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…
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.
Predictive Rate-Distortion for Infinite-Order Markov Processes
NASA Astrophysics Data System (ADS)
Marzen, Sarah E.; Crutchfield, James P.
2016-05-01
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.
State space orderings for Gauss-Seidel in Markov chains revisited
Dayar, T.
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
Kinetics and thermodynamics of first-order Markov chain copolymerization
NASA Astrophysics Data System (ADS)
Gaspard, P.; Andrieux, D.
2014-07-01
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
Kinetics and thermodynamics of first-order Markov chain copolymerization.
Gaspard, P; Andrieux, D
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer. PMID:25084957
Kinetics and thermodynamics of first-order Markov chain copolymerization
Gaspard, P.; Andrieux, D.
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
First and second order semi-Markov chains for wind speed modeling
NASA Astrophysics Data System (ADS)
Prattico, F.; Petroni, F.; D'Amico, G.
2012-04-01
Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling
Multiple pattern matching: a Markov chain approach.
Lladser, Manuel E; Betterton, M D; Knight, Rob
2008-01-01
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text. PMID:17668213
Post processing with first- and second-order hidden Markov models
NASA Astrophysics Data System (ADS)
Taghva, Kazem; Poudel, Srijana; Malreddy, Spandana
2013-01-01
In this paper, we present the implementation and evaluation of first order and second order Hidden Markov Models to identify and correct OCR errors in the post processing of books. Our experiments show that the first order model approximately corrects 10% of the errors with 100% precision, while the second order model corrects a higher percentage of errors with much lower precision.
Lee, Lee-Min; Jean, Fu-Rong
2016-08-01
The hidden Markov models have been widely applied to systems with sequential data. However, the conditional independence of the state outputs will limit the output of a hidden Markov model to be a piecewise constant random sequence, which is not a good approximation for many real processes. In this paper, a high-order hidden Markov model for piecewise linear processes is proposed to better approximate the behavior of a real process. A parameter estimation method based on the expectation-maximization algorithm was derived for the proposed model. Experiments on speech recognition of noisy Mandarin digits were conducted to examine the effectiveness of the proposed method. Experimental results show that the proposed method can reduce the recognition error rate compared to a baseline hidden Markov model. PMID:27586781
Fitting optimum order of Markov chain models for daily rainfall occurrences in Peninsular Malaysia
NASA Astrophysics Data System (ADS)
Deni, Sayang Mohd; Jemain, Abdul Aziz; Ibrahim, Kamarulzaman
2009-06-01
The analysis of the daily rainfall occurrence behavior is becoming more important, particularly in water-related sectors. Many studies have identified a more comprehensive pattern of the daily rainfall behavior based on the Markov chain models. One of the aims in fitting the Markov chain models of various orders to the daily rainfall occurrence is to determine the optimum order. In this study, the optimum order of the Markov chain models for a 5-day sequence will be examined in each of the 18 rainfall stations in Peninsular Malaysia, which have been selected based on the availability of the data, using the Akaike’s (AIC) and Bayesian information criteria (BIC). The identification of the most appropriate order in describing the distribution of the wet (dry) spells for each of the rainfall stations is obtained using the Kolmogorov-Smirnov goodness-of-fit test. It is found that the optimum order varies according to the levels of threshold used (e.g., either 0.1 or 10.0 mm), the locations of the region and the types of monsoon seasons. At most stations, the Markov chain models of a higher order are found to be optimum for rainfall occurrence during the northeast monsoon season for both levels of threshold. However, it is generally found that regardless of the monsoon seasons, the first-order model is optimum for the northwestern and eastern regions of the peninsula when the level of thresholds of 10.0 mm is considered. The analysis indicates that the first order of the Markov chain model is found to be most appropriate for describing the distribution of wet spells, whereas the higher-order models are found to be adequate for the dry spells in most of the rainfall stations for both threshold levels and monsoon seasons.
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Using higher-order Markov models to reveal flow-based communities in networks
NASA Astrophysics Data System (ADS)
Salnikov, Vsevolod; Schaub, Michael T.; Lambiotte, Renaud
2016-03-01
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions. Despite the success of this modelling perspective for numerous applications, it represents an over-simplification of several real-world systems. Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice. Here, we explore possibilities to enrich the system description by means of second-order Markov models, exploiting empirical pathway information. We focus on the problem of community detection and show that standard network algorithms can be generalized in order to extract novel temporal information about the system under investigation. We also apply our methodology to temporal networks, where we can uncover communities shaped by the temporal correlations in the system. Finally, we discuss relations of the framework of second order Markov processes and the recently proposed formalism of using non-backtracking matrices for community detection.
Using higher-order Markov models to reveal flow-based communities in networks
Salnikov, Vsevolod; Schaub, Michael T.; Lambiotte, Renaud
2016-01-01
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions. Despite the success of this modelling perspective for numerous applications, it represents an over-simplification of several real-world systems. Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice. Here, we explore possibilities to enrich the system description by means of second-order Markov models, exploiting empirical pathway information. We focus on the problem of community detection and show that standard network algorithms can be generalized in order to extract novel temporal information about the system under investigation. We also apply our methodology to temporal networks, where we can uncover communities shaped by the temporal correlations in the system. Finally, we discuss relations of the framework of second order Markov processes and the recently proposed formalism of using non-backtracking matrices for community detection. PMID:27029508
Using higher-order Markov models to reveal flow-based communities in networks.
Salnikov, Vsevolod; Schaub, Michael T; Lambiotte, Renaud
2016-01-01
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions. Despite the success of this modelling perspective for numerous applications, it represents an over-simplification of several real-world systems. Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice. Here, we explore possibilities to enrich the system description by means of second-order Markov models, exploiting empirical pathway information. We focus on the problem of community detection and show that standard network algorithms can be generalized in order to extract novel temporal information about the system under investigation. We also apply our methodology to temporal networks, where we can uncover communities shaped by the temporal correlations in the system. Finally, we discuss relations of the framework of second order Markov processes and the recently proposed formalism of using non-backtracking matrices for community detection. PMID:27029508
The optimum order of a Markov chain model for daily rainfall in Nigeria
NASA Astrophysics Data System (ADS)
Jimoh, O. D.; Webster, P.
1996-11-01
Markov type models are often used to describe the occurrence of daily rainfall. Although models of Order 1 have been successfully employed, there remains uncertainty concerning the optimum order for such models. This paper is concerned with estimation of the optimum order of Markov chains and, in particular, the use of objective criteria of the Akaike and Bayesian Information Criteria (AIC and BIC, respectively). Using daily rainfall series for five stations in Nigeria, it has been found that the AIC and BIC estimates vary with month as well as the value of the rainfall threshold used to define a wet day. There is no apparent system to this variation, although AIC estimates are consistently greater than or equal to BIC estimates, with values of the latter limited to zero or unity. The optimum order is also investigated through generation of synthetic sequences of wet and dry days using the transition matrices of zero-, first- and second-order Markov chains. It was found that the first-order model is superior to the zero-order model in representing the characteristics of the historical sequence as judged using frequency duration curves. There was no discernible difference between the model performance for first- and second-order models. There was no seasonal varation in the model performance, which contrasts with the optimum models identified using AIC and BIC estimates. It is concluded that caution is needed with the use of objective criteria for determining the optimum order of the Markov model and that the use of frequency duration curves can provide a robust alternative method of model identification. Comments are also made on the importance of record length and non-stationarity for model identification
A new approach to simulating stream isotope dynamics using Markov switching autoregressive models
NASA Astrophysics Data System (ADS)
Birkel, Christian; Paroli, Roberta; Spezia, Luigi; Dunn, Sarah M.; Tetzlaff, Doerthe; Soulsby, Chris
2012-09-01
In this study we applied Markov switching autoregressive models (MSARMs) as a proof-of-concept to analyze the temporal dynamics and statistical characteristics of the time series of two conservative water isotopes, deuterium (δ2H) and oxygen-18 (δ18O), in daily stream water samples over two years in a small catchment in eastern Scotland. MSARMs enabled us to explicitly account for the identified non-linear, non-Normal and non-stationary isotope dynamics of both time series. The hidden states of the Markov chain could also be associated with meteorological and hydrological drivers identifying the short (event) and longer-term (inter-event) transport mechanisms for both isotopes. Inference was based on the Bayesian approach performed through Markov Chain Monte Carlo algorithms, which also allowed us to deal with a high rate of missing values (17%). Although it is usually assumed that both isotopes are conservative and exhibit similar dynamics, δ18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but δ18O demanded autoregressions of the first order, whereas δ2H of the second. Moreover, both the dynamics of observations and the hidden states of the two isotopes were explained by two different sets of covariates. Consequently use of the two tracers for transit time modelling and hydrograph separation may result in different interpretations on the functioning of a catchment system.
Meeting the NICE requirements: a Markov model approach.
Mauskopf, J
2000-01-01
The National Institute of Clinical Excellence (NICE) was established in the United Kingdom in April 1999 to issue guidance for the National Health Service (NHS) on the use of selective new health care interventions. This article describes the NICE requirements for both incidence-based cost-effectiveness analyses and prevalence-based estimates of the aggregate NHS impact of the new drug. The article demonstrates how both of these requirements can be met using Markov modeling techniques. A Markov model for a hypothetical new treatment for HIV infection is used as an illustration of how to generate the estimates that are required by NICE. The article concludes with a discussion of the difficulties of obtaining data of sufficient quality to include in the Markov model to ensure that the submission meets all the NICE requirements and is credible to the NICE advisory board. PMID:16464193
NASA Astrophysics Data System (ADS)
Vaglica, Gabriella; Lillo, Fabrizio; Mantegna, Rosario N.
2010-07-01
Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders, we fit hidden Markov models to the time series of the sign of the tick-by-tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a significant majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transaction size distributions of these patches are fat tailed. Long patches are characterized by a large fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly dependent on the local market trend. We also compare the hidden Markov model patches with those obtained with the segmentation method used in Vaglica et al (2008 Phys. Rev. E 77 036110), and we conclude that the former ones can be interpreted as a partition of the latter ones.
A graph theoretic approach to global earthquake sequencing: A Markov chain model
NASA Astrophysics Data System (ADS)
Vasudevan, K.; Cavers, M. S.
2012-12-01
We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. For earthquake zonation, we consider the simplified plate boundary template of Kagan, Bird, and Jackson (KBJ template, 2010). We demonstrate the applicability of the directed graph approach to hazard-related forecasting using some of the properties of graphs that represent the finite Markov chain. We extend the present study to consider Bird's 52-plate zonation (2003) describing the global earthquakes at and within plate boundaries to gain further insight into the usefulness of digraphs corresponding to a Markov chain model.
A clustering approach for estimating parameters of a profile hidden Markov model.
Aghdam, Rosa; Pezeshk, Hamid; Malekpour, Seyed Amir; Shemehsavar, Soudabeh; Eslahchi, Changiz
2013-01-01
A Profile Hidden Markov Model (PHMM) is a standard form of a Hidden Markov Models used for modeling protein and DNA sequence families based on multiple alignment. In this paper, we implement Baum-Welch algorithm and the Bayesian Monte Carlo Markov Chain (BMCMC) method for estimating parameters of small artificial PHMM. In order to improve the prediction accuracy of the estimation of the parameters of the PHMM, we classify the training data using the weighted values of sequences in the PHMM then apply an algorithm for estimating parameters of the PHMM. The results show that the BMCMC method performs better than the Maximum Likelihood estimation. PMID:23865165
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.
A Hidden Markov Approach to Modeling Interevent Earthquake Times
NASA Astrophysics Data System (ADS)
Chambers, D.; Ebel, J. E.; Kafka, A. L.; Baglivo, J.
2003-12-01
A hidden Markov process, in which the interevent time distribution is a mixture of exponential distributions with different rates, is explored as a model for seismicity that does not follow a Poisson process. In a general hidden Markov model, one assumes that a system can be in any of a finite number k of states and there is a random variable of interest whose distribution depends on the state in which the system resides. The system moves probabilistically among the states according to a Markov chain; that is, given the history of visited states up to the present, the conditional probability that the next state is a specified one depends only on the present state. Thus the transition probabilities are specified by a k by k stochastic matrix. Furthermore, it is assumed that the actual states are unobserved (hidden) and that only the values of the random variable are seen. From these values, one wishes to estimate the sequence of states, the transition probability matrix, and any parameters used in the state-specific distributions. The hidden Markov process was applied to a data set of 110 interevent times for earthquakes in New England from 1975 to 2000. Using the Baum-Welch method (Baum et al., Ann. Math. Statist. 41, 164-171), we estimate the transition probabilities, find the most likely sequence of states, and estimate the k means of the exponential distributions. Using k=2 states, we found the data were fit well by a mixture of two exponential distributions, with means of approximately 5 days and 95 days. The steady state model indicates that after approximately one fourth of the earthquakes, the waiting time until the next event had the first exponential distribution and three fourths of the time it had the second. Three and four state models were also fit to the data; the data were inconsistent with a three state model but were well fit by a four state model.
NASA Astrophysics Data System (ADS)
Schreiber, Tomasz
2010-08-01
We consider polygonal Markov fields originally introduced by Arak in 4th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Abstracts of Communications, 1982; Arak and Surgailis in Probab. Theory Relat. Fields 80:543-579, 1989. Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of salient features with the two-dimensional Ising model. The purpose of this paper is to establish an explicit stochastic representation for the higher-order correlation functions of polygonal Markov fields in their consistency regime. The representation is given in terms of the so-called crop functionals (defined by a Möbius-type formula) of polygonal webs which arise in a graphical construction dual to that giving rise to polygonal fields. The proof of our representation formula goes by constructing a martingale interpolation between the correlation functions of polygonal fields and crop functionals of polygonal webs.
