M.; Fernandez-Galiana, A.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fong, H.; Forsyth, P. W. F.; Forsyth, S. S.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fries, E. M.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H.; Gabel, M.; Gadre, B. U.; Gaebel, S. M.; Gair, J. R.; Gammaitoni, L.; Ganija, M. R.; Gaonkar, S. G.; Garufi, F.; Gaudio, S.; Gaur, G.; Gayathri, V.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; George, D.; George, J.; Gergely, L.; Germain, V.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glover, L.; Goetz, E.; Goetz, R.; Gomes, S.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Gruning, P.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannuksela, O. A.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Henry, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Horst, C.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Ingram, D. R.; Inta, R.; Intini, G.; Isa, H. N.; Isac, J.-M.; Isi, M.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Junker, J.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katolik, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kawabe, K.; Kéfélian, F.; Keitel, D.; Kemball, A. J.; Kennedy, R.; Kent, C.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chunglee; Kim, J. C.; Kim, W.; Kim, W. S.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kirchhoff, R.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koch, P.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Krämer, C.; Kringel, V.; Krishnan, B.; Królak, A.; Kuehn, G.; Kumar, P.; Kumar, R.; Kumar, S.; Kuo, L.; Kutynia, A.; Kwang, S.; Lackey, B. D.; Lai, K. H.; Landry, M.; Lang, R. N.; Lange, J.; Lantz, B.; Lanza, R. K.; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, H. W.; Lee, K.; Lehmann, J.; Lenon, A.; Leonardi, M.; Leroy, N.; Letendre, N.; Levin, Y.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Liu, J.; Lockerbie, N. A.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lovelace, G.; Lück, H.; Lumaca, D.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macfoy, S.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña Hernandez, I.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markakis, C.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matas, A.; Matichard, F.; Matone, L.; Mavalvala, N.; Mayani, R.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McCuller, L.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Mejuto-Villa, E.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B. B.; Miller, J.; Millhouse, M.; Minazzoli, O.; Minenkov, Y.; Ming, J.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Muniz, E. A. M.; Murray, P. G.; Napier, K.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Nelemans, G.; Nelson, T. J. N.; Neri, M.; Nery, M.; Neunzert, A.; Newport, J. M.; Newton, G.; Ng, K. K. Y.; Nguyen, T. T.; Nichols, D.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Noack, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; Ormiston, R.; Ortega, L. F.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pace, A. E.; Page, J.; Page, M. A.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pang, B.; Pang, P. T. H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perez, C. J.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Popolizio, P.; Porter, E. K.; Post, A.; Powell, J.; Prasad, J.; Pratt, J. W. W.; Predoi, V.; Prestegard, T.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L. G.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Qiu, S.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rakhmanov, M.; Ramirez, K. E.; Rapagnani, P.; Raymond, V.; Razzano, M.; Read, J.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Ricci, F.; Ricker, P. M.; Rieger, S.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, R.; Romel, C. L.; Romie, J. H.; Rosińska, D.; Ross, M. P.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Rynge, M.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sampson, L. M.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Scheuer, J.; Schmidt, E.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schulte, B. W.; Schutz, B. F.; Schwalbe, S. G.; Scott, J.; Scott, S. M.; Seidel, E.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Shaddock, D. A.; Shaffer, T. J.; Shah, A. A.; Shahriar, M. S.; Shao, L.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, B.; Smith, J. R.; Smith, R. J. E.; Son, E. J.; Sonnenberg, J. A.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Spencer, A. P.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Stratta, G.; Strigin, S. E.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Taracchini, A.; Taylor, J. A.; Taylor, R.; Theeg, T.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tonelli, M.; Tornasi, Z.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Trinastic, J.; Tringali, M. C.; Trozzo, L.; Tsang, K. W.; Tse, M.; Tso, R.; Tuyenbayev, D.; Ueno, K.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahi, K.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Varma, V.; Vass, S.; Vasúth, M.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Venugopalan, G.; Verkindt, D.; Vetrano, F.; Viceré, A.; Viets, A. D.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D. V.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walet, R.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, J. Z.; Wang, M.; Wang, Y.-F.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Watchi, J.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Wessel, E. K.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Whittle, C.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Wofford, J.; Wong, K. W. K.; Worden, J.; Wright, J. L.; Wu, D. S.; Wu, G.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, Hang; Yu, Haocun; Yvert, M.; ZadroŻny, A.; Zanolin, M.; Zelenova, T.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.-H.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zweizig, J.; Suvorova, S.; Moran, W.; Evans, R. J.; LIGO Scientific Collaboration; Virgo Collaboration

2017-06-01

Results are presented from a semicoherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run. The search combines a frequency domain matched filter (Bessel-weighted F -statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60-650 Hz. Frequentist 95% confidence strain upper limits, h095 %=4.0 ×1 0-25, 8.3 ×1 0-25, and 3.0 ×1 0-25 for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are ≤10 times higher than the theoretical torque-balance limit at 106 Hz.

Markov state models of protein misfolding

NASA Astrophysics Data System (ADS)

Sirur, Anshul; De Sancho, David; Best, Robert B.

2016-02-01

Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.

Brain tumor segmentation in 3D MRIs using an improved Markov random field model

NASA Astrophysics Data System (ADS)

Yousefi, Sahar; Azmi, Reza; Zahedi, Morteza

2011-10-01

Markov Random Field (MRF) models have been recently suggested for MRI brain segmentation by a large number of researchers. By employing Markovianity, which represents the local property, MRF models are able to solve a global optimization problem locally. But they still have a heavy computation burden, especially when they use stochastic relaxation schemes such as Simulated Annealing (SA). In this paper, a new 3D-MRF model is put forward to raise the speed of the convergence. Although, search procedure of SA is fairly localized and prevents from exploring the same diversity of solutions, it suffers from several limitations. In comparison, Genetic Algorithm (GA) has a good capability of global researching but it is weak in hill climbing. Our proposed algorithm combines SA and an improved GA (IGA) to optimize the solution which speeds up the computation time. What is more, this proposed algorithm outperforms the traditional 2D-MRF in quality of the solution.

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.