Bartolucci, Francesco; Farcomeni, Alessio
2015-03-01
Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-fixed and time-varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation-maximization algorithm, we extend the usual forward-backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non-informative drop-out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary. PMID:25227970
Partially ordered mixed hidden Markov model for the disablement process of older adults
Ip, Edward H.; Zhang, Qiang; Rejeski, W. Jack; Harris, Tamara B.; Kritchevsky, Stephen
2013-01-01
At both the individual and societal levels, the health and economic burden of disability in older adults is enormous in developed countries, including the U.S. Recent studies have revealed that the disablement process in older adults often comprises episodic periods of impaired functioning and periods that are relatively free of disability, amid a secular and natural trend of decline in functioning. Rather than an irreversible, progressive event that is analogous to a chronic disease, disability is better conceptualized and mathematically modeled as states that do not necessarily follow a strict linear order of good-to-bad. Statistical tools, including Markov models, which allow bidirectional transition between states, and random effects models, which allow individual-specific rate of secular decline, are pertinent. In this paper, we propose a mixed effects, multivariate, hidden Markov model to handle partially ordered disability states. The model generalizes the continuation ratio model for ordinal data in the generalized linear model literature and provides a formal framework for testing the effects of risk factors and/or an intervention on the transitions between different disability states. Under a generalization of the proportional odds ratio assumption, the proposed model circumvents the problem of a potentially large number of parameters when the number of states and the number of covariates are substantial. We describe a maximum likelihood method for estimating the partially ordered, mixed effects model and show how the model can be applied to a longitudinal data set that consists of N = 2,903 older adults followed for 10 years in the Health Aging and Body Composition Study. We further statistically test the effects of various risk factors upon the probabilities of transition into various severe disability states. The result can be used to inform geriatric and public health science researchers who study the disablement process. PMID:24058222
A Markov random field approach for microstructure synthesis
NASA Astrophysics Data System (ADS)
Kumar, A.; Nguyen, L.; DeGraef, M.; Sundararaghavan, V.
2016-03-01
We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure are generally ‘statistically similar’. To enable computation of such a probability distribution, microstructures are represented in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, algorithms are developed to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. 2D microstructures are artificially synthesized using the sampled probabilities. Statistical features such as grain size distribution and autocorrelation functions closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using the finite element method and were also found to match the experimental values.
A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields.
Fix, Alexander; Gruber, Aritanan; Boros, Endre; Zabih, Ramin
2015-07-01
Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1], [2], both theoretically and experimentally. While [1], [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n non-submodular terms, while [1], [2] produces O(nk). We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. We show experimentally that our method produces smaller weight of non-submodular edges, and that this metric is directly related to the effectiveness of QPBO [3]. Running on the same field of experts dataset used in [1], [2] we optimally label significantly more variables (96 versus 80 percent) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higher-order MRF's used in stereo [4] and segmentation [5] are also locally complete and would thus benefit from our work. PMID:26352447
Markov-chain approach to the distribution of ancestors in species of biparental reproduction
NASA Astrophysics Data System (ADS)
Caruso, M.; Jarne, C.
2014-08-01
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This presents huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values with respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under a gauge (local) group of dilations. These ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provides some elements that can be used to improve models of animal reproduction.
A Markov Chain Approach to Probabilistic Swarm Guidance
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Bayard, David S.
2012-01-01
This paper introduces a probabilistic guidance approach for the coordination of swarms of autonomous agents. The main idea is to drive the swarm to a prescribed density distribution in a prescribed region of the configuration space. In its simplest form, the probabilistic approach is completely decentralized and does not require communication or collabo- ration between agents. Agents make statistically independent probabilistic decisions based solely on their own state, that ultimately guides the swarm to the desired density distribution in the configuration space. In addition to being completely decentralized, the probabilistic guidance approach has a novel autonomous self-repair property: Once the desired swarm density distribution is attained, the agents automatically repair any damage to the distribution without collaborating and without any knowledge about the damage.
A Comparison of Proliferation Resistance Measures of Misuse Scenarios Using a Markov Approach
Yue,M.; Cheng, L.-Y.; Bari, R.
2008-05-11
Misuse of declared nuclear facilities is one of the important proliferation threats. The robustness of a facility against these threats is characterized by a number of proliferation resistance (PR) measures. This paper evaluates and compares PR measures for several misuse scenarios using a Markov model approach to implement the pathway analysis methodology being developed by the PR&PP (Proliferation Resistance and Physical Protection) Expert Group. Different misue strategies can be adopted by a proliferator and each strategy is expected to have different impacts on the proliferator's success. Selected as the probabilistic measure to represent proliferation resistance, the probabilities of the proliferator's success of misusing a hypothetical ESFR (Example Sodium Fast Reactor) facility system are calculated using the Markov model based on the pathways constructed for individual misuse scenarios. Insights from a comparison of strategies that are likely to be adopted by the proliferator are discussed in this paper.
Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks
NASA Astrophysics Data System (ADS)
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011), 10.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011), 10.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
NASA Astrophysics Data System (ADS)
Espinoza-Molina, Daniela; Datcu, Mihai
2010-10-01
TerraSAR-X is the Synthetic Aperture Radar (SAR) German satellite which provides a high diversity of information due to its high-resolution. TerraSAR-X acquires daily a volume of up to 100 GB of high complexity, multi-mode SAR images, i.e. SpotLight, StripMap, and ScanSAR data, with dual or quad-polarization, and with different look angles. The high and multiple resolutions of the instrument (1m, 3m or 10m) open perspectives for new applications, that were not possible with past lower resolution sensors (20-30m). Mainly the 1m and 3m modes we expect to support a broad range of new applications related to human activities with relevant structures and objects at the 1m scale. Thus, among the most interesting scenes are: urban, industrial, and rural data. In addition, the global coverage and the relatively frequent repeat pass will definitely help to acquire extremely relevant data sets. To analyze the available TerrrSAR-X data we rely on model based methods for feature extraction and despeckling. The image information content is extracted using model-based methods based on Gauss Markov Random Field (GMRF) and Bayesian inference approach. This approach enhances the local adaptation by using a prior model, which learns the image structure and enables to estimate the local description of the structures, acting as primitive feature extraction method. However, the GMRF model-based method uses as input parameters the Model Order (MO) and the size of Estimation Window (EW). The appropriated selection of these parameters allows us to improve the classification and indexing results due to the number of well separated classes could be determined by them. Our belief is that the selection of the MO depends on the kind of information that the image contains, explaining how well the model can recognize complex structures as objects, and according to the size of EW the accuracy of the estimation is determined. In the following, we present an evaluation of the impact of the model
Wang, Ying; Hu, Haiyan; Li, Xiaoman
2016-08-01
Metagenomics is a next-generation omics field currently impacting postgenomic life sciences and medicine. Binning metagenomic reads is essential for the understanding of microbial function, compositions, and interactions in given environments. Despite the existence of dozens of computational methods for metagenomic read binning, it is still very challenging to bin reads. This is especially true for reads from unknown species, from species with similar abundance, and/or from low-abundance species in environmental samples. In this study, we developed a novel taxonomy-dependent and alignment-free approach called MBMC (Metagenomic Binning by Markov Chains). Different from all existing methods, MBMC bins reads by measuring the similarity of reads to the trained Markov chains for different taxa instead of directly comparing reads with known genomic sequences. By testing on more than 24 simulated and experimental datasets with species of similar abundance, species of low abundance, and/or unknown species, we report here that MBMC reliably grouped reads from different species into separate bins. Compared with four existing approaches, we demonstrated that the performance of MBMC was comparable with existing approaches when binning reads from sequenced species, and superior to existing approaches when binning reads from unknown species. MBMC is a pivotal tool for binning metagenomic reads in the current era of Big Data and postgenomic integrative biology. The MBMC software can be freely downloaded at http://hulab.ucf.edu/research/projects/metagenomics/MBMC.html . PMID:27447888
The Scalarization Approach to Multiobjective Markov Control Problems: Why Does It Work?
Hernandez-Lerma, Onesimo Romera, Rosario
2004-10-15
This paper concerns discrete-time multiobjective Markov control processes on Borel spaces and unbounded costs. Under mild assumptions, it is shown that the usual 'scalarization approach' to obtain Pareto policies for the multiobjective control problem is in fact equivalent to solving the dual of a certain multiobjective infinite-dimensional linear program. The latter program is obtained from a multiobjective measure problem which is also used to prove the existence of strong Pareto policies, that is, Paretopolicies whose cost vector is the closest to the control problem's virtual minimum.
Switched Fault Diagnosis Approach for Industrial Processes based on Hidden Markov Model
NASA Astrophysics Data System (ADS)
Wang, Lin; Yang, Chunjie; Sun, Youxian; Pan, Yijun; An, Ruqiao
2015-11-01
Traditional fault diagnosis methods based on hidden Markov model (HMM) use a unified method for feature extraction, such as principal component analysis (PCA), kernel principal component analysis (KPCA) and independent component analysis (ICA). However, every method has its own limitations. For example, PCA cannot extract nonlinear relationships among process variables. So it is inappropriate to extract all features of variables by only one method, especially when data characteristics are very complex. This article proposes a switched feature extraction procedure using PCA and KPCA based on nonlinearity measure. By the proposed method, we are able to choose the most suitable feature extraction method, which could improve the accuracy of fault diagnosis. A simulation from the Tennessee Eastman (TE) process demonstrates that the proposed approach is superior to the traditional one based on HMM and could achieve more accurate classification of various process faults.
A computationally efficient approach for hidden-Markov model-augmented fingerprint-based positioning
NASA Astrophysics Data System (ADS)
Roth, John; Tummala, Murali; McEachen, John
2016-09-01
This paper presents a computationally efficient approach for mobile subscriber position estimation in wireless networks. A method of data scaling assisted by timing adjust is introduced in fingerprint-based location estimation under a framework which allows for minimising computational cost. The proposed method maintains a comparable level of accuracy to the traditional case where no data scaling is used and is evaluated in a simulated environment under varying channel conditions. The proposed scheme is studied when it is augmented by a hidden-Markov model to match the internal parameters to the channel conditions that present, thus minimising computational cost while maximising accuracy. Furthermore, the timing adjust quantity, available in modern wireless signalling messages, is shown to be able to further reduce computational cost and increase accuracy when available. The results may be seen as a significant step towards integrating advanced position-based modelling with power-sensitive mobile devices.
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…
A Markov Random Field Model-Based Approach To Image Interpretation
NASA Astrophysics Data System (ADS)
Zhang, Jun; Modestino, James W.
1989-11-01
In this paper, a Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph and the image interpretation problem is formulated as a maximum a posteriori (MAP) estimation rule. Simulated annealing is used to find the best realization, or optimal MAP interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the pdf of the underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described and appear promising.
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. PMID:26584064
An information theoretic approach for generating an aircraft avoidance Markov Decision Process
NASA Astrophysics Data System (ADS)
Weinert, Andrew J.
Developing a collision avoidance system that can meet safety standards required of commercial aviation is challenging. A dynamic programming approach to collision avoidance has been developed to optimize and generate logics that are robust to the complex dynamics of the national airspace. The current approach represents the aircraft avoidance problem as Markov Decision Processes and independently optimizes a horizontal and vertical maneuver avoidance logics. This is a result of the current memory requirements for each logic, simply combining the logics will result in a significantly larger representation. The "curse of dimensionality" makes it computationally inefficient and unfeasible to optimize this larger representation. However, existing and future collision avoidance systems have mostly defined the decision process by hand. In response, a simulation-based framework was built to better understand how each potential state quantifies the aircraft avoidance problem with regards to safety and operational components. The framework leverages recent advances in signals processing and database, while enabling the highest fidelity analysis of Monte Carlo aircraft encounter simulations to date. This framework enabled the calculation of how well each state of the decision process quantifies the collision risk and the associated memory requirements. Using this analysis, a collision avoidance logic that leverages both horizontal and vertical actions was built and optimized using this simulation based approach.
Song, Changyue; Liu, Kaibo; Zhang, Xi; Chen, Lili; Xian, Xiaochen
2016-07-01
Obstructive sleep apnea (OSA) syndrome is a common sleep disorder suffered by an increasing number of people worldwide. As an alternative to polysomnography (PSG) for OSA diagnosis, the automatic OSA detection methods used in the current practice mainly concentrate on feature extraction and classifier selection based on collected physiological signals. However, one common limitation in these methods is that the temporal dependence of signals are usually ignored, which may result in critical information loss for OSA diagnosis. In this study, we propose a novel OSA detection approach based on ECG signals by considering temporal dependence within segmented signals. A discriminative hidden Markov model (HMM) and corresponding parameter estimation algorithms are provided. In addition, subject-specific transition probabilities within the model are employed to characterize the subject-to-subject differences of potential OSA patients. To validate our approach, 70 recordings obtained from the Physionet Apnea-ECG database were used. Accuracies of 97.1% for per-recording classification and 86.2% for per-segment OSA detection with satisfactory sensitivity and specificity were achieved. Compared with other existing methods that simply ignore the temporal dependence of signals, the proposed HMM-based detection approach delivers more satisfactory detection performance and could be extended to other disease diagnosis applications. PMID:26560867
Gold price effect on stock market: A Markov switching vector error correction approach
NASA Astrophysics Data System (ADS)
Wai, Phoong Seuk; Ismail, Mohd Tahir; Kun, Sek Siok
2014-06-01
Gold is a popular precious metal where the demand is driven not only for practical use but also as a popular investments commodity. While stock market represents a country growth, thus gold price effect on stock market behavior as interest in the study. Markov Switching Vector Error Correction Models are applied to analysis the relationship between gold price and stock market changes since real financial data always exhibit regime switching, jumps or missing data through time. Besides, there are numerous specifications of Markov Switching Vector Error Correction Models and this paper will compare the intercept adjusted Markov Switching Vector Error Correction Model and intercept adjusted heteroskedasticity Markov Switching Vector Error Correction Model to determine the best model representation in capturing the transition of the time series. Results have shown that gold price has a positive relationship with Malaysia, Thailand and Indonesia stock market and a two regime intercept adjusted heteroskedasticity Markov Switching Vector Error Correction Model is able to provide the more significance and reliable result compare to intercept adjusted Markov Switching Vector Error Correction Models.
Buendia, Patricia; Cadwallader, Brice; DeGruttola, Victor
2009-01-01
Motivation: Modern HIV-1, hepatitis B virus and hepatitis C virus antiviral therapies have been successful at keeping viruses suppressed for prolonged periods of time, but therapy failures attributable to the emergence of drug resistant mutations continue to be a distressing reminder that no therapy can fully eradicate these viruses from their host organisms. To better understand the emergence of drug resistance, we combined phylogenetic and statistical models of viral evolution in a 2-phase computational approach that reconstructs mutational pathways of drug resistance. Results: The first phase of the algorithm involved the modeling of the evolution of the virus within the human host environment. The inclusion of longitudinal clonal sequence data was a key aspect of the model due to the progressive fashion in which multiple mutations become linked in the same genome creating drug resistant genotypes. The second phase involved the development of a Markov model to calculate the transition probabilities between the different genotypes. The proposed method was applied to data from an HIV-1 Efavirenz clinical trial study. The obtained model revealed the direction of evolution over time with greater detail than previous models. Our results show that the mutational pathways facilitate the identification of fast versus slow evolutionary pathways to drug resistance. Availability: Source code for the algorithm is publicly available at http://biorg.cis.fiu.edu/vPhyloMM/ Contact: pbuendia@miami.edu PMID:19654117
NASA Astrophysics Data System (ADS)
Kim, M.; Ghate, A.; Phillips, M. H.
2009-07-01
The current state of the art in cancer treatment by radiation optimizes beam intensity spatially such that tumors receive high dose radiation whereas damage to nearby healthy tissues is minimized. It is common practice to deliver the radiation over several weeks, where the daily dose is a small constant fraction of the total planned. Such a 'fractionation schedule' is based on traditional models of radiobiological response where normal tissue cells possess the ability to repair sublethal damage done by radiation. This capability is significantly less prominent in tumors. Recent advances in quantitative functional imaging and biological markers are providing new opportunities to measure patient response to radiation over the treatment course. This opens the door for designing fractionation schedules that take into account the patient's cumulative response to radiation up to a particular treatment day in determining the fraction on that day. We propose a novel approach that, for the first time, mathematically explores the benefits of such fractionation schemes. This is achieved by building a stylistic Markov decision process (MDP) model, which incorporates some key features of the problem through intuitive choices of state and action spaces, as well as transition probability and reward functions. The structure of optimal policies for this MDP model is explored through several simple numerical examples.
A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.
Apenteng, Ofosuhene O; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection
Apenteng, Ofosuhene O.; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
Seifert, Michael; Abou-El-Ardat, Khalil; Friedrich, Betty; Klink, Barbara; Deutsch, Andreas
2014-01-01
Changes in gene expression programs play a central role in cancer. Chromosomal aberrations such as deletions, duplications and translocations of DNA segments can lead to highly significant positive correlations of gene expression levels of neighboring genes. This should be utilized to improve the analysis of tumor expression profiles. Here, we develop a novel model class of autoregressive higher-order Hidden Markov Models (HMMs) that carefully exploit local data-dependent chromosomal dependencies to improve the identification of differentially expressed genes in tumor. Autoregressive higher-order HMMs overcome generally existing limitations of standard first-order HMMs in the modeling of dependencies between genes in close chromosomal proximity by the simultaneous usage of higher-order state-transitions and autoregressive emissions as novel model features. We apply autoregressive higher-order HMMs to the analysis of breast cancer and glioma gene expression data and perform in-depth model evaluation studies. We find that autoregressive higher-order HMMs clearly improve the identification of overexpressed genes with underlying gene copy number duplications in breast cancer in comparison to mixture models, standard first- and higher-order HMMs, and other related methods. The performance benefit is attributed to the simultaneous usage of higher-order state-transitions in combination with autoregressive emissions. This benefit could not be reached by using each of these two features independently. We also find that autoregressive higher-order HMMs are better able to identify differentially expressed genes in tumors independent of the underlying gene copy number status in comparison to the majority of related methods. This is further supported by the identification of well-known and of previously unreported hotspots of differential expression in glioblastomas demonstrating the efficacy of autoregressive higher-order HMMs for the analysis of individual tumor expression
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.
Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.
Trägårdh, Magnus; Chappell, Michael J; Ahnmark, Andrea; Lindén, Daniel; Evans, Neil D; Gennemark, Peter
2016-04-01
Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery. PMID:26932466
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…
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…
One-Way Markov Process Approach to Repeat Times of Large Earthquakes in Faults
NASA Astrophysics Data System (ADS)
Tejedor, Alejandro; Gomez, Javier B.; Pacheco, Amalio F.
2012-11-01
One of the uses of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. We propose a general one-way Markovian model in which the waiting time distribution, its first moments, coefficient of variation, and functions of error and alarm (related to the predictability of the model) can be obtained analytically. The fact that in any one-way Markov cycle the coefficient of variation of the corresponding distribution of cycle lengths is always lower than one concurs with observations of large earthquakes in seismic faults. The waiting time distribution of one of the limits of this model is the negative binomial distribution; as an application, we use it to fit the Parkfield earthquake series in the San Andreas fault, California.
NASA Astrophysics Data System (ADS)
Bacher, C.; Filgueira, R.; Guyondet, T.
2016-01-01
Markov chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g., depletion index, carrying capacity assessment. Markov chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.
Hidden Markov models and other machine learning approaches in computational molecular biology
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 this 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.
NASA Technical Reports Server (NTRS)
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
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.
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.
Ficz, Gabriella; Wolf, Verena; Walter, Jörn
2016-01-01
DNA methylation and demethylation are opposing processes that when in balance create stable patterns of epigenetic memory. The control of DNA methylation pattern formation by replication dependent and independent demethylation processes has been suggested to be influenced by Tet mediated oxidation of 5mC. Several alternative mechanisms have been proposed suggesting that 5hmC influences either replication dependent maintenance of DNA methylation or replication independent processes of active demethylation. Using high resolution hairpin oxidative bisulfite sequencing data, we precisely determine the amount of 5mC and 5hmC and model the contribution of 5hmC to processes of demethylation in mouse ESCs. We develop an extended hidden Markov model capable of accurately describing the regional contribution of 5hmC to demethylation dynamics. Our analysis shows that 5hmC has a strong impact on replication dependent demethylation, mainly by impairing methylation maintenance. PMID:27224554
Hidden Markov model approach to skill learning and its application to telerobotics
Yang, J. . Robotics Inst. Univ. of Akron, OH . Dept. of Electrical Engineering); Xu, Y. . Robotics Inst.); Chen, C.S. . Dept. of Electrical Engineering)
1994-10-01
In this paper, the authors discuss the problem of how human skill can be represented as a parametric model using a hidden Markov model (HMM), and how an HMM-based skill model can be used to learn human skill. HMM is feasible to characterize a doubly stochastic process--measurable action and immeasurable mental states--that is involved in the skill learning. The authors formulated the learning problem as a multidimensional HMM and developed a testbed for a variety of skill learning applications. Based on ''the most likely performance'' criterion, the best action sequence can be selected from all previously measured action data by modeling the skill as an HMM. The proposed method has been implemented in the teleoperation control of a space station robot system, and some important implementation issues have been discussed. The method allows a robot to learn human skill certain tasks and to improve motion performance.
CIGALEMC: GALAXY PARAMETER ESTIMATION USING A MARKOV CHAIN MONTE CARLO APPROACH WITH CIGALE
Serra, Paolo; Amblard, Alexandre; Temi, Pasquale; Im, Stephen; Noll, Stefan
2011-10-10
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code Code Investigating GALaxy Emission (CIGALE). The original CIGALE builds a grid of theoretical spectral energy distribution (SED) models and fits to photometric fluxes from ultraviolet to infrared to put constraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. MCMC methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well-known and -studied Spitzer Infrared Nearby Galaxy Survey sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
Oh, Jung Hun; Gurnani, Prem; Schorge, John; Rosenblatt, Kevin P; Gao, Jean X
2009-03-01
High-resolution matrix-assisted laser desorption/ionization time-of-flight mass spectrometry has recently shown promise as a screening tool for detecting discriminatory peptide/protein patterns. The major computational obstacle in finding such patterns is the large number of mass/charge peaks (features, biomarkers, data points) in a spectrum. To tackle this problem, we have developed methods for data preprocessing and biomarker selection. The preprocessing consists of binning, baseline correction, and normalization. An algorithm, extended Markov blanket, is developed for biomarker detection, which combines redundant feature removal and discriminant feature selection. The biomarker selection couples with support vector machine to achieve sample prediction from high-resolution proteomic profiles. Our algorithm is applied to recurrent ovarian cancer study that contains platinum-sensitive and platinum-resistant samples after treatment. Experiments show that the proposed method performs better than other feature selection algorithms. In particular, our algorithm yields good performance in terms of both sensitivity and specificity as compared to other methods. PMID:19126475
Link between unemployment and crime in the US: a Markov-Switching approach.
Fallahi, Firouz; Rodríguez, Gabriel
2014-05-01
This study has two goals. The first is to use Markov Switching models to identify and analyze the cycles in the unemployment rate and four different types of property-related criminal activities in the US. The second is to apply the nonparametric concordance index of Harding and Pagan (2006) to determine the correlation between the cycles of unemployment rate and property crimes. Findings show that there is a positive but insignificant relationship between the unemployment rate, burglary, larceny, and robbery. However, the unemployment rate has a significant and negative (i.e., a counter-cyclical) relationship with motor-vehicle theft. Therefore, more motor-vehicle thefts occur during economic expansions relative to contractions. Next, we divide the sample into three different subsamples to examine the consistency of the findings. The results show that the co-movements between the unemployment rate and property crimes during recession periods are much weaker, when compared with that of the normal periods of the US economy. PMID:24576625
Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach
Xu, Lixin; Lu, Jianbo E-mail: lvjianbo819@163.com
2010-03-01
We use the Markov Chain Monte Carlo method to investigate a global constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Constitution dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a non-flat universe, the constraint results for GCG model are, Ω{sub b}h{sup 2} = 0.0235{sup +0.0021}{sub −0.0018} (1σ) {sup +0.0028}{sub −0.0022} (2σ), Ω{sub k} = 0.0035{sup +0.0172}{sub −0.0182} (1σ) {sup +0.0226}{sub −0.0204} (2σ), A{sub s} = 0.753{sup +0.037}{sub −0.035} (1σ) {sup +0.045}{sub −0.044} (2σ), α = 0.043{sup +0.102}{sub −0.106} (1σ) {sup +0.134}{sub −0.117} (2σ), and H{sub 0} = 70.00{sup +3.25}{sub −2.92} (1σ) {sup +3.77}{sub −3.67} (2σ), which is more stringent than the previous results for constraint on GCG model parameters. Furthermore, according to the information criterion, it seems that the current observations much support ΛCDM model relative to the GCG model.
Johannesson, G; Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2005-02-07
Estimating unknown system configurations/parameters by combining system knowledge gained from a computer simulation model on one hand and from observed data on the other hand is challenging. An example of such inverse problem is detecting and localizing potential flaws or changes in a structure by using a finite-element model and measured vibration/displacement data. We propose a probabilistic approach based on Bayesian methodology. This approach does not only yield a single best-guess solution, but a posterior probability distribution over the parameter space. In addition, the Bayesian approach provides a natural framework to accommodate prior knowledge. A Markov chain Monte Carlo (MCMC) procedure is proposed to generate samples from the posterior distribution (an ensemble of likely system configurations given the data). The MCMC procedure proposed explores the parameter space at different resolutions (scales), resulting in a more robust and efficient procedure. The large-scale exploration steps are carried out using coarser-resolution finite-element models, yielding a considerable decrease in computational time, which can be a crucial for large finite-element models. An application is given using synthetic displacement data from a simple cantilever beam with MCMC exploration carried out at three different resolutions.
Huda, Shamsul; Yearwood, John; Togneri, Roberto
2014-10-01
The expectation maximization (EM) is the standard training algorithm for hidden Markov model (HMM). However, EM faces a local convergence problem in HMM estimation. This paper attempts to overcome this problem of EM and proposes hybrid metaheuristic approaches to EM for HMM. In our earlier research, a hybrid of a constraint-based evolutionary learning approach to EM (CEL-EM) improved HMM estimation. In this paper, we propose a hybrid simulated annealing stochastic version of EM (SASEM) that combines simulated annealing (SA) with EM. The novelty of our approach is that we develop a mathematical reformulation of HMM estimation by introducing a stochastic step between the EM steps and combine SA with EM to provide better control over the acceptance of stochastic and EM steps for better HMM estimation. We also extend our earlier work and propose a second hybrid which is a combination of an EA and the proposed SASEM, (EA-SASEM). The proposed EA-SASEM uses the best constraint-based EA strategies from CEL-EM and stochastic reformulation of HMM. The complementary properties of EA and SA and stochastic reformulation of HMM of SASEM provide EA-SASEM with sufficient potential to find better estimation for HMM. To the best of our knowledge, this type of hybridization and mathematical reformulation have not been explored in the context of EM and HMM training. The proposed approaches have been evaluated through comprehensive experiments to justify their effectiveness in signal modeling using the speech corpus: TIMIT. Experimental results show that proposed approaches obtain higher recognition accuracies than the EM algorithm and CEL-EM as well. PMID:24686310
Bibliometric Application of Markov Chains.