Did the ever dead outnumber the living and when? A birth-and-death approach

NASA Astrophysics Data System (ADS)

Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

2015-02-01

This paper is an attempt to formalize analytically the question raised in 'World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?' Huffington Post, Howard (2012). We start developing simple deterministic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both linear birth and death Markov chain models and age-structured models.

Avian life history profiles for use in the Markov chain nest productivity model (MCnest)

EPA Science Inventory

The Markov Chain nest productivity model, or MCnest, quantitatively estimates the effects of pesticides or other toxic chemicals on annual reproductive success of avian species (Bennett and Etterson 2013, Etterson and Bennett 2013). The Basic Version of MCnest was developed as a...

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.

HIPPI: highly accurate protein family classification with ensembles of HMMs.

PubMed

Nguyen, Nam-Phuong; Nute, Michael; Mirarab, Siavash; Warnow, Tandy

2016-11-11

Given a new biological sequence, detecting membership in a known family is a basic step in many bioinformatics analyses, with applications to protein structure and function prediction and metagenomic taxon identification and abundance profiling, among others. Yet family identification of sequences that are distantly related to sequences in public databases or that are fragmentary remains one of the more difficult analytical problems in bioinformatics. We present a new technique for family identification called HIPPI (Hierarchical Profile Hidden Markov Models for Protein family Identification). HIPPI uses a novel technique to represent a multiple sequence alignment for a given protein family or superfamily by an ensemble of profile hidden Markov models computed using HMMER. An evaluation of HIPPI on the Pfam database shows that HIPPI has better overall precision and recall than blastp, HMMER, and pipelines based on HHsearch, and maintains good accuracy even for fragmentary query sequences and for protein families with low average pairwise sequence identity, both conditions where other methods degrade in accuracy. HIPPI provides accurate protein family identification and is robust to difficult model conditions. Our results, combined with observations from previous studies, show that ensembles of profile Hidden Markov models can better represent multiple sequence alignments than a single profile Hidden Markov model, and thus can improve downstream analyses for various bioinformatic tasks. Further research is needed to determine the best practices for building the ensemble of profile Hidden Markov models. HIPPI is available on GitHub at https://github.com/smirarab/sepp .

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.

Detection of long term persistence in time series of the Neuquen River (Argentina)

NASA Astrophysics Data System (ADS)

Seoane, Rafael; Paz González, Antonio

2014-05-01

In the Patagonian region (Argentina), previous hydrometeorological studies that have been developed using general circulation models show variations in annual mean flows. Future climate scenarios obtained from high-resolution models indicate decreases in total annual precipitation, and these scenarios are more important in the Neuquén river basin (23000 km2). The aim of this study was the estimation of long term persistence in the Neuquén River basin (Argentina). The detection of variations in the long range dependence term and long memory of time series was evaluated with the Hurst exponent. We applied rescaled adjusted range analysis (R/S) to time series of River discharges measured from 1903 to 2011 and this time series was divided into two subperiods: the first was from 1903 to 1970 and the second from 1970 to 2011. Results show a small increase in persistence for the second period. Our results are consistent with those obtained by Koch and Markovic (2007), who observed and estimated an increase of the H exponent for the period 1960-2000 in the Elbe River (Germany). References Hurst, H. (1951).Long term storage capacities of reservoirs". Trans. Am. Soc. Civil Engrs., 116:776-808. Koch and Markovic (2007). Evidences for Climate Change in Germany over the 20th Century from the Stochastic Analysis of hydro-meteorological Time Series, MODSIM07, International Congress on Modelling and Simulation, Christchurch, New Zealand.

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.

A hierarchical approach to reliability modeling of fault-tolerant systems. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gossman, W. E.

1986-01-01

A methodology for performing fault tolerant system reliability analysis is presented. The method decomposes a system into its subsystems, evaluates vent rates derived from the subsystem's conditional state probability vector and incorporates those results into a hierarchical Markov model of the system. This is done in a manner that addresses failure sequence dependence associated with the system's redundancy management strategy. The method is derived for application to a specific system definition. Results are presented that compare the hierarchical model's unreliability prediction to that of a more complicated tandard Markov model of the system. The results for the example given indicate that the hierarchical method predicts system unreliability to a desirable level of accuracy while achieving significant computational savings relative to component level Markov model of the system.

Treatment evolution and new standards of care: implications for cost-effectiveness analysis.

PubMed

Shechter, Steven M

2011-01-01

Traditional approaches to cost-effectiveness analysis have not considered the downstream possibility of a new standard of care coming out of the research and development pipeline. However, the treatment landscape for patients may change significantly over the course of their lifetimes. To present a Markov modeling framework that incorporates the possibility of treatment evolution into the incremental cost-effectiveness ratio (ICER) that compares treatments available at the present time. . Markov model evaluated by matrix algebra. Measurements. The author evaluates the difference between the new and traditional ICER calculations for patients with chronic diseases facing a lifetime of treatment. The bias of the traditional ICER calculation may be substantial, with further testing revealing that it may be either positive or negative depending on the model parameters. The author also performs probabilistic sensitivity analyses with respect to the possible timing of a new treatment discovery and notes the increase in the magnitude of the bias when the new treatment is likely to appear sooner rather than later. Limitations. The modeling framework is intended as a proof of concept and therefore makes simplifying assumptions such as time stationarity of model parameters and consideration of a single new drug discovery. For diseases with a more active research and development pipeline, the possibility of a new treatment paradigm may be at least as important to consider in sensitivity analysis as other parameters that are often considered.

Preliminary testing for the Markov property of the fifteen chromatin states of the Broad Histone Track.

PubMed

Lee, Kyung-Eun; Park, Hyun-Seok

2015-01-01

Epigenetic computational analyses based on Markov chains can integrate dependencies between regions in the genome that are directly adjacent. In this paper, the BED files of fifteen chromatin states of the Broad Histone Track of the ENCODE project are parsed, and comparative nucleotide frequencies of regional chromatin blocks are thoroughly analyzed to detect the Markov property in them. We perform various tests to examine the Markov property embedded in a frequency domain by checking for the presence of the Markov property in the various chromatin states. We apply these tests to each region of the fifteen chromatin states. The results of our simulation indicate that some of the chromatin states possess a stronger Markov property than others. We discuss the significance of our findings in statistical models of nucleotide sequences that are necessary for the computational analysis of functional units in noncoding DNA.