ERIC Educational Resources Information Center
Pao, Miranda Lee; McCreery, Laurie
1986-01-01
A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)
Lin, Zhixiang; Li, Mingfeng; Sestan, Nenad; Zhao, Hongyu
2016-04-01
The statistical methodology developed in this study was motivated by our interest in studying neurodevelopment using the mouse brain RNA-Seq data set, where gene expression levels were measured in multiple layers in the somatosensory cortex across time in both female and male samples. We aim to identify differentially expressed genes between adjacent time points, which may provide insights on the dynamics of brain development. Because of the extremely small sample size (one male and female at each time point), simple marginal analysis may be underpowered. We propose a Markov random field (MRF)-based approach to capitalizing on the between layers similarity, temporal dependency and the similarity between sex. The model parameters are estimated by an efficient EM algorithm with mean field-like approximation. Simulation results and real data analysis suggest that the proposed model improves the power to detect differentially expressed genes than simple marginal analysis. Our method also reveals biologically interesting results in the mouse brain RNA-Seq data set. PMID:26926866
Benoit, Julia S; Chan, Wenyaw; Luo, Sheng; Yeh, Hung-Wen; Doody, Rachelle
2016-04-30
Understanding the dynamic disease process is vital in early detection, diagnosis, and measuring progression. Continuous-time Markov chain (CTMC) methods have been used to estimate state-change intensities but challenges arise when stages are potentially misclassified. We present an analytical likelihood approach where the hidden state is modeled as a three-state CTMC model allowing for some observed states to be possibly misclassified. Covariate effects of the hidden process and misclassification probabilities of the hidden state are estimated without information from a 'gold standard' as comparison. Parameter estimates are obtained using a modified expectation-maximization (EM) algorithm, and identifiability of CTMC estimation is addressed. Simulation studies and an application studying Alzheimer's disease caregiver stress-levels are presented. The method was highly sensitive to detecting true misclassification and did not falsely identify error in the absence of misclassification. In conclusion, we have developed a robust longitudinal method for analyzing categorical outcome data when classification of disease severity stage is uncertain and the purpose is to study the process' transition behavior without a gold standard. PMID:26782946
NASA Astrophysics Data System (ADS)
Haruna, T.; Nakajima, K.
2013-06-01
The duality between values and orderings is a powerful tool to discuss relationships between various information-theoretic measures and their permutation analogues for discrete-time finite-alphabet stationary stochastic processes (SSPs). Applying it to output processes of hidden Markov models with ergodic internal processes, we have shown in our previous work that the excess entropy and the transfer entropy rate coincide with their permutation analogues. In this paper, we discuss two permutation characterizations of the two measures for general ergodic SSPs not necessarily having the Markov property assumed in our previous work. In the first approach, we show that the excess entropy and the transfer entropy rate of an ergodic SSP can be obtained as the limits of permutation analogues of them for the N-th order approximation by hidden Markov models, respectively. In the second approach, we employ the modified permutation partition of the set of words which considers equalities of symbols in addition to permutations of words. We show that the excess entropy and the transfer entropy rate of an ergodic SSP are equal to their modified permutation analogues, respectively.
Cordero-Grande, Lucilio; Vegas-Sánchez-Ferrero, Gonzalo; Casaseca-de-la-Higuera, Pablo; Alberola-López, Carlos
2012-04-01
This paper proposes a topology-preserving multiresolution elastic registration method based on a discrete Markov random field of deformations and a block-matching procedure. The method is applied to the object-based interpolation of tomographic slices. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy based on intensity- and gradient-related features, the smoothness of the transformation is favored by an appropriate prior on the field, and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori configuration. Additionally, the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters. In order to obtain an unbiased interpolation result, the registration is performed both in the forward and backward directions, and the resulting transformations are combined by using the local information content of the deformation. The method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso. Quantitative comparisons offer an overall improvement in performance with respect to related works in the literature. Additionally, the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant. PMID:21997265
Geng, Bo; Zhou, Xiaobo; Zhu, Jinmin; Hung, Y S; Wong, Stephen T C
2008-04-01
Computational identification of missing enzymes plays a significant role in accurate and complete reconstruction of metabolic network for both newly sequenced and well-studied organisms. For a metabolic reaction, given a set of candidate enzymes identified according to certain biological evidences, a powerful mathematical model is required to predict the actual enzyme(s) catalyzing the reactions. In this study, several plausible predictive methods are considered for the classification problem in missing enzyme identification, and comparisons are performed with an aim to identify a method with better performance than the Bayesian model used in previous work. In particular, a regression model consisting of a linear term and a nonlinear term is proposed to apply to the problem, in which the reversible jump Markov-chain-Monte-Carlo (MCMC) learning technique (developed in [Andrieu C, Freitas Nando de, Doucet A. Robust full Bayesian learning for radial basis networks 2001;13:2359-407.]) is adopted to estimate the model order and the parameters. We evaluated the models using known reactions in Escherichia coli, Mycobacterium tuberculosis, Vibrio cholerae and Caulobacter cresentus bacteria, as well as one eukaryotic organism, Saccharomyces Cerevisiae. Although support vector regression also exhibits comparable performance in this application, it was demonstrated that the proposed model achieves favorable prediction performance, particularly sensitivity, compared with the Bayesian method. PMID:17950040
Kelley, Nicholas W.; Vishal, V.; Krafft, Grant A.; Pande, Vijay S.
2008-01-01
Here, we present a novel computational approach for describing the formation of oligomeric assemblies at experimental concentrations and timescales. We propose an extension to the Markovian state model approach, where one includes low concentration oligomeric states analytically. This allows simulation on long timescales (seconds timescale) and at arbitrarily low concentrations (e.g., the micromolar concentrations found in experiments), while still using an all-atom model for protein and solvent. As a proof of concept, we apply this methodology to the oligomerization of an Aβ peptide fragment (Aβ21–43). Aβ oligomers are now widely recognized as the primary neurotoxic structures leading to Alzheimer’s disease. Our computational methods predict that Aβ trimers form at micromolar concentrations in 10 ms, while tetramers form 1000 times more slowly. Moreover, the simulation results predict specific intermonomer contacts present in the oligomer ensemble as well as putative structures for small molecular weight oligomers. Based on our simulations and statistical models, we propose a novel mutation to stabilize the trimeric form of Aβ in an experimentally verifiable manner. PMID:19063575
NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-06-01
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
Borchani, Hanen; Bielza, Concha; Martı Nez-Martı N, Pablo; Larrañaga, Pedro
2012-12-01
Multi-dimensional Bayesian network classifiers (MBCs) are probabilistic graphical models recently proposed to deal with multi-dimensional classification problems, where each instance in the data set has to be assigned to more than one class variable. In this paper, we propose a Markov blanket-based approach for learning MBCs from data. Basically, it consists of determining the Markov blanket around each class variable using the HITON algorithm, then specifying the directionality over the MBC subgraphs. Our approach is applied to the prediction problem of the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39) in order to estimate the health-related quality of life of Parkinson's patients. Fivefold cross-validation experiments were carried out on randomly generated synthetic data sets, Yeast data set, as well as on a real-world Parkinson's disease data set containing 488 patients. The experimental study, including comparison with additional Bayesian network-based approaches, back propagation for multi-label learning, multi-label k-nearest neighbor, multinomial logistic regression, ordinary least squares, and censored least absolute deviations, shows encouraging results in terms of predictive accuracy as well as the identification of dependence relationships among class and feature variables. PMID:22897950
Stochastic Inversion of Electrical Resistivity Changes Using a Markov Chain, Monte Carlo Approach
Ramirez, A; Nitao, J; Hanley, W; Aines, R; Glaser, R; Sengupta, S; Dyer, K; Hickling, T; Daily, W
2004-09-21
We describe a stochastic inversion method for mapping subsurface regions where the electrical resistivity is changing. The technique combines prior information, electrical resistance data and forward models to produce subsurface resistivity models that are most consistent with all available data. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. Attractive features include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate and, (2) allow alternative model estimates to be identified, compared and ranked. Methods that monitor convergence and summarize important trends of the posterior distribution are introduced. Results from a physical model test and a field experiment were used to assess performance. The stochastic inversions presented provide useful estimates of the most probable location, shape, and volume of the changing region, and the most likely resistivity change. The proposed method is computationally expensive, requiring the use of extensive computational resources to make its application practical.
Markov Analysis of Sleep Dynamics
NASA Astrophysics Data System (ADS)
Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.
2009-05-01
A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.
Isojunno, Saana; Miller, Patrick J O
2016-01-01
The biological consequences of behavioral responses to anthropogenic noise depend on context. We explore the links between individual motivation, condition, and external constraints in a concept model and illustrate the use of motivational-behavioral states as a means to quantify the biologically relevant effects of tagging. Behavioral states were estimated from multiple streams of data in a hidden Markov model and used to test the change in foraging effort and the change in energetic success or cost given the effort. The presence of a tag boat elicited a short-term reduction in time spent in foraging states but not for proxies for success or cost within foraging states. PMID:26610996
An Approach to World Order Studies and the World System.
ERIC Educational Resources Information Center
Falk, Richard; Kim, Samuel S.
This paper discusses an approach to world order studies which can be used to supplant traditional international relations courses. It is one of a series of working papers commissioned by the World Order Models Project (WOMP) in its effort to stimulate research, education, dialogue, and political action aimed at contributing to a movement for a…
Zhang, Lixian; Ning, Zepeng; Shi, Peng
2015-11-01
This paper is concerned with H∞ control problem for a class of discrete-time Takagi-Sugeno fuzzy Markov jump systems with time-varying delays under unreliable communication links. It is assumed that the data transmission between the plant and the controller are subject to randomly occurred packet dropouts satisfying Bernoulli distribution and the dropout rate is uncertain. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the existence conditions of the desired H∞ state-feedback controllers are derived by employing the scaled small gain theorem such that the closed-loop system is stochastically stable and achieves a guaranteed H∞ performance. The gains of the controllers are constructed by solving a set of linear matrix inequalities. Finally, a practical example of robot arm is provided to illustrate the performance of the proposed approach. PMID:26470060
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.…
Narasimhan, Vagheesh; Danecek, Petr; Scally, Aylwyn; Xue, Yali; Tyler-Smith, Chris; Durbin, Richard
2016-01-01
Summary: Runs of homozygosity (RoHs) are genomic stretches of a diploid genome that show identical alleles on both chromosomes. Longer RoHs are unlikely to have arisen by chance but are likely to denote autozygosity, whereby both copies of the genome descend from the same recent ancestor. Early tools to detect RoH used genotype array data, but substantially more information is available from sequencing data. Here, we present and evaluate BCFtools/RoH, an extension to the BCFtools software package, that detects regions of autozygosity in sequencing data, in particular exome data, using a hidden Markov model. By applying it to simulated data and real data from the 1000 Genomes Project we estimate its accuracy and show that it has higher sensitivity and specificity than existing methods under a range of sequencing error rates and levels of autozygosity. Availability and implementation: BCFtools/RoH and its associated binary/source files are freely available from https://github.com/samtools/BCFtools. Contact: vn2@sanger.ac.uk or pd3@sanger.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26826718
Borodovsky, M.
2013-04-11
Algorithmic methods for gene prediction have been developed and successfully applied to many different prokaryotic genome sequences. As the set of genes in a particular genome is not homogeneous with respect to DNA sequence composition features, the GeneMark.hmm program utilizes two Markov models representing distinct classes of protein coding genes denoted "typical" and "atypical". Atypical genes are those whose DNA features deviate significantly from those classified as typical and they represent approximately 10% of any given genome. In addition to the inherent interest of more accurately predicting genes, the atypical status of these genes may also reflect their separate evolutionary ancestry from other genes in that genome. We hypothesize that atypical genes are largely comprised of those genes that have been relatively recently acquired through lateral gene transfer (LGT). If so, what fraction of atypical genes are such bona fide LGTs? We have made atypical gene predictions for all fully completed prokaryotic genomes; we have been able to compare these results to other "surrogate" methods of LGT prediction.
Coupled two-order-parameter approach to granular superconductors
Falci, G.; Fazio, R.; Giaquinta, G.
1989-05-01
A two-order-parameter approach to the theory of granular superconductors is presented, in which the paracoherent transition and the superconductive one are treated accounting for their mutual coupling. The appearance of a tricritical line in the phase diagram is discussed. Renormalization of the amplitude of the order parameter is predicted in the whole temperature range, leading to a satisfactory understanding of experimental data previously unexplained.
Hogden, J.
1996-11-05
The goal of the proposed research is to test a statistical model of speech recognition that incorporates the knowledge that speech is produced by relatively slow motions of the tongue, lips, and other speech articulators. This model is called Maximum Likelihood Continuity Mapping (Malcom). Many speech researchers believe that by using constraints imposed by articulator motions, we can improve or replace the current hidden Markov model based speech recognition algorithms. Unfortunately, previous efforts to incorporate information about articulation into speech recognition algorithms have suffered because (1) slight inaccuracies in our knowledge or the formulation of our knowledge about articulation may decrease recognition performance, (2) small changes in the assumptions underlying models of speech production can lead to large changes in the speech derived from the models, and (3) collecting measurements of human articulator positions in sufficient quantity for training a speech recognition algorithm is still impractical. The most interesting (and in fact, unique) quality of Malcom is that, even though Malcom makes use of a mapping between acoustics and articulation, Malcom can be trained to recognize speech using only acoustic data. By learning the mapping between acoustics and articulation using only acoustic data, Malcom avoids the difficulties involved in collecting articulator position measurements and does not require an articulatory synthesizer model to estimate the mapping between vocal tract shapes and speech acoustics. Preliminary experiments that demonstrate that Malcom can learn the mapping between acoustics and articulation are discussed. Potential applications of Malcom aside from speech recognition are also discussed. Finally, specific deliverables resulting from the proposed research are described.
NASA Astrophysics Data System (ADS)
Farr, Benjamin; Kalogera, Vicky; Luijten, Erik
2014-07-01
We introduce a new Markov-chain Monte Carlo (MCMC) approach designed for the efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our approach minimizes the use of parallel tempering, only applying it for a short time to build a proposal distribution that is based upon estimation of the kernel density and tuned to the target posterior. This proposal makes subsequent use of parallel tempering unnecessary, allowing all chains to be cooled to sample the target distribution. Gains in efficiency are found to increase with increasing posterior complexity, ranging from tens of percent in the simplest cases to over a factor of 10 for the more complex cases. Our approach is particularly useful in the context of parameter estimation of gravitational-wave signals measured by ground-based detectors, which is currently done through Bayesian inference with MCMC, one of the leading sampling methods. Posteriors for these signals are typically multimodal with strong nonlinear correlations, making sampling difficult. As we enter the advanced-detector era, improved sensitivities and wider bandwidths will drastically increase the computational cost of analyses, demanding more efficient search algorithms to meet these challenges.
NASA Technical Reports Server (NTRS)
Panday, Prajjwal K.; Williams, Christopher A.; Frey, Karen E.; Brown, Molly E.
2013-01-01
Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree
Anatomy Ontology Matching Using Markov Logic Networks
Li, Chunhua; Zhao, Pengpeng; Wu, Jian; Cui, Zhiming
2016-01-01
The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. Markov logic networks which unify probabilistic graphical model and first-order logic provide an excellent framework for ontology matching. We combine several different matching strategies through first-order logic formulas according to the structure of anatomy ontologies. Experiments on the adult mouse anatomy and the human anatomy have demonstrated the effectiveness of proposed approach in terms of the quality of result alignment. PMID:27382498
Stroeer, Alexander; Veitch, John
2009-09-15
The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme-mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals ''out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.
Ma, Junsheng; Chan, Wenyaw; Tsai, Chu-Lin; Xiong, Momiao; Tilley, Barbara C
2015-11-30
Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. PMID:26123093
Indexed semi-Markov process for wind speed modeling.
NASA Astrophysics Data System (ADS)
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating
Structure of ordered coaxial and scroll nanotubes: general approach.
Khalitov, Zufar; Khadiev, Azat; Valeeva, Diana; Pashin, Dmitry
2016-01-01
The explicit formulas for atomic coordinates of multiwalled coaxial and cylindrical scroll nanotubes with ordered structure are developed on the basis of a common oblique lattice. According to this approach, a nanotube is formed by transfer of its bulk analogue structure onto a cylindrical surface (with a circular or spiral cross section) and the chirality indexes of the tube are expressed in the number of unit cells. The monoclinic polytypic modifications of ordered coaxial and scroll nanotubes are also discussed and geometrical conditions of their formation are analysed. It is shown that tube radii of ordered multiwalled coaxial nanotubes are multiples of the layer thickness, and the initial turn radius of the orthogonal scroll nanotube is a multiple of the same parameter or its half. PMID:26697865
Speckle reduction via higher order total variation approach.
Wensen Feng; Hong Lei; Yang Gao
2014-04-01
Multiplicative noise (also known as speckle) reduction is a prerequisite for many image-processing tasks in coherent imaging systems, such as the synthetic aperture radar. One approach extensively used in this area is based on total variation (TV) regularization, which can recover significantly sharp edges of an image, but suffers from the staircase-like artifacts. In order to overcome the undesirable deficiency, we propose two novel models for removing multiplicative noise based on total generalized variation (TGV) penalty. The TGV regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness. Furthermore, an efficient algorithm is developed for solving the TGV-based optimization problems. Numerical experiments demonstrate that our proposed methods achieve state-of-the-art results, both visually and quantitatively. In particular, when the image has some higher order smoothness, our methods outperform the TV-based algorithms. PMID:24808350
Stochastic seismic tomography by interacting Markov chains
NASA Astrophysics Data System (ADS)
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-07-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Yamamoto, Toshiyuki; Shimojima, Keiko; Ondo, Yumiko; Imai, Katsumi; Chong, Pin Fee; Kira, Ryutaro; Amemiya, Mitsuhiro; Saito, Akira; Okamoto, Nobuhiko
2016-01-01
Next-generation sequencing (NGS) is widely used for the detection of disease-causing nucleotide variants. The challenges associated with detecting copy number variants (CNVs) using NGS analysis have been reported previously. Disease-related exome panels such as Illumina TruSight One are more cost-effective than whole-exome sequencing (WES) because of their selective target regions (~21% of the WES). In this study, CNVs were analyzed using data extracted through a disease-related exome panel analysis and the eXome Hidden Markov Model (XHMM). Samples from 61 patients with undiagnosed developmental delays and 52 healthy parents were included in this study. In the preliminary study to validate the constructed XHMM system (microarray-first approach), 34 patients who had previously been analyzed by chromosomal microarray testing were used. Among the five CNVs larger than 200 kb that were considered as non-pathogenic CNVs and were used as positive controls, four CNVs was successfully detected. The system was subsequently used to analyze different samples from 27 patients (NGS-first approach); 2 of these patients were successfully diagnosed as having pathogenic CNVs (an unbalanced translocation der(5)t(5;14) and a 16p11.2 duplication). These diagnoses were re-confirmed by chromosomal microarray testing and/or fluorescence in situ hybridization. The NGS-first approach generated no false-negative or false-positive results for pathogenic CNVs, indicating its high sensitivity and specificity in detecting pathogenic CNVs. The results of this study show the possible clinical utility of pathogenic CNV screening using disease-related exome panel analysis and XHMM. PMID:27579173
Yamamoto, Toshiyuki; Shimojima, Keiko; Ondo, Yumiko; Imai, Katsumi; Chong, Pin Fee; Kira, Ryutaro; Amemiya, Mitsuhiro; Saito, Akira; Okamoto, Nobuhiko
2016-01-01
Next-generation sequencing (NGS) is widely used for the detection of disease-causing nucleotide variants. The challenges associated with detecting copy number variants (CNVs) using NGS analysis have been reported previously. Disease-related exome panels such as Illumina TruSight One are more cost-effective than whole-exome sequencing (WES) because of their selective target regions (~21% of the WES). In this study, CNVs were analyzed using data extracted through a disease-related exome panel analysis and the eXome Hidden Markov Model (XHMM). Samples from 61 patients with undiagnosed developmental delays and 52 healthy parents were included in this study. In the preliminary study to validate the constructed XHMM system (microarray-first approach), 34 patients who had previously been analyzed by chromosomal microarray testing were used. Among the five CNVs larger than 200 kb that were considered as non-pathogenic CNVs and were used as positive controls, four CNVs was successfully detected. The system was subsequently used to analyze different samples from 27 patients (NGS-first approach); 2 of these patients were successfully diagnosed as having pathogenic CNVs (an unbalanced translocation der(5)t(5;14) and a 16p11.2 duplication). These diagnoses were re-confirmed by chromosomal microarray testing and/or fluorescence in situ hybridization. The NGS-first approach generated no false-negative or false-positive results for pathogenic CNVs, indicating its high sensitivity and specificity in detecting pathogenic CNVs. The results of this study show the possible clinical utility of pathogenic CNV screening using disease-related exome panel analysis and XHMM. PMID:27579173
A new approach for second-order perturbation theory.
Tomlinson, David G; Asadchev, Andrey; Gordon, Mark S
2016-05-30
A new second-order perturbation theory (MP2) approach is presented for closed shell energy evaluations. The new algorithm has a significantly lower memory footprint, a lower FLOP (floating point operations) count, and a lower time to solution compared to previously implemented parallel MP2 methods in the GAMESS software package. Additionally, this algorithm features an adaptive approach for the disk/distributed memory storage of the MP2 amplitudes. The algorithm works well on a single workstation, small cluster, and large Cray cluster, and it allows one to perform large calculations with thousands of basis functions in a matter of hours on a single workstation. The same algorithm has been adapted for graphical processing unit (GPU) architecture. The performance of the new GPU algorithm is also discussed. © 2016 Wiley Periodicals, Inc. PMID:26940648
Markov state models of protein misfolding.
Sirur, Anshul; De Sancho, David; Best, Robert B
2016-02-21
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. PMID:26897000
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.
Gao, Hong; Williamson, Scott; Bustamante, Carlos D.
2007-01-01
Nonrandom mating induces correlations in allelic states within and among loci that can be exploited to understand the genetic structure of natural populations (Wright 1965). For many species, it is of considerable interest to quantify the contribution of two forms of nonrandom mating to patterns of standing genetic variation: inbreeding (mating among relatives) and population substructure (limited dispersal of gametes). Here, we extend the popular Bayesian clustering approach STRUCTURE (Pritchard et al. 2000) for simultaneous inference of inbreeding or selfing rates and population-of-origin classification using multilocus genetic markers. This is accomplished by eliminating the assumption of Hardy–Weinberg equilibrium within clusters and, instead, calculating expected genotype frequencies on the basis of inbreeding or selfing rates. We demonstrate the need for such an extension by showing that selfing leads to spurious signals of population substructure using the standard STRUCTURE algorithm with a bias toward spurious signals of admixture. We gauge the performance of our method using extensive coalescent simulations and demonstrate that our approach can correct for this bias. We also apply our approach to understanding the population structure of the wild relative of domesticated rice, Oryza rufipogon, an important partially selfing grass species. Using a sample of n = 16 individuals sequenced at 111 random loci, we find strong evidence for existence of two subpopulations, which correlates well with geographic location of sampling, and estimate selfing rates for both groups that are consistent with estimates from experimental data (s ≈ 0.48–0.70). PMID:17483417
Huda, Shamsul; Yearwood, John; Togneri, Roberto
2009-02-01
This paper attempts to overcome the tendency of the expectation-maximization (EM) algorithm to locate a local rather than global maximum when applied to estimate the hidden Markov model (HMM) parameters in speech signal modeling. We propose a hybrid algorithm for estimation of the HMM in automatic speech recognition (ASR) using a constraint-based evolutionary algorithm (EA) and EM, the CEL-EM. The novelty of our hybrid algorithm (CEL-EM) is that it is applicable for estimation of the constraint-based models with many constraints and large numbers of parameters (which use EM) like HMM. Two constraint-based versions of the CEL-EM with different fusion strategies have been proposed using a constraint-based EA and the EM for better estimation of HMM in ASR. The first one uses a traditional constraint-handling mechanism of EA. The other version transforms a constrained optimization problem into an unconstrained problem using Lagrange multipliers. Fusion strategies for the CEL-EM use a staged-fusion approach where EM has been plugged with the EA periodically after the execution of EA for a specific period of time to maintain the global sampling capabilities of EA in the hybrid algorithm. A variable initialization approach (VIA) has been proposed using a variable segmentation to provide a better initialization for EA in the CEL-EM. Experimental results on the TIMIT speech corpus show that CEL-EM obtains higher recognition accuracies than the traditional EM algorithm as well as a top-standard EM (VIA-EM, constructed by applying the VIA to EM). PMID:19068441
NASA Astrophysics Data System (ADS)
MacBean, Natasha; Disney, Mathias; Lewis, Philip; Ineson, Phil
2010-05-01
profile as a whole. We present results from an Observing System Simulation Experiment (OSSE) designed to investigate the impact of management and climate change on peatland carbon fluxes, as well as how observations from satellites may be able to constrain modeled carbon fluxes. We use an adapted version of the Carnegie-Ames-Stanford Approach (CASA) model (Potter et al., 1993) that includes a representation of methane dynamics (Potter, 1997). The model formulation is further modified to allow for assimilation of satellite observations of surface soil moisture and land surface temperature. The observations are used to update model estimates using a Metropolis Hastings Markov Chain Monte Carlo (MCMC) approach. We examine the effect of temporal frequency and precision of satellite observations with a view to establishing how, and at what level, such observations would make a significant improvement in model uncertainty. We compare this with the system characteristics of existing and future satellites. We believe this is the first attempt to assimilate surface soil moisture and land surface temperature into an ecosystem model that includes a full representation of CH4 flux. Bubier, J., and T. Moore (1994), An ecological perspective on methane emissions from northern wetlands, TREE, 9, 460-464. Charman, D. (2002), Peatlands and Environmental Change, JohnWiley and Sons, Ltd, England. Gorham, E. (1991), Northern peatlands: Role in the carbon cycle and probable responses to climatic warming, Ecological Applications, 1, 182-195. Lai, D. (2009), Methane dynamics in northern peatlands: A review, Pedosphere, 19, 409-421. Le Mer, J., and P. Roger (2001), Production, oxidation, emission and consumption of methane by soils: A review, European Journal of Soil Biology, 37, 25-50. Limpens, J., F. Berendse, J. Canadell, C. Freeman, J. Holden, N. Roulet, H. Rydin, and Potter, C. (1997), An ecosystem simulation model for methane production and emission from wetlands, Global Biogeochemical
Fridman, Arthur
2003-01-01
Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford [Mumford, D. (1996) in ICIAM 95, eds. Kirchgassner, K., Marenholtz, O. & Mennicken, R. (Akademie Verlag, Berlin), pp. 233–256] proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. PMID:12829802
Zeroth-order regular approximation approach to molecular parity violation
Berger, Robert; Langermann, Norbert; Wuellen, Christoph van
2005-04-01
We present an ab initio (quasirelativistic) two-component approach to the computation of molecular parity-violating effects which is based on the zeroth-order regular approximation (ZORA). As a first application, we compute the parity-violating energy differences between various P and M conformations of C{sub 2}-symmetric molecules belonging to the series H{sub 2}X{sub 2} with X=O, S, Se, Te, Po. The results are compared to previously reported (relativistic) four-component Dirac-Hartree-Fock-Coulomb (DHFC) data. Relative deviations between ZORA and DHFC values are well below 2% for diselane and the heavier homologs whereas somewhat larger relative deviations are observed for the lighter homologs. The larger deviations for lighter systems are attributed to the (nonlocal) exchange terms coupling large and small components, which have been neglected in the present ZORA implementation. For heavier systems these play a minor role, which explains the good performance of the ZORA approach. An excellent performance, even for lighter systems, is expected for a related density-functional-theory-based ZORA because then the exchange terms coupling large and small components are absent.