Entanglement revival can occur only when the system-environment state is not a Markov state

NASA Astrophysics Data System (ADS)

Sargolzahi, Iman

2018-06-01

Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will call strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the whole system-environment is a Markov state, then each localized dynamics of the whole system-environment reduces to a localized subdynamics of the system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system-environment state is not a Markov state. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system-environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.

Human Behavior Drift Detection in a Smart Home Environment.

PubMed

Masciadri, Andrea; Trofimova, Anna A; Matteucci, Matteo; Salice, Fabio

2017-01-01

The proposed system aims at elderly people independent living by providing an early indicator of habits changes which might be relevant for a diagnosis of diseases. It relies on Hidden Markov Model to describe the behavior observing sensors data, while Likelihood Ratio Test gives the variation within different time periods.

A systematic review of quality and cost-effectiveness derived from Markov models evaluating smoking cessation interventions in patients with chronic obstructive pulmonary disease.

PubMed

Kirsch, Florian

2015-04-01

Smoking cessation is the only strategy that has shown a lasting reduction in the decline of lung function in patients with chronic obstructive pulmonary disease. This study aims to evaluate the cost-effectiveness of smoking cessation interventions in patients with chronic obstructive pulmonary disease, to assess the quality of the Markov models and to estimate the consequences of model structure and input data on cost-effectiveness. A systematic literature search was conducted in PubMed, Embase, BusinessSourceComplete and Econlit on June 11, 2014. Data were extracted, and costs were inflated. Model quality was evaluated by a quality appraisal, and results were interpreted. Ten studies met the inclusion criteria. The results varied widely from cost savings to additional costs of €17,004 per quality adjusted life year. The models scored best in the category structure, followed by data and consistency. The quality of the models seems to rise over time, and regarding the results there is no economic reason to refuse the reimbursement of any smoking cessation intervention.

Adaptive hidden Markov model with anomaly States for price manipulation detection.

PubMed

Cao, Yi; Li, Yuhua; Coleman, Sonya; Belatreche, Ammar; McGinnity, Thomas Martin

2015-02-01

Price manipulation refers to the activities of those traders who use carefully designed trading behaviors to manually push up or down the underlying equity prices for making profits. With increasing volumes and frequency of trading, price manipulation can be extremely damaging to the proper functioning and integrity of capital markets. The existing literature focuses on either empirical studies of market abuse cases or analysis of particular manipulation types based on certain assumptions. Effective approaches for analyzing and detecting price manipulation in real time are yet to be developed. This paper proposes a novel approach, called adaptive hidden Markov model with anomaly states (AHMMAS) for modeling and detecting price manipulation activities. Together with wavelet transformations and gradients as the feature extraction methods, the AHMMAS model caters to price manipulation detection and basic manipulation type recognition. The evaluation experiments conducted on seven stock tick data from NASDAQ and the London Stock Exchange and 10 simulated stock prices by stochastic differential equation show that the proposed AHMMAS model can effectively detect price manipulation patterns and outperforms the selected benchmark models.

A stochastic HMM-based forecasting model for fuzzy time series.

PubMed

Li, Sheng-Tun; Cheng, Yi-Chung

2010-10-01

Recently, fuzzy time series have attracted more academic attention than traditional time series due to their capability of dealing with the uncertainty and vagueness inherent in the data collected. The formulation of fuzzy relations is one of the key issues affecting forecasting results. Most of the present works adopt IF-THEN rules for relationship representation, which leads to higher computational overhead and rule redundancy. Sullivan and Woodall proposed a Markov-based formulation and a forecasting model to reduce computational overhead; however, its applicability is limited to handling one-factor problems. In this paper, we propose a novel forecasting model based on the hidden Markov model by enhancing Sullivan and Woodall's work to allow handling of two-factor forecasting problems. Moreover, in order to make the nature of conjecture and randomness of forecasting more realistic, the Monte Carlo method is adopted to estimate the outcome. To test the effectiveness of the resulting stochastic model, we conduct two experiments and compare the results with those from other models. The first experiment consists of forecasting the daily average temperature and cloud density in Taipei, Taiwan, and the second experiment is based on the Taiwan Weighted Stock Index by forecasting the exchange rate of the New Taiwan dollar against the U.S. dollar. In addition to improving forecasting accuracy, the proposed model adheres to the central limit theorem, and thus, the result statistically approximates to the real mean of the target value being forecast.

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

This paper focuses on a class of generalized Ginzburg-Landau equations with random switching. In our formulation, the nonlinear term is allowed to have higher polynomial growth rate than the usual cubic polynomials. The random switching is modeled by a continuous-time Markov chain with a finite state space. First, an explicit solution is obtained. Then properties such as stochastic-ultimate boundedness and permanence of the solution processes are investigated. Finally, two-time-scale models are examined leading to a reduction of complexity.

Modeling the Distribution of Fingerprint Characteristics. Revision 1.

DTIC Science & Technology

1980-09-19

the details of the print. The ridge-line details are termed Galton characteristics since Sir Francis Galton was among the first to study them...U.S.A. CONTENTS Abstract 1. Introduction 2. Background Information on Fingerprints 2.1. Types 2.2. Ridge counts 2.3. The Galton details 3. Data...The Multinomial Markov Model 7. The Poisson Markov Model 8. The Infinitely Divisible Model Acknowledgements References Appendices A The Galton

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.

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.

Evaluation of Usability Utilizing Markov Models

ERIC Educational Resources Information Center

Penedo, Janaina Rodrigues; Diniz, Morganna; Ferreira, Simone Bacellar Leal; Silveira, Denis S.; Capra, Eliane

2012-01-01

Purpose: The purpose of this paper is to analyze the usability of a remote learning system in its initial development phase, using a quantitative usability evaluation method through Markov models. Design/methodology/approach: The paper opted for an exploratory study. The data of interest of the research correspond to the possible accesses of users…

A Test of the Need Hierarchy Concept by a Markov Model of Change in Need Strength.

ERIC Educational Resources Information Center

Rauschenberger, John; And Others

1980-01-01

In this study of 547 high school graduates, Alderfer's and Maslow's need hierarchy theories were expressed in Markov chain form and were subjected to empirical test. Both models were disconfirmed. Corroborative multiwave correlational analysis also failed to support the need hierarchy concept. (Author/IRT)

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.

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

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.

Real-time human versus animal classification using pyro-electric sensor array and Hidden Markov Model

NASA Astrophysics Data System (ADS)

Hossen, Jakir; Jacobs, Eddie L.; Chari, Srikant

2014-03-01

In this paper, we propose a real-time human versus animal classification technique using a pyro-electric sensor array and Hidden Markov Model. The technique starts with the variational energy functional level set segmentation technique to separate the object from background. After segmentation, we convert the segmented object to a signal by considering column-wise pixel values and then finding the wavelet coefficients of the signal. HMMs are trained to statistically model the wavelet features of individuals through an expectation-maximization learning process. Human versus animal classifications are made by evaluating a set of new wavelet feature data against the trained HMMs using the maximum-likelihood criterion. Human and animal data acquired-using a pyro-electric sensor in different terrains are used for performance evaluation of the algorithms. Failures of the computationally effective SURF feature based approach that we develop in our previous research are because of distorted images produced when the object runs very fast or if the temperature difference between target and background is not sufficient to accurately profile the object. We show that wavelet based HMMs work well for handling some of the distorted profiles in the data set. Further, HMM achieves improved classification rate over the SURF algorithm with almost the same computational time.

RadVel: General toolkit for modeling Radial Velocities

NASA Astrophysics Data System (ADS)

Fulton, Benjamin J.; Petigura, Erik A.; Blunt, Sarah; Sinukoff, Evan

2018-01-01

RadVel models Keplerian orbits in radial velocity (RV) time series. The code is written in Python with a fast Kepler's equation solver written in C. It provides a framework for fitting RVs using maximum a posteriori optimization and computing robust confidence intervals by sampling the posterior probability density via Markov Chain Monte Carlo (MCMC). RadVel can perform Bayesian model comparison and produces publication quality plots and LaTeX tables.

a Probability Model for Drought Prediction Using Fusion of Markov Chain and SAX Methods

NASA Astrophysics Data System (ADS)

Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.

2017-09-01

Drought is one of the most powerful natural disasters which are affected on different aspects of the environment. Most of the time this phenomenon is immense in the arid and semi-arid area. Monitoring and prediction the severity of the drought can be useful in the management of the natural disaster caused by drought. Many indices were used in predicting droughts such as SPI, VCI, and TVX. In this paper, based on three data sets (rainfall, NDVI, and land surface temperature) which are acquired from MODIS satellite imagery, time series of SPI, VCI, and TVX in time limited between winters 2000 to summer 2015 for the east region of Isfahan province were created. Using these indices and fusion of symbolic aggregation approximation and hidden Markov chain drought was predicted for fall 2015. For this purpose, at first, each time series was transformed into the set of quality data based on the state of drought (5 group) by using SAX algorithm then the probability matrix for the future state was created by using Markov hidden chain. The fall drought severity was predicted by fusion the probability matrix and state of drought severity in summer 2015. The prediction based on the likelihood for each state of drought includes severe drought, middle drought, normal drought, severe wet and middle wet. The analysis and experimental result from proposed algorithm show that the product of this algorithm is acceptable and the proposed algorithm is appropriate and efficient for predicting drought using remote sensor data.

Evaluation of Markov-Decision Model for Instructional Sequence Optimization. Semi-Annual Technical Report for the period 1 July-31 December 1975. Technical Report No. 76.

ERIC Educational Resources Information Center

Wollmer, Richard D.; Bond, Nicholas A.

Two computer-assisted instruction programs were written in electronics and trigonometry to test the Wollmer Markov Model for optimizing hierarchial learning; calibration samples totalling 110 students completed these programs. Since the model postulated that transfer effects would be a function of the amount of practice, half of the students were…

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.

Physical time scale in kinetic Monte Carlo simulations of continuous-time Markov chains.

PubMed

Serebrinsky, Santiago A

2011-03-01

We rigorously establish a physical time scale for a general class of kinetic Monte Carlo algorithms for the simulation of continuous-time Markov chains. This class of algorithms encompasses rejection-free (or BKL) and rejection (or "standard") algorithms. For rejection algorithms, it was formerly considered that the availability of a physical time scale (instead of Monte Carlo steps) was empirical, at best. Use of Monte Carlo steps as a time unit now becomes completely unnecessary.

Quantum Mechanics, Pattern Recognition, and the Mammalian Brain

NASA Astrophysics Data System (ADS)

Chapline, George

2008-10-01

Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

Markov-switching multifractal models as another class of random-energy-like models in one-dimensional space

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.

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.

Sorting processes with energy-constrained comparisons*

NASA Astrophysics Data System (ADS)

Geissmann, Barbara; Penna, Paolo

2018-05-01

We study very simple sorting algorithms based on a probabilistic comparator model. In this model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared elements. Such algorithms repeatedly compare and swap pairs of randomly chosen elements, and they correspond to natural Markovian processes. The study of these Markov chains reveals an interesting phenomenon. Namely, in several cases, the algorithm that repeatedly compares only adjacent elements is better than the one making arbitrary comparisons: in the long-run, the former algorithm produces sequences that are "better sorted". The analysis of the underlying Markov chain poses interesting questions as the latter algorithm yields a nonreversible chain, and therefore its stationary distribution seems difficult to calculate explicitly. We nevertheless provide bounds on the stationary distributions and on the mixing time of these processes in several restrictions.

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

Traces of business cycles in credit-rating migrations

PubMed Central

Boreiko, Dmitri; Kaniovski, Serguei; Pflug, Georg

2017-01-01

Using migration data of a rating agency, this paper attempts to quantify the impact of macroeconomic conditions on credit-rating migrations. The migrations are modeled as a coupled Markov chain, where the macroeconomic factors are represented by unobserved tendency variables. In the simplest case, these binary random variables are static and credit-class-specific. A generalization treats tendency variables evolving as a time-homogeneous Markov chain. A more detailed analysis assumes a tendency variable for every combination of a credit class and an industry. The models are tested on a Standard and Poor’s (S&P’s) dataset. Parameters are estimated by the maximum likelihood method. According to the estimates, the investment-grade financial institutions evolve independently of the rest of the economy represented by the data. This might be an evidence of implicit too-big-to-fail bail-out guarantee policies of the regulatory authorities. PMID:28426758

Traces of business cycles in credit-rating migrations.