Jacob, Benjamin G; Griffith, Daniel A; Muturi, Ephantus J; Caamano, Erick X; Githure, John I; Novak, Robert J
2009-01-01
configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix. Results By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with An. arabiensis aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled An. arabiensis aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat. Conclusion An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific An. arabiensis aquatic habitats based on larval/pupal productivity. PMID:19772590
Zhou, Ping; Bai, Rongji
2014-01-01
Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207
Leng, Ning; Li, Yuan; McIntosh, Brian E.; Nguyen, Bao Kim; Duffin, Bret; Tian, Shulan; Thomson, James A.; Dewey, Colin N.; Stewart, Ron; Kendziorski, Christina
2015-01-01
Motivation: With improvements in next-generation sequencing technologies and reductions in price, ordered RNA-seq experiments are becoming common. Of primary interest in these experiments is identifying genes that are changing over time or space, for example, and then characterizing the specific expression changes. A number of robust statistical methods are available to identify genes showing differential expression among multiple conditions, but most assume conditions are exchangeable and thereby sacrifice power and precision when applied to ordered data. Results: We propose an empirical Bayes mixture modeling approach called EBSeq-HMM. In EBSeq-HMM, an auto-regressive hidden Markov model is implemented to accommodate dependence in gene expression across ordered conditions. As demonstrated in simulation and case studies, the output proves useful in identifying differentially expressed genes and in specifying gene-specific expression paths. EBSeq-HMM may also be used for inference regarding isoform expression. Availability and implementation: An R package containing examples and sample datasets is available at Bioconductor. Contact: kendzior@biostat.wisc.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25847007
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. PMID:26353069
Fractional System Identification: An Approach Using Continuous Order-Distributions
NASA Technical Reports Server (NTRS)
Hartley, Tom T.; Lorenzo, Carl F.
1999-01-01
This paper discusses the identification of fractional- and integer-order systems using the concept of continuous order-distribution. Based on the ability to define systems using continuous order-distributions, it is shown that frequency domain system identification can be performed using least squares techniques after discretizing the order-distribution.
Performability analysis using semi-Markov reward processes
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Marie, Raymond A.; Sericola, Bruno; Trivedi, Kishor S.
1990-01-01
Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.
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…
Homogeneous Superpixels from Markov Random Walks
NASA Astrophysics Data System (ADS)
Perbet, Frank; Stenger, Björn; Maki, Atsuto
This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact pruning in order to capture intrinsic local image structure. The resulting superpixels are homogeneous, i.e. uniform in size and compact in shape. The original MCL algorithm does not scale well to a graph of an image due to the square computation of the Markov matrix which is necessary for circulating the flow. The proposed pruning scheme has the advantages of faster computation, smaller memory footprint, and straightforward parallel implementation. Through comparisons with other recent techniques, we show that the proposed algorithm achieves state-of-the-art performance.
Document Ranking Based upon Markov Chains.
ERIC Educational Resources Information Center
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
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.
An extensive Markov system for ECG exact coding.
Tai, S C
1995-02-01
In this paper, an extensive Markov process, which considers both the coding redundancy and the intersample redundancy, is presented to measure the entropy value of an ECG signal more accurately. It utilizes the intersample correlations by predicting the incoming n samples based on the previous m samples which constitute an extensive Markov process state. Theories of the extensive Markov process and conventional n repeated applications of m-th order Markov process are studied first in this paper. After that, they are realized for ECG exact coding. Results show that a better performance can be achieved by our system. The average code length for the extensive Markov system on the second difference signals was 2.512 b/sample, while the average Huffman code length for the second difference signals was 3.326 b/sample. PMID:7868151
General and specific consciousness: a first-order representationalist approach
Mehta, Neil; Mashour, George A.
2013-01-01
It is widely acknowledged that a complete theory of consciousness should explain general consciousness (what makes a state conscious at all) and specific consciousness (what gives a conscious state its particular phenomenal quality). We defend first-order representationalism, which argues that consciousness consists of sensory representations directly available to the subject for action selection, belief formation, planning, etc. We provide a neuroscientific framework for this primarily philosophical theory, according to which neural correlates of general consciousness include prefrontal cortex, posterior parietal cortex, and non-specific thalamic nuclei, while neural correlates of specific consciousness include sensory cortex and specific thalamic nuclei. We suggest that recent data support first-order representationalism over biological theory, higher-order representationalism, recurrent processing theory, information integration theory, and global workspace theory. PMID:23882231
Reduced-Order Modeling: New Approaches for Computational Physics
NASA Technical Reports Server (NTRS)
Beran, Philip S.; Silva, Walter A.
2001-01-01
In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.
Automated Approach to Very High-Order Aeroacoustic Computations. Revision
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Goodrich, John W.
2001-01-01
Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.
All-order approach to high-precision atomic calculation
NASA Astrophysics Data System (ADS)
Iskrenova-Tchoukova, Eugeniya
High-precision atomic calculations combined with experiments of matching accuracy provide an excellent opportunity to test our understanding of atomic structure and properties as well as the many-body atomic theories. The relativistic all-order method, which is a linearized version of the coupled-cluster singles-doubles method, has proven to yield high precision results for a variety of atomic properties. In this thesis, we study the atomic properties of neutral atoms and ions by means of the relativistic all-order method. The lifetimes and ground state static polarizabilities of a singly ionized barium atom are studied in comparison with the isoelectronic neutral cesium atom and with a singly ionized calcium atom. The lifetimes of a number of excited states in atomic potassium, rubidium, and francium are theoretically calculated and compared with the available experimental data. The magnetic dipole hyperfine constant of the 9S1/2 state in 210Fr is calculated and the result is combined with the experimental one to extract the value of the 210Fr nuclear magnetic moment. Another part of the thesis work focuses on the development and implementation of an extension of the currently used all-order singles-doubles (SD) method to include all valence triple excitations in an iterative way, all-order SD+vT approximation. Some of the ideas and results presented in Chapters 4, 5, and 6 have been published and are subject to copyright laws. These publications are cited accordingly.
Markov Modeling with Soft Aggregation for Safety and Decision Analysis
COOPER,J. ARLIN
1999-09-01
The methodology in this report improves on some of the limitations of many conventional safety assessment and decision analysis methods. A top-down mathematical approach is developed for decomposing systems and for expressing imprecise individual metrics as possibilistic or fuzzy numbers. A ''Markov-like'' model is developed that facilitates combining (aggregating) inputs into overall metrics and decision aids, also portraying the inherent uncertainty. A major goal of Markov modeling is to help convey the top-down system perspective. One of the constituent methodologies allows metrics to be weighted according to significance of the attribute and aggregated nonlinearly as to contribution. This aggregation is performed using exponential combination of the metrics, since the accumulating effect of such factors responds less and less to additional factors. This is termed ''soft'' mathematical aggregation. Dependence among the contributing factors is accounted for by incorporating subjective metrics on ''overlap'' of the factors as well as by correspondingly reducing the overall contribution of these combinations to the overall aggregation. Decisions corresponding to the meaningfulness of the results are facilitated in several ways. First, the results are compared to a soft threshold provided by a sigmoid function. Second, information is provided on input ''Importance'' and ''Sensitivity,'' in order to know where to place emphasis on considering new controls that may be necessary. Third, trends in inputs and outputs are tracked in order to obtain significant information% including cyclic information for the decision process. A practical example from the air transportation industry is used to demonstrate application of the methodology. Illustrations are given for developing a structure (along with recommended inputs and weights) for air transportation oversight at three different levels, for developing and using cycle information, for developing Importance and
Hidden Markov Models for Detecting Aseismic Events in Southern California
NASA Astrophysics Data System (ADS)
Granat, R.
2004-12-01
We employ a hidden Markov model (HMM) to segment surface displacement time series collection by the Southern California Integrated Geodetic Network (SCIGN). These segmented time series are then used to detect regional events by observing the number of simultaneous mode changes across the network; if a large number of stations change at the same time, that indicates an event. The hidden Markov model (HMM) approach assumes that the observed data has been generated by an unobservable dynamical statistical process. The process is of a particular form such that each observation is coincident with the system being in a particular discrete state, which is interpreted as a behavioral mode. The dynamics are the model are constructed so that the next state is directly dependent only on the current state -- it is a first order Markov process. The model is completely described by a set of parameters: the initial state probabilities, the first order Markov chain state-to-state transition probabilities, and the probability distribution of observable outputs associated with each state. The result of this approach is that our segmentation decisions are based entirely on statistical changes in the behavior of the observed daily displacements. In general, finding the optimal model parameters to fit the data is a difficult problem. We present an innovative model fitting method that is unsupervised (i.e., it requires no labeled training data) and uses a regularized version of the expectation-maximization (EM) algorithm to ensure that model solutions are both robust with respect to initial conditions and of high quality. We demonstrate the reliability of the method as compared to standard model fitting methods and show that it results in lower noise in the mode change correlation signal used to detect regional events. We compare candidate events detected by this method to the seismic record and observe that most are not correlated with a significant seismic event. Our analysis
Thermal nanostructure: An order parameter multiscale ensemble approach
NASA Astrophysics Data System (ADS)
Cheluvaraja, S.; Ortoleva, P.
2010-02-01
Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD™, achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.
A Recurrence Relation Approach to Higher Order Quantum Superintegrability
NASA Astrophysics Data System (ADS)
Kalnins, Ernie G.; Kress, Jonathan M.; Miller, Willard
2011-03-01
We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of superintegrability and explicit constructions of higher order generators for the symmetry algebra. We apply the method to 5 families of systems, each depending on a parameter k, including most notably the caged anisotropic oscillator, the Tremblay, Turbiner and Winternitz system and a deformed Kepler-Coulomb system, and we give proofs of quantum superintegrability for all rational values of k, new for 4 of these systems. In addition, we show that the explicit information supplied by the special function recurrence relations allows us to prove, for the first time in 4 cases, that the symmetry algebra generated by our lowest order symmetries closes and to determine the associated structure equations of the algebras for each k. We have no proof that our generating symmetries are of lowest possible order, but we have no counterexamples, and we are confident we can can always find any missing generators from our raising and lowering operator recurrences. We also get for free, one variable models of the action of the symmetry algebra in terms of difference operators. We describe how the Stäckel transform acts and show that it preserves the structure equations.
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.
Using Markov state models to study self-assembly.
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. PMID:24907984
Using Markov state models to study self-assembly
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
Stochastic motif extraction using hidden Markov model
Fujiwara, Yukiko; Asogawa, Minoru; Konagaya, Akihiko
1994-12-31
In this paper, we study the application of an HMM (hidden Markov model) to the problem of representing protein sequences by a stochastic motif. A stochastic protein motif represents the small segments of protein sequences that have a certain function or structure. The stochastic motif, represented by an HMM, has conditional probabilities to deal with the stochastic nature of the motif. This HMM directive reflects the characteristics of the motif, such as a protein periodical structure or grouping. In order to obtain the optimal HMM, we developed the {open_quotes}iterative duplication method{close_quotes} for HMM topology learning. It starts from a small fully-connected network and iterates the network generation and parameter optimization until it achieves sufficient discrimination accuracy. Using this method, we obtained an HMM for a leucine zipper motif. Compared to the accuracy of a symbolic pattern representation with accuracy of 14.8 percent, an HMM achieved 79.3 percent in prediction. Additionally, the method can obtain an HMM for various types of zinc finger motifs, and it might separate the mixed data. We demonstrated that this approach is applicable to the validation of the protein databases; a constructed HMM b as indicated that one protein sequence annotated as {open_quotes}lencine-zipper like sequence{close_quotes} in the database is quite different from other leucine-zipper sequences in terms of likelihood, and we found this discrimination is plausible.
Optimal q-Markov COVER for finite precision implementation
NASA Technical Reports Server (NTRS)
Williamson, Darrell; Skelton, Robert E.
1989-01-01
The existing q-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced order model. All q-Markov COVERs allow some freedom in the choice of parameters. Here, researchers exploit this freedom in the existing theory to optimize the models with respect to these finite wordlength effects.
Markov Chains For Testing Redundant Software
NASA Technical Reports Server (NTRS)
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Koukounari, Artemis; Donnelly, Christl A.; Moustaki, Irini; Tukahebwa, Edridah M.; Kabatereine, Narcis B.; Wilson, Shona; Webster, Joanne P.; Deelder, André M.; Vennervald, Birgitte J.; van Dam, Govert J.
2013-01-01
Regular treatment with praziquantel (PZQ) is the strategy for human schistosomiasis control aiming to prevent morbidity in later life. With the recent resolution on schistosomiasis elimination by the 65th World Health Assembly, appropriate diagnostic tools to inform interventions are keys to their success. We present a discrete Markov chains modelling framework that deals with the longitudinal study design and the measurement error in the diagnostic methods under study. A longitudinal detailed dataset from Uganda, in which one or two doses of PZQ treatment were provided, was analyzed through Latent Markov Models (LMMs). The aim was to evaluate the diagnostic accuracy of Circulating Cathodic Antigen (CCA) and of double Kato-Katz (KK) faecal slides over three consecutive days for Schistosoma mansoni infection simultaneously by age group at baseline and at two follow-up times post treatment. Diagnostic test sensitivities and specificities and the true underlying infection prevalence over time as well as the probabilities of transitions between infected and uninfected states are provided. The estimated transition probability matrices provide parsimonious yet important insights into the re-infection and cure rates in the two age groups. We show that the CCA diagnostic performance remained constant after PZQ treatment and that this test was overall more sensitive but less specific than single-day double KK for the diagnosis of S. mansoni infection. The probability of clearing infection from baseline to 9 weeks was higher among those who received two PZQ doses compared to one PZQ dose for both age groups, with much higher re-infection rates among children compared to adolescents and adults. We recommend LMMs as a useful methodology for monitoring and evaluation and treatment decision research as well as CCA for mapping surveys of S. mansoni infection, although additional diagnostic tools should be incorporated in schistosomiasis elimination programs. PMID:24367250
A semi-Markov model for price returns
NASA Astrophysics Data System (ADS)
D'Amico, Guglielmo; Petroni, Filippo
2012-10-01
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.
A non-homogeneous Markov model for phased-mission reliability analysis
NASA Technical Reports Server (NTRS)
Smotherman, Mark; Zemoudeh, Kay
1989-01-01
Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation.
A path-independent method for barrier option pricing in hidden Markov models
NASA Astrophysics Data System (ADS)
Rashidi Ranjbar, Hedieh; Seifi, Abbas
2015-12-01
This paper presents a method for barrier option pricing under a Black-Scholes model with Markov switching. We extend the option pricing method of Buffington and Elliott to price continuously monitored barrier options under a Black-Scholes model with regime switching. We use a regime switching random Esscher transform in order to determine an equivalent martingale pricing measure, and then solve the resulting multidimensional integral for pricing barrier options. We have calculated prices for down-and-out call options under a two-state hidden Markov model using two different Monte-Carlo simulation approaches and the proposed method. A comparison of the results shows that our method is faster than Monte-Carlo simulation methods.