PubMed

Boreiko, Dmitri; Kaniovski, Serguei; Kaniovski, Yuri; Pflug, Georg

2017-01-01

Using migration data of a rating agency, this paper attempts to quantify the impact of macroeconomic conditions on credit-rating migrations. The migrations are modeled as a coupled Markov chain, where the macroeconomic factors are represented by unobserved tendency variables. In the simplest case, these binary random variables are static and credit-class-specific. A generalization treats tendency variables evolving as a time-homogeneous Markov chain. A more detailed analysis assumes a tendency variable for every combination of a credit class and an industry. The models are tested on a Standard and Poor's (S&P's) dataset. Parameters are estimated by the maximum likelihood method. According to the estimates, the investment-grade financial institutions evolve independently of the rest of the economy represented by the data. This might be an evidence of implicit too-big-to-fail bail-out guarantee policies of the regulatory authorities.

Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression

PubMed Central

Wiedenhoeft, John; Brugel, Eric; Schliep, Alexander

2016-01-01

By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings. PMID:27177143

Multivariate longitudinal data analysis with mixed effects hidden Markov models.

PubMed

Raffa, Jesse D; Dubin, Joel A

2015-09-01

Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. © 2015, The International Biometric Society.

A 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.

Two fundamental questions about protein evolution.

PubMed

Penny, David; Zhong, Bojian

2015-12-01

Two basic questions are considered that approach protein evolution from different directions; the problems arising from using Markov models for the deeper divergences, and then the origin of proteins themselves. The real problem for the first question (going backwards in time) is that at deeper phylogenies the Markov models of sequence evolution must lose information exponentially at deeper divergences, and several testable methods are suggested that should help resolve these deeper divergences. For the second question (coming forwards in time) a problem is that most models for the origin of protein synthesis do not give a role for the very earliest stages of the process. From our knowledge of the importance of replication accuracy in limiting the length of a coding molecule, a testable hypothesis is proposed. The length of the code, the code itself, and tRNAs would all have prior roles in increasing the accuracy of RNA replication; thus proteins would have been formed only after the tRNAs and the length of the triplet code are already formed. Both questions lead to testable predictions. Copyright © 2014 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

An integrated framework for detecting suspicious behaviors in video surveillance

NASA Astrophysics Data System (ADS)

Zin, Thi Thi; Tin, Pyke; Hama, Hiromitsu; Toriu, Takashi

2014-03-01

In this paper, we propose an integrated framework for detecting suspicious behaviors in video surveillance systems which are established in public places such as railway stations, airports, shopping malls and etc. Especially, people loitering in suspicion, unattended objects left behind and exchanging suspicious objects between persons are common security concerns in airports and other transit scenarios. These involve understanding scene/event, analyzing human movements, recognizing controllable objects, and observing the effect of the human movement on those objects. In the proposed framework, multiple background modeling technique, high level motion feature extraction method and embedded Markov chain models are integrated for detecting suspicious behaviors in real time video surveillance systems. Specifically, the proposed framework employs probability based multiple backgrounds modeling technique to detect moving objects. Then the velocity and distance measures are computed as the high level motion features of the interests. By using an integration of the computed features and the first passage time probabilities of the embedded Markov chain, the suspicious behaviors in video surveillance are analyzed for detecting loitering persons, objects left behind and human interactions such as fighting. The proposed framework has been tested by using standard public datasets and our own video surveillance scenarios.

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.

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

PubMed Central

Chen, Rui; Hyrien, Ollivier

2011-01-01

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356

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

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

A Markov Chain Model for Changes in Users' Assessment of Search Results.

PubMed

Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark

2016-01-01

Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same"coarse" relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users' judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results.

A Markov Chain Model for Changes in Users’ Assessment of Search Results

PubMed Central

Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark

2016-01-01

Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results. PMID:27171426

Reservoir optimisation using El Niño information. Case study of Daule Peripa (Ecuador)

NASA Astrophysics Data System (ADS)

Gelati, Emiliano; Madsen, Henrik; Rosbjerg, Dan

2010-05-01

The optimisation of water resources systems requires the ability to produce runoff scenarios that are consistent with available climatic information. We approach stochastic runoff modelling with a Markov-modulated autoregressive model with exogenous input, which belongs to the class of Markov-switching models. The model assumes runoff parameterisation to be conditioned on a hidden climatic state following a Markov chain, whose state transition probabilities depend on climatic information. This approach allows stochastic modeling of non-stationary runoff, as runoff anomalies are described by a mixture of autoregressive models with exogenous input, each one corresponding to a climate state. We calibrate the model on the inflows of the Daule Peripa reservoir located in western Ecuador, where the occurrence of El Niño leads to anomalously heavy rainfall caused by positive sea surface temperature anomalies along the coast. El Niño - Southern Oscillation (ENSO) information is used to condition the runoff parameterisation. Inflow predictions are realistic, especially at the occurrence of El Niño events. The Daule Peripa reservoir serves a hydropower plant and a downstream water supply facility. Using historical ENSO records, synthetic monthly inflow scenarios are generated for the period 1950-2007. These scenarios are used as input to perform stochastic optimisation of the reservoir rule curves with a multi-objective Genetic Algorithm (MOGA). The optimised rule curves are assumed to be the reservoir base policy. ENSO standard indices are currently forecasted at monthly time scale with nine-month lead time. These forecasts are used to perform stochastic optimisation of reservoir releases at each monthly time step according to the following procedure: (i) nine-month inflow forecast scenarios are generated using ENSO forecasts; (ii) a MOGA is set up to optimise the upcoming nine monthly releases; (iii) the optimisation is carried out by simulating the releases on the inflow forecasts, and by applying the base policy on a subsequent synthetic inflow scenario in order to account for long-term costs; (iv) the optimised release for the first month is implemented; (v) the state of the system is updated and (i), (ii), (iii), and (iv) are iterated for the following time step. The results highlight the advantages of using a climate-driven stochastic model to produce inflow scenarios and forecasts for reservoir optimisation, showing potential improvements with respect to the current management. Dynamic programming was used to find the best possible release time series given the inflow observations, in order to benchmark any possible operational improvement.

Inference of epidemiological parameters from household stratified data

PubMed Central

Walker, James N.; Ross, Joshua V.

2017-01-01

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters—governing within-household transmission, recovery, and between-household transmission—from data of the day upon which each individual became infectious and the household in which each infection occurred, as might be available from First Few Hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be a good approximation and remains computationally efficient as the amount of data is increased. PMID:29045456

Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain

NASA Astrophysics Data System (ADS)

Sund, Nicole L.; Porta, Giovanni M.; Bolster, Diogo

2017-05-01

The Spatial Markov Model (SMM) is an upscaled model that has been used successfully to predict effective mean transport across a broad range of hydrologic settings. Here we propose a novel variant of the SMM, applicable to spatially periodic systems. This SMM is built using particle trajectories, rather than travel times. By applying the proposed SMM to a simple benchmark problem we demonstrate that it can predict mean effective transport, when compared to data from fully resolved direct numerical simulations. Next we propose a methodology for using this SMM framework to predict measures of mixing and dilution, that do not just depend on mean concentrations, but are strongly impacted by pore-scale concentration fluctuations. We use information from trajectories of particles to downscale and reconstruct pore-scale approximate concentration fields from which mixing and dilution measures are then calculated. The comparison between measurements from fully resolved simulations and predictions with the SMM agree very favorably.

Continuous-time discrete-space models for animal movement

USGS Publications Warehouse

Hanks, Ephraim M.; Hooten, Mevin B.; Alldredge, Mat W.

2015-01-01

The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.

Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms

ERIC Educational Resources Information Center

Anderson, John R.

2012-01-01

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…

A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

ERIC Educational Resources Information Center

Edwards, Michael C.

2010-01-01

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model

ERIC Educational Resources Information Center

de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.

2006-01-01

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

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...

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.

Monte Carlo estimation of total variation distance of Markov chains on large spaces, with application to phylogenetics.

PubMed

Herbei, Radu; Kubatko, Laura

2013-03-26

Markov chains are widely used for modeling in many areas of molecular biology and genetics. As the complexity of such models advances, it becomes increasingly important to assess the rate at which a Markov chain converges to its stationary distribution in order to carry out accurate inference. A common measure of convergence to the stationary distribution is the total variation distance, but this measure can be difficult to compute when the state space of the chain is large. We propose a Monte Carlo method to estimate the total variation distance that can be applied in this situation, and we demonstrate how the method can be efficiently implemented by taking advantage of GPU computing techniques. We apply the method to two Markov chains on the space of phylogenetic trees, and discuss the implications of our findings for the development of algorithms for phylogenetic inference.

Analysis of a first order phase locked loop in the presence of Gaussian noise

NASA Technical Reports Server (NTRS)

Blasche, P. R.

1977-01-01

A first-order digital phase locked loop is analyzed by application of a Markov chain model. Steady state loop error probabilities, phase standard deviation, and mean loop transient times are determined for various input signal to noise ratios. Results for direct loop simulation are presented for comparison.

A systematic review of Markov models evaluating multicomponent disease management programs in diabetes.

PubMed

Kirsch, Florian

2015-01-01

Diabetes is the most expensive chronic disease; therefore, disease management programs (DMPs) were introduced. The aim of this review is to determine whether Markov models are adequate to evaluate the cost-effectiveness of complex interventions such as DMPs. Additionally, the quality of the models was evaluated using Philips and Caro quality appraisals. The five reviewed models incorporated the DMP into the model differently: two models integrated effectiveness rates derived from one clinical trial/meta-analysis and three models combined interventions from different sources into a DMP. The results range from cost savings and a QALY gain to costs of US$85,087 per QALY. The Spearman's rank coefficient assesses no correlation between the quality appraisals. With restrictions to the data selection process, Markov models are adequate to determine the cost-effectiveness of DMPs; however, to allow prioritization of medical services, more flexibility in the models is necessary to enable the evaluation of single additional interventions.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates

PubMed Central

Gill, Mandev S.; Lemey, Philippe; Bennett, Shannon N.; Biek, Roman; Suchard, Marc A.

2016-01-01

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman’s coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics. PMID:27368344

Semi-Markov Approach to the Shipping Safety Modelling

NASA Astrophysics Data System (ADS)

Guze, Sambor; Smolarek, Leszek

2012-02-01

In the paper the navigational safety model of a ship on the open area has been studied under conditions of incomplete information. Moreover the structure of semi-Markov processes is used to analyse the stochastic ship safety according to the subjective acceptance of risk by the navigator. In addition, the navigator’s behaviour can be analysed by using the numerical simulation to estimate the probability of collision in the safety model.

Three Dimensional Object Recognition Using a Complex Autoregressive Model

DTIC Science & Technology

1993-12-01

3.4.2 Template Matching Algorithm ...................... 3-16 3.4.3 K-Nearest-Neighbor ( KNN ) Techniques ................. 3-25 3.4.4 Hidden Markov Model...Neighbor ( KNN ) Test Results ...................... 4-13 4.2.1 Single-Look 1-NN Testing .......................... 4-14 4.2.2 Multiple-Look 1-NN Testing...4-15 4.2.3 Discussion of KNN Test Results ...................... 4-15 4.3 Hidden Markov Model (HMM) Test Results

An Application of the H-Function to Curve-Fitting and Density Estimation.

DTIC Science & Technology

1983-12-01

equations into a model that is linear in its coefficients. Nonlinear least squares estimation is a relatively new area developed to accomodate models which...to converge on a solution (10:9-10). For the simple linear model and when general assump- tions are made, the Gauss-Markov theorem states that the...distribution. For example, if the analyst wants to model the time between arrivals to a queue for a computer simulation, he infers the true probability

Multimodal brain-tumor segmentation based on Dirichlet process mixture model with anisotropic diffusion and Markov random field prior.

PubMed

Lu, Yisu; Jiang, Jun; Yang, Wei; Feng, Qianjin; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use.