Estimating Neuronal Ageing with Hidden Markov Models
NASA Astrophysics Data System (ADS)
Wang, Bing; Pham, Tuan D.
2011-06-01
Neuronal degeneration is widely observed in normal ageing, meanwhile the neurode-generative disease like Alzheimer's disease effects neuronal degeneration in a faster way which is considered as faster ageing. Early intervention of such disease could benefit subjects with potentials of positive clinical outcome, therefore, early detection of disease related brain structural alteration is required. In this paper, we propose a computational approach for modelling the MRI-based structure alteration with ageing using hidden Markov model. The proposed hidden Markov model based brain structural model encodes intracortical tissue/fluid distribution using discrete wavelet transformation and vector quantization. Further, it captures gray matter volume loss, which is capable of reflecting subtle intracortical changes with ageing. Experiments were carried out on healthy subjects to validate its accuracy and robustness. Results have shown its ability of predicting the brain age with prediction error of 1.98 years without training data, which shows better result than other age predition methods.
Markov Processes: Linguistics and Zipf's Law
NASA Astrophysics Data System (ADS)
Kanter, I.; Kessler, D. A.
1995-05-01
It is shown that a 2-parameter random Markov process constructed with N states and biased random transitions gives rise to a stationary distribution where the probabilities of occurrence of the states, P\\(k\\), k = 1,...,N, exhibit the following three universal behaviors which characterize biological sequences and texts in natural languages: (a) the rank-ordered frequencies of occurrence of words are given by Zipf's law P\\(k\\)~1/kρ, where ρ\\(k\\) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P\\(k\\) = A-Dln\\(k\\); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.
Decentralized learning in Markov games.
Vrancx, Peter; Verbeeck, Katja; Nowé, Ann
2008-08-01
Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies. PMID:18632387
A Markov Model for Assessing the Reliability of a Digital Feedwater Control System
Chu,T.L.; Yue, M.; Martinez-Guridi, G.; Lehner, J.
2009-02-11
A Markov approach has been selected to represent and quantify the reliability model of a digital feedwater control system (DFWCS). The system state, i.e., whether a system fails or not, is determined by the status of the components that can be characterized by component failure modes. Starting from the system state that has no component failure, possible transitions out of it are all failure modes of all components in the system. Each additional component failure mode will formulate a different system state that may or may not be a system failure state. The Markov transition diagram is developed by strictly following the sequences of component failures (i.e., failure sequences) because the different orders of the same set of failures may affect the system in completely different ways. The formulation and quantification of the Markov model, together with the proposed FMEA (Failure Modes and Effects Analysis) approach, and the development of the supporting automated FMEA tool are considered the three major elements of a generic conceptual framework under which the reliability of digital systems can be assessed.
Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.
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. PMID:24246289
Markov models and the ensemble Kalman filter for estimation of sorption rates.
Vugrin, Eric D.; McKenna, Sean Andrew; Vugrin, Kay White
2007-09-01
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude.
Metrics for Labeled Markov Systems
NASA Technical Reports Server (NTRS)
Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash
1999-01-01
Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.
Raberto, Marco; Rapallo, Fabio; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245
Hidden Markov Model Analysis of Multichromophore Photobleaching
Messina, Troy C.; Kim, Hiyun; Giurleo, Jason T.; Talaga, David S.
2007-01-01
The interpretation of single-molecule measurements is greatly complicated by the presence of multiple fluorescent labels. However, many molecular systems of interest consist of multiple interacting components. We investigate this issue using multiply labeled dextran polymers that we intentionally photobleach to the background on a single-molecule basis. Hidden Markov models allow for unsupervised analysis of the data to determine the number of fluorescent subunits involved in the fluorescence intermittency of the 6-carboxy-tetramethylrhodamine labels by counting the discrete steps in fluorescence intensity. The Bayes information criterion allows us to distinguish between hidden Markov models that differ by the number of states, that is, the number of fluorescent molecules. We determine information-theoretical limits and show via Monte Carlo simulations that the hidden Markov model analysis approaches these theoretical limits. This technique has resolving power of one fluorescing unit up to as many as 30 fluorescent dyes with the appropriate choice of dye and adequate detection capability. We discuss the general utility of this method for determining aggregation-state distributions as could appear in many biologically important systems and its adaptability to general photometric experiments. PMID:16913765
Phase transitions in Hidden Markov Models
NASA Astrophysics Data System (ADS)
Bechhoefer, John; Lathouwers, Emma
In Hidden Markov Models (HMMs), a Markov process is not directly accessible. In the simplest case, a two-state Markov model ``emits'' one of two ``symbols'' at each time step. We can think of these symbols as noisy measurements of the underlying state. With some probability, the symbol implies that the system is in one state when it is actually in the other. The ability to judge which state the system is in sets the efficiency of a Maxwell demon that observes state fluctuations in order to extract heat from a coupled reservoir. The state-inference problem is to infer the underlying state from such noisy measurements at each time step. We show that there can be a phase transition in such measurements: for measurement error rates below a certain threshold, the inferred state always matches the observation. For higher error rates, there can be continuous or discontinuous transitions to situations where keeping a memory of past observations improves the state estimate. We can partly understand this behavior by mapping the HMM onto a 1d random-field Ising model at zero temperature. We also present more recent work that explores a larger parameter space and more states. Research funded by NSERC, Canada.
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
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.
Generator estimation of Markov jump processes
NASA Astrophysics Data System (ADS)
Metzner, P.; Dittmer, E.; Jahnke, T.; Schütte, Ch.
2007-11-01
Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782-805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419-441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753-764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421-430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395-410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.
Teaching Higher Order Thinking in the Introductory MIS Course: A Model-Directed Approach
ERIC Educational Resources Information Center
Wang, Shouhong; Wang, Hai
2011-01-01
One vision of education evolution is to change the modes of thinking of students. Critical thinking, design thinking, and system thinking are higher order thinking paradigms that are specifically pertinent to business education. A model-directed approach to teaching and learning higher order thinking is proposed. An example of application of the…
On Markov parameters in system identification
NASA Technical Reports Server (NTRS)
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
NASA Astrophysics Data System (ADS)
Lalande, Jean-Marie; Waxler, Roger; Velea, Doru
2016-04-01
As infrasonic waves propagate at long ranges through atmospheric ducts it has been suggested that observations of such waves can be used as a remote sensing techniques in order to update properties such as temperature and wind speed. In this study we investigate a new inverse approach based on Markov Chain Monte Carlo methods. This approach as the advantage of searching for the full Probability Density Function in the parameter space at a lower computational cost than extensive parameters search performed by the standard Monte Carlo approach. We apply this inverse methods to observations from the Humming Roadrunner experiment (New Mexico) and discuss implications for atmospheric updates, explosion characterization, localization and yield estimation.
Markov counting models for correlated binary responses.
Crawford, Forrest W; Zelterman, Daniel
2015-07-01
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many previous models for correlated outcomes, admits easily interpretable parameterizations, allows different cluster sizes, and incorporates ascertainment bias in a natural way. We demonstrate several new models for dependent outcomes and provide algorithms for computing maximum likelihood estimates. We show how to incorporate cluster-specific covariates in a regression setting and demonstrate improved fits to well-known datasets from familial disease epidemiology and developmental toxicology. PMID:25792624
A new approach to the implementation of direct care-provider order entry.
Geissbühler, A.; Miller, R. A.
1996-01-01
Successful implementation of direct computer-based care-provider order entry traditionally relies on one of two different approaches development from scratch or installation of a commercial product. The former requires extensive resources; the latter, by its proprietary nature, limits extension of the system beyond capabilities supplied by the vendor. This paper describes an intermediate approach using the association of a locally-developed and controlled set of distributed microcomputer based applications and a commercial, mainframe-based order entry application used as an order transaction processing system. This combination provides both an intuitive user interface and a platform for implementing clinical decision-support tools. PMID:8947753
Alignment of multiple proteins with an ensemble of Hidden Markov Models
Song, Yinglei; Qu, Junfeng; Hura, Gurdeep S.
2011-01-01
In this paper, we developed a new method that progressively construct and update a set of alignments by adding sequences in certain order to each of the existing alignments. Each of the existing alignments is modelled with a profile Hidden Markov Model (HMM) and an added sequence is aligned to each of these profile HMMs. We introduced an integer parameter for the number of profile HMMs. The profile HMMs are then updated based on the alignments with leading scores. Our experiments on BaliBASE showed that our approach could efficiently explore the alignment space and significantly improve the alignment accuracy. PMID:20376922
NASA Astrophysics Data System (ADS)
Granat, R. A.; Clayton, R.; Kedar, S.; Kaneko, Y.
2003-12-01
We employ a robust hidden Markov model (HMM) based technique to perform statistical pattern analysis of suspected seismic and aseismic events in the poorly explored period band of minutes to hours. The technique allows us to classify known events and provides a statistical basis for finding and cataloging similar events represented elsewhere in the observations. In this work, we focus on data collected by the Southern California TriNet system. The hidden Markov model (HMM) approach assumes that the observed data has been generated by an unobservable dynamical statistical process. The process is of a particular form such that each observation is coincident with the system being in a particular discrete state. The dynamics are the model are constructed so that the next state is directly dependent only on the current state -- it is a first order Markov process. The model is completely described by a set of parameters: the initial state probabilities, the first order Markov chain state-to-state transition probabilities, and the probability distribution of observable outputs associated with each state. Application of the model to data involves optimizing these model parameters with respect to some function of the observations, typically the likelihood of the observations given the model. Our work focused on the fact that this objective function has a number of local maxima that is exponential in the model size (the number of states). This means that not only is it very difficult to discover the global maximum, but also that results can vary widely between applications of the model. For some domains which employ HMMs for such purposes, such as speech processing, sufficient a priori information about the system is available to avoid this problem. However, for seismic data in general such a priori information is not available. Our approach involves analytical location of sub-optimal local maxima; once the locations of these maxima have been found, then we can employ a
Likelihood free inference for Markov processes: a comparison.
Owen, Jamie; Wilkinson, Darren J; Gillespie, Colin S
2015-04-01
Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka-Volterra predator-prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schlögl system, a test case which exhibits bi-modal state stability in some regions of parameter space. PMID:25720092
Efficient maximum likelihood parameterization of continuous-time Markov processes
McGibbon, Robert T.; Pande, Vijay S.
2015-01-01
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce a maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models such as detailed balance. We demonstrate and discuss the advantages of these models over existing discrete-time Markov models for the analysis of molecular dynamics simulations. PMID:26203016
Assessment of optimized Markov models in protein fold classification.
Lampros, Christos; Simos, Thomas; Exarchos, Themis P; Exarchos, Konstantinos P; Papaloukas, Costas; Fotiadis, Dimitrios I
2014-08-01
Protein fold classification is a challenging task strongly associated with the determination of proteins' structure. In this work, we tested an optimization strategy on a Markov chain and a recently introduced Hidden Markov Model (HMM) with reduced state-space topology. The proteins with unknown structure were scored against both these models. Then the derived scores were optimized following a local optimization method. The Protein Data Bank (PDB) and the annotation of the Structural Classification of Proteins (SCOP) database were used for the evaluation of the proposed methodology. The results demonstrated that the fold classification accuracy of the optimized HMM was substantially higher compared to that of the Markov chain or the reduced state-space HMM approaches. The proposed methodology achieved an accuracy of 41.4% on fold classification, while Sequence Alignment and Modeling (SAM), which was used for comparison, reached an accuracy of 38%. PMID:25152041
Students' Progress throughout Examination Process as a Markov Chain
ERIC Educational Resources Information Center
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
On a Result for Finite Markov Chains
ERIC Educational Resources Information Center
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
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.
Nonparametric identification and maximum likelihood estimation for hidden Markov models
Alexandrovich, G.; Holzmann, H.; Leister, A.
2016-01-01
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop a nonparametric maximum likelihood estimation theory. First, we show that the asymptotic contrast, the Kullback–Leibler divergence of the hidden Markov model, also identifies the true parameter vector nonparametrically. Second, for classes of state-dependent densities which are arbitrary mixtures of a parametric family, we establish the consistency of the nonparametric maximum likelihood estimator. Here, identification of the mixing distributions need not be assumed. Numerical properties of the estimates and of nonparametric goodness of fit tests are investigated in a simulation study.
Bayesian restoration of a hidden Markov chain with applications to DNA sequencing.
Churchill, G A; Lazareva, B
1999-01-01
Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution determined by the state of the hidden Markov chain. We present a Bayesian solution to the problem of restoring the sequence of states visited by the hidden Markov chain from a given sequence of observed outputs. Our approach is based on a Monte Carlo Markov chain algorithm that allows us to draw samples from the full posterior distribution of the hidden Markov chain paths. The problem of estimating the probability of individual paths and the associated Monte Carlo error of these estimates is addressed. The method is illustrated by considering a problem of DNA sequence multiple alignment. The special structure for the hidden Markov model used in the sequence alignment problem is considered in detail. In conclusion, we discuss certain interesting aspects of biological sequence alignments that become accessible through the Bayesian approach to HMM restoration. PMID:10421527
Robust Hidden Markov Models for Geophysical Data Analysis
NASA Astrophysics Data System (ADS)
Granat, R. A.