Multimodal Brain-Tumor Segmentation Based on Dirichlet Process Mixture Model with Anisotropic Diffusion and Markov Random Field Prior

PubMed Central

Lu, Yisu; Jiang, Jun; Chen, Wufan

2014-01-01

Brain-tumor segmentation is an important clinical requirement for brain-tumor diagnosis and radiotherapy planning. It is well-known that the number of clusters is one of the most important parameters for automatic segmentation. However, it is difficult to define owing to the high diversity in appearance of tumor tissue among different patients and the ambiguous boundaries of lesions. In this study, a nonparametric mixture of Dirichlet process (MDP) model is applied to segment the tumor images, and the MDP segmentation can be performed without the initialization of the number of clusters. Because the classical MDP segmentation cannot be applied for real-time diagnosis, a new nonparametric segmentation algorithm combined with anisotropic diffusion and a Markov random field (MRF) smooth constraint is proposed in this study. Besides the segmentation of single modal brain-tumor images, we developed the algorithm to segment multimodal brain-tumor images by the magnetic resonance (MR) multimodal features and obtain the active tumor and edema in the same time. The proposed algorithm is evaluated using 32 multimodal MR glioma image sequences, and the segmentation results are compared with other approaches. The accuracy and computation time of our algorithm demonstrates very impressive performance and has a great potential for practical real-time clinical use. PMID:25254064

A Context-Recognition-Aided PDR Localization Method Based on the Hidden Markov Model

PubMed Central

Lu, Yi; Wei, Dongyan; Lai, Qifeng; Li, Wen; Yuan, Hong

2016-01-01

Indoor positioning has recently become an important field of interest because global navigation satellite systems (GNSS) are usually unavailable in indoor environments. Pedestrian dead reckoning (PDR) is a promising localization technique for indoor environments since it can be implemented on widely used smartphones equipped with low cost inertial sensors. However, the PDR localization severely suffers from the accumulation of positioning errors, and other external calibration sources should be used. In this paper, a context-recognition-aided PDR localization model is proposed to calibrate PDR. The context is detected by employing particular human actions or characteristic objects and it is matched to the context pre-stored offline in the database to get the pedestrian’s location. The Hidden Markov Model (HMM) and Recursive Viterbi Algorithm are used to do the matching, which reduces the time complexity and saves the storage. In addition, the authors design the turn detection algorithm and take the context of corner as an example to illustrate and verify the proposed model. The experimental results show that the proposed localization method can fix the pedestrian’s starting point quickly and improves the positioning accuracy of PDR by 40.56% at most with perfect stability and robustness at the same time. PMID:27916922

Mathematical modeling, analysis and Markov Chain Monte Carlo simulation of Ebola epidemics

NASA Astrophysics Data System (ADS)

Tulu, Thomas Wetere; Tian, Boping; Wu, Zunyou

Ebola virus infection is a severe infectious disease with the highest case fatality rate which become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed. The existence as well as uniqueness of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both Euler method and one of the top ten most influential algorithm known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least real data has been fitted to the model, showing that it can used to predict the dynamic of Ebola epidemic.

Quadratic adaptive algorithm for solving cardiac action potential models.

PubMed

Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

2016-10-01

An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights reserved.

Measuring Years of Inactivity, Years in Retirement, Time to Retirement, and Age at Retirement Within the Markov Model

PubMed Central

SKOOG, GARY R.; CIECKA, JAMES E.

2010-01-01

Retirement-related concepts are treated as random variables within Markov process models that capture multiple labor force entries and exits. The expected number of years spent outside of the labor force, expected years in retirement, and expected age at retirement are computed—all of which are of immense policy interest but have been heretofore reported with less precisely measured proxies. Expected age at retirement varies directly with a person’s age; but even younger people can expect to retire at ages substantially older than those commonly associated with retirement, such as age 60, 62, or 65. Between 1970 and 2003, men allocated most of their increase in life expectancy to increased time in retirement, but women allocated most of their increased life expectancy to labor force activity. Although people can exit and reenter the labor force at older ages, most 65-year-old men who are active in the labor force will not reenter after they eventually exit. At age 65, the probability that those who are inactive will reenter the labor force at some future time is .38 for men and .27 for women. Life expectancy at exact ages is decomposed into the sum of the expected time spent active and inactive in the labor force, and also as the sum of the expected time to labor force separation and time in retirement. PMID:20879680

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.

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

Esposito, L. W.; House, L. L.

1978-01-01

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Rainfall Stochastic models

NASA Astrophysics Data System (ADS)

Campo, M. A.; Lopez, J. J.; Rebole, J. P.

2012-04-01

This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series were recorded every ten minutes and hourly, aggregated. Preliminary results show adequate simulation of the main features of rain. Main variables are well simulated for time series of ten minutes, also over one hour precipitation time series, which are those that generate higher rainfall hydrologic design. For coarse scales, less than one hour, rainfall durations are not appropriate under the simulation. A hypothesis may be an excessive number of simulated events, which causes further fragmentation of storms, resulting in an excess of rain "short" (less than 1 hour), and therefore also among rain events, compared with the ones that occur in the actual series.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

An Evaluation of a Markov Chain Monte Carlo Method for the Two-Parameter Logistic Model.

ERIC Educational Resources Information Center

Kim, Seock-Ho; Cohen, Allan S.

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies

ERIC Educational Resources Information Center

Bartolucci, Francesco; Pennoni, Fulvia; Vittadini, Giorgio

2016-01-01

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is…

Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.

ERIC Educational Resources Information Center

Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun

2002-01-01

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

An NCME Instructional Module on Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods

ERIC Educational Resources Information Center

Kim, Jee-Seon; Bolt, Daniel M.

2007-01-01

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

Identification of linear system models and state estimators for controls

NASA Technical Reports Server (NTRS)

Chen, Chung-Wen

1992-01-01

The following paper is presented in viewgraph format and covers topics including: (1) linear state feedback control system; (2) Kalman filter state estimation; (3) relation between residual and stochastic part of output; (4) obtaining Kalman filter gain; (5) state estimation under unknown system model and unknown noises; and (6) relationship between filter Markov parameters and system Markov parameters.

Markov model plus k-word distributions: a synergy that produces novel statistical measures for sequence comparison.

PubMed

Dai, Qi; Yang, Yanchun; Wang, Tianming

2008-10-15

Many proposed statistical measures can efficiently compare biological sequences to further infer their structures, functions and evolutionary information. They are related in spirit because all the ideas for sequence comparison try to use the information on the k-word distributions, Markov model or both. Motivated by adding k-word distributions to Markov model directly, we investigated two novel statistical measures for sequence comparison, called wre.k.r and S2.k.r. The proposed measures were tested by similarity search, evaluation on functionally related regulatory sequences and phylogenetic analysis. This offers the systematic and quantitative experimental assessment of our measures. Moreover, we compared our achievements with these based on alignment or alignment-free. We grouped our experiments into two sets. The first one, performed via ROC (receiver operating curve) analysis, aims at assessing the intrinsic ability of our statistical measures to search for similar sequences from a database and discriminate functionally related regulatory sequences from unrelated sequences. The second one aims at assessing how well our statistical measure is used for phylogenetic analysis. The experimental assessment demonstrates that our similarity measures intending to incorporate k-word distributions into Markov model are more efficient.

Markov Task Network: A Framework for Service Composition under Uncertainty in Cyber-Physical Systems.

PubMed

Mohammed, Abdul-Wahid; Xu, Yang; Hu, Haixiao; Agyemang, Brighter

2016-09-21

In novel collaborative systems, cooperative entities collaborate services to achieve local and global objectives. With the growing pervasiveness of cyber-physical systems, however, such collaboration is hampered by differences in the operations of the cyber and physical objects, and the need for the dynamic formation of collaborative functionality given high-level system goals has become practical. In this paper, we propose a cross-layer automation and management model for cyber-physical systems. This models the dynamic formation of collaborative services pursuing laid-down system goals as an ontology-oriented hierarchical task network. Ontological intelligence provides the semantic technology of this model, and through semantic reasoning, primitive tasks can be dynamically composed from high-level system goals. In dealing with uncertainty, we further propose a novel bridge between hierarchical task networks and Markov logic networks, called the Markov task network. This leverages the efficient inference algorithms of Markov logic networks to reduce both computational and inferential loads in task decomposition. From the results of our experiments, high-precision service composition under uncertainty can be achieved using this approach.

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.

Urban change analysis and future growth of Istanbul.

PubMed

Akın, Anıl; Sunar, Filiz; Berberoğlu, Süha

2015-08-01

This study is aimed at analyzing urban change within Istanbul and assessing the city's future growth potential using appropriate approach modeling for the year 2040. Urban growth is a major driving force of land-use change, and spatial and temporal components of urbanization can be identified through accurate spatial modeling. In this context, widely used urban modeling approaches, such as the Markov chain and logistic regression based on cellular automata (CA), were used to simulate urban growth within Istanbul. The distance from each pixel to the urban and road classes, elevation, and slope, together with municipality and land use maps (as an excluded layer), were identified as factors. Calibration data were obtained from remotely sensed data recorded in 1972, 1986, and 2013. Validation was performed by overlaying the simulated and actual 2013 urban maps, and a kappa index of agreement was derived. The results indicate that urban expansion will influence mainly forest areas during the time period of 2013-2040. The urban expansion was predicted as 429 and 327 km(2) with the Markov chain and logistic regression models, respectively.

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.

Discrete Event Simulation for Decision Modeling in Health Care: Lessons from Abdominal Aortic Aneurysm Screening

PubMed Central

Jones, Edmund; Masconi, Katya L.; Sweeting, Michael J.; Thompson, Simon G.; Powell, Janet T.

2018-01-01

Markov models are often used to evaluate the cost-effectiveness of new healthcare interventions but they are sometimes not flexible enough to allow accurate modeling or investigation of alternative scenarios and policies. A Markov model previously demonstrated that a one-off invitation to screening for abdominal aortic aneurysm (AAA) for men aged 65 y in the UK and subsequent follow-up of identified AAAs was likely to be highly cost-effective at thresholds commonly adopted in the UK (£20,000 to £30,000 per quality adjusted life-year). However, new evidence has emerged and the decision problem has evolved to include exploration of the circumstances under which AAA screening may be cost-effective, which the Markov model is not easily able to address. A new model to handle this more complex decision problem was needed, and the case of AAA screening thus provides an illustration of the relative merits of Markov models and discrete event simulation (DES) models. An individual-level DES model was built using the R programming language to reflect possible events and pathways of individuals invited to screening v. those not invited. The model was validated against key events and cost-effectiveness, as observed in a large, randomized trial. Different screening protocol scenarios were investigated to demonstrate the flexibility of the DES. The case of AAA screening highlights the benefits of DES, particularly in the context of screening studies.

STDP Installs in Winner-Take-All Circuits an Online Approximation to Hidden Markov Model Learning

PubMed Central

Kappel, David; Nessler, Bernhard; Maass, Wolfgang

2014-01-01

In order to cross a street without being run over, we need to be able to extract very fast hidden causes of dynamically changing multi-modal sensory stimuli, and to predict their future evolution. We show here that a generic cortical microcircuit motif, pyramidal cells with lateral excitation and inhibition, provides the basis for this difficult but all-important information processing capability. This capability emerges in the presence of noise automatically through effects of STDP on connections between pyramidal cells in Winner-Take-All circuits with lateral excitation. In fact, one can show that these motifs endow cortical microcircuits with functional properties of a hidden Markov model, a generic model for solving such tasks through probabilistic inference. Whereas in engineering applications this model is adapted to specific tasks through offline learning, we show here that a major portion of the functionality of hidden Markov models arises already from online applications of STDP, without any supervision or rewards. We demonstrate the emergent computing capabilities of the model through several computer simulations. The full power of hidden Markov model learning can be attained through reward-gated STDP. This is due to the fact that these mechanisms enable a rejection sampling approximation to theoretically optimal learning. We investigate the possible performance gain that can be achieved with this more accurate learning method for an artificial grammar task. PMID:24675787

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.

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.

Reconciling a geophysical model to data using a Markov chain Monte Carlo algorithm: An application to the Yellow Sea-Korean Peninsula region

NASA Astrophysics Data System (ADS)

Pasyanos, Michael E.; Franz, Gregory A.; Ramirez, Abelardo L.

2006-03-01

In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude-longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data-rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.

Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.

PubMed

Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka

2014-02-01

In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain.

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.