2002-12-01
We employed robust hidden Markov models (HMMs) to perform statistical analysis of seismic events and crustal deformation. These models allowed us to classify different kinds of events or modes of deformation, and furthermore gave us a statistical basis for understanding relationships between different classes. A hidden Markov model is a statistical model for ordered data (typically in time). The observed data is assumed to have been generated by an unobservable statistical process of a particular form. This process is such that each observation is coincident with the system being in a particular discrete state. Furthermore, the next state is dependent on the current state; in other words, it is a first order Markov process. The model is completely described by a set of model parameters: the initial state probabilities, the first order Markov chain state-to-state transition probabilities, and the probabilities of observable outputs associated with each state. Application of the model to data involves optimizing these model parameters with respect to some function of the observations, typically the likelihood of the observations given the model. Our work focused on the fact that this objective function typically has a number of local maxima that is exponential in the model size (the number of states). This means that not only is it very difficult to discover the global maximum, but also that results can vary widely between applications of the model. For some domains, such as speech processing, sufficient a priori information about the system is available such that this problem can be avoided. However, for general scientific analysis, such a priori information is often not available, especially in cases where the HMM is being used as an exploratory tool for scientific understanding. Such was the case for the geophysical data sets used in this work. Our approach involves analytical location of sub-optimal local maxima; once the locations of these maxima have been found
A fourth order spline collocation approach for a business cycle model
NASA Astrophysics Data System (ADS)
Sayfy, A.; Khoury, S.; Ibdah, H.
2013-10-01
A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.
Modelling modal gating of ion channels with hierarchical Markov models
Fackrell, Mark; Crampin, Edmund J.; Taylor, Peter
2016-01-01
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models. PMID:27616917
[Towards a clinical approach in institutions in order to enable dreams].
Ponroy, Annabelle
2013-01-01
Care protocols and their proliferation tend to dampen the enthusiasm of professionals in their daily practice. An institution's clinical approach must be designed in terms of admission in order notto leave madness on the threshold of care. Trusting the enthusiasm and desire of nurses means favouring creativity within practices. PMID:24059145
Contemplative Practices and Orders of Consciousness: A Constructive-Developmental Approach
ERIC Educational Resources Information Center
Silverstein, Charles H.
2012-01-01
This qualitative study explores the correspondence between contemplative practices and "orders of consciousness" from a constructive-developmental perspective, using Robert Kegan's approach. Adult developmental growth is becoming an increasingly important influence on humanity's ability to deal effectively with the growing…
NASA Astrophysics Data System (ADS)
Garcia Fernandez, M.; Butala, M.; Komjathy, A.; Desai, S. D.
2012-12-01
Correcting GNSS tracking data for the effects of second order ionospheric effects have been shown to cause a southward shift in GNSS-based precise point positioning solutions by as much as 10 mm, depending on the solar cycle conditions. The most commonly used approaches for modeling the higher order ionospheric effect include, (a) the use of global ionosphere maps to determine vertical total electron content (VTEC) and convert to slant TEC (STEC) assuming a thin shell ionosphere, and (b) using the dual-frequency measurements themselves to determine STEC. The latter approach benefits from not requiring ionospheric mapping functions between VTEC and STEC. However, this approach will require calibrations with receiver and transmitter Differential Code Biases (DCBs). We present results from comparisons of the two approaches. For the first approach, we also compare the use of VTEC observations from IONEX maps compared to climatological model-derived VTEC as provided by the International Reference Ionosphere (IRI2012). We consider various metrics to evaluate the relative performance of the different approaches, including station repeatability, GNSS-based reference frame recovery, and post-fit measurement residuals. Overall, the GIM-based approaches tend to provide lower noise in second order ionosphere correction and positioning solutions. The use of IONEX and IRI2012 models of VTEC provide similar results, especially in periods of low solar activity periods. The use of the IRI2012 model provides a convenient approach for operational scenarios by eliminating the dependence on routine updates of the GIMs, and also serves as a useful source of VTEC when IONEX maps may not be readily available.
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
NASA Astrophysics Data System (ADS)
Poya, Roman; Sevilla, Ruben; Gil, Antonio J.
2016-06-01
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
NASA Astrophysics Data System (ADS)
Poya, Roman; Sevilla, Ruben; Gil, Antonio J.
2016-09-01
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
Hidden order and flux attachment in symmetry-protected topological phases: A Laughlin-like approach
NASA Astrophysics Data System (ADS)
Ringel, Zohar; Simon, Steven H.
2015-05-01
Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here, we introduce a new approach for generating SPT ground states, based on a generalization of the Laughlin wave function. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wave functions obtained in this manner and group cohomology wave functions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wave function obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.
A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2009-01-01
We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.
Markov Chain Monte Carlo and Irreversibility
NASA Astrophysics Data System (ADS)
Ottobre, Michela
2016-06-01
Markov Chain Monte Carlo (MCMC) methods are statistical methods designed to sample from a given measure π by constructing a Markov chain that has π as invariant measure and that converges to π. Most MCMC algorithms make use of chains that satisfy the detailed balance condition with respect to π; such chains are therefore reversible. On the other hand, recent work [18, 21, 28, 29] has stressed several advantages of using irreversible processes for sampling. Roughly speaking, irreversible diffusions converge to equilibrium faster (and lead to smaller asymptotic variance as well). In this paper we discuss some of the recent progress in the study of nonreversible MCMC methods. In particular: i) we explain some of the difficulties that arise in the analysis of nonreversible processes and we discuss some analytical methods to approach the study of continuous-time irreversible diffusions; ii) most of the rigorous results on irreversible diffusions are available for continuous-time processes; however, for computational purposes one needs to discretize such dynamics. It is well known that the resulting discretized chain will not, in general, retain all the good properties of the process that it is obtained from. In particular, if we want to preserve the invariance of the target measure, the chain might no longer be reversible. Therefore iii) we conclude by presenting an MCMC algorithm, the SOL-HMC algorithm [23], which results from a nonreversible discretization of a nonreversible dynamics.
A Markov model of the Indus script
Rao, Rajesh P. N.; Yadav, Nisha; Vahia, Mayank N.; Joglekar, Hrishikesh; Adhikari, R.; Mahadevan, Iravatham
2009-01-01
Although no historical information exists about the Indus civilization (flourished ca. 2600–1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571
A Markov model of the Indus script.
Rao, Rajesh P N; Yadav, Nisha; Vahia, Mayank N; Joglekar, Hrishikesh; Adhikari, R; Mahadevan, Iravatham
2009-08-18
Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571
Approximating Markov Chains: What and why
Pincus, S.
1996-06-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to {open_quote}{open_quote}solve,{close_quote}{close_quote} or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the {ital attractor}, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. {copyright} {ital 1996 American Institute of Physics.}
Equilibrium Control Policies for Markov Chains
Malikopoulos, Andreas
2011-01-01
The average cost criterion has held great intuitive appeal and has attracted considerable attention. It is widely employed when controlling dynamic systems that evolve stochastically over time by means of formulating an optimization problem to achieve long-term goals efficiently. The average cost criterion is especially appealing when the decision-making process is long compared to other timescales involved, and there is no compelling motivation to select short-term optimization. This paper addresses the problem of controlling a Markov chain so as to minimize the average cost per unit time. Our approach treats the problem as a dual constrained optimization problem. We derive conditions guaranteeing that a saddle point exists for the new dual problem and we show that this saddle point is an equilibrium control policy for each state of the Markov chain. For practical situations with constraints consistent to those we study here, our results imply that recognition of such saddle points may be of value in deriving in real time an optimal control policy.
Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
NASA Astrophysics Data System (ADS)
Vidybida, Alexander K.
2015-09-01
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order.
Higher-order prediction terms and fixing the renormalization scale using the BLM approach
NASA Astrophysics Data System (ADS)
Mirjalili, Abolfazl; Khellat, Mohammad Reza
2014-12-01
There is an ambiguity in the perturbative series of QCD observables on how to choose the renormalization and even more the factorization scale. There are many approaches to overcome this obstacle and to fix the scales. Among them, there is the Brodsky-Lepage-Mackenzie (BLM) approach which is based on an intriguing principle. Based on the BLM approach, we intend to absorb the nf-terms in the pQCD series that rightly determines the running behavior of the running coupling into the running coupling. We make an extensive use of the BLM approach to investigate the details of predicting higher order correction terms of some QCD observables. By this way we test different methods to improve the prediction process. It is also found out that an overall normalization could change BLM predictions effectively.
NASA Astrophysics Data System (ADS)
Bauer, Johannes; Sachdev, Subir
2015-08-01
We study charge-ordered solutions for fermions on a square lattice interacting with dynamic antiferromagnetic fluctuations. Our approach is based on real-space Eliashberg equations, which are solved self-consistently. We first show that the antiferromagnetic fluctuations can induce arc features in the spectral functions, as spectral weight is suppressed at the hot spots; however, no real pseudogap is generated. At low temperature, spontaneous charge order with a d -form factor can be stabilized for certain parameters. As long as the interacting Fermi surfaces possess hot spots, the ordering wave vector corresponds to the diagonal connection of the hot spots, similar to the non-self-consistent case. Tendencies towards observed axial order only appear in situations without hot spots.
The Analysis of Rush Orders Risk in Supply Chain: A Simulation Approach
NASA Technical Reports Server (NTRS)
Mahfouz, Amr; Arisha, Amr
2011-01-01
Satisfying customers by delivering demands at agreed time, with competitive prices, and in satisfactory quality level are crucial requirements for supply chain survival. Incidence of risks in supply chain often causes sudden disruptions in the processes and consequently leads to customers losing their trust in a company's competence. Rush orders are considered to be one of the main types of supply chain risks due to their negative impact on the overall performance, Using integrated definition modeling approaches (i.e. IDEF0 & IDEF3) and simulation modeling technique, a comprehensive integrated model has been developed to assess rush order risks and examine two risk mitigation strategies. Detailed functions sequence and objects flow were conceptually modeled to reflect on macro and micro levels of the studied supply chain. Discrete event simulation models were then developed to assess and investigate the mitigation strategies of rush order risks, the objective of this is to minimize order cycle time and cost.
Multiensemble Markov models of molecular thermodynamics and kinetics
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
Multiensemble Markov models of molecular thermodynamics and kinetics.
Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank
2016-06-01
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
Yao, Weiguang; Leszczynski, Konrad W
2009-07-01
Recently, the authors proposed an analytical scheme to estimate the first order x-ray scatter by approximating the Klein-Nishina formula so that the first order scatter fluence is expressed as a function of the primary photon fluence on the detector. In this work, the authors apply the scheme to experimentally obtained 6 MV cone beam CT projections in which the primary photon fluence is the unknown of interest. With the assumption that the higher-order scatter fluence is either constant or proportional to the first order scatter fluence, an iterative approach is proposed to estimate both primary and scatter fluences from projections by utilizing their relationship. The iterative approach is evaluated by comparisons with experimentally measured scatter-primary ratios of a Catphan phantom and with Monte Carlo simulations of virtual phantoms. The convergence of the iterations is fast and the accuracy of scatter correction is high. For a sufficiently long cylindrical water phantom with 10 cm of radius, the relative error of estimated primary photon fluence was within +/- 2% and +/- 4% when the phantom was projected with 6 MV and 120 kVp x-ray imaging systems, respectively. In addition, the iterative approach for scatter estimation is applied to 6 MV x-ray projections of a QUASAR and anthropomorphic phantoms (head and pelvis). The scatter correction is demonstrated to significantly improve the accuracy of the reconstructed linear attenuation coefficient and the contrast of the projections and reconstructed volumetric images generated with a linac 6 MV beam. PMID:19673214
Symbolic Heuristic Search for Factored Markov Decision Processes
NASA Technical Reports Server (NTRS)
Morris, Robert (Technical Monitor); Feng, Zheng-Zhu; Hansen, Eric A.
2003-01-01
We describe a planning algorithm that integrates two approaches to solving Markov decision processes with large state spaces. State abstraction is used to avoid evaluating states individually. Forward search from a start state, guided by an admissible heuristic, is used to avoid evaluating all states. We combine these two approaches in a novel way that exploits symbolic model-checking techniques and demonstrates their usefulness for decision-theoretic planning.
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.
Orbiting binary black hole evolutions with a multipatch high order finite-difference approach
Pazos, Enrique; Tiglio, Manuel; Duez, Matthew D.; Kidder, Lawrence E.; Teukolsky, Saul A.
2009-07-15
We present numerical simulations of orbiting black holes for around 12 cycles, using a high order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to adaptive mesh refinement, with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.
Mapping eQTL Networks with Mixed Graphical Markov Models
Tur, Inma; Roverato, Alberto; Castelo, Robert
2014-01-01
Expression quantitative trait loci (eQTL) mapping constitutes a challenging problem due to, among other reasons, the high-dimensional multivariate nature of gene-expression traits. Next to the expression heterogeneity produced by confounding factors and other sources of unwanted variation, indirect effects spread throughout genes as a result of genetic, molecular, and environmental perturbations. From a multivariate perspective one would like to adjust for the effect of all of these factors to end up with a network of direct associations connecting the path from genotype to phenotype. In this article we approach this challenge with mixed graphical Markov models, higher-order conditional independences, and q-order correlation graphs. These models show that additive genetic effects propagate through the network as function of gene–gene correlations. Our estimation of the eQTL network underlying a well-studied yeast data set leads to a sparse structure with more direct genetic and regulatory associations that enable a straightforward comparison of the genetic control of gene expression across chromosomes. Interestingly, it also reveals that eQTLs explain most of the expression variability of network hub genes. PMID:25271303
Kerfriden, P.; Goury, O.; Rabczuk, T.; Bordas, S.P.A.
2013-01-01
We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. PMID:23750055
Bayesian seismic tomography by parallel interacting Markov chains
NASA Astrophysics Data System (ADS)
Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas
2014-05-01
The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the
NASA Astrophysics Data System (ADS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2016-09-01
We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time.
Lagrange-Function Approach to Real-Space Order-N Electronic-Structure Calculations
Varga, Kalman; Pantelides, Sokrates T
2006-01-01
The Lagrange functions are a family of analytical, complete, and orthonormal basis sets that are suitable for efficient, accurate, real-space, order-N electronic-structure calculations. Convergence is controlled by a single monotonic parameter, the dimension of the basis set, and computational complexity is lower than that of conventional approaches. In this paper we review their construction and applications in linearscaling electronic-structure calculations.
Markov Models and the Ensemble Kalman Filter for Estimation of Sorption Rates
NASA Astrophysics Data System (ADS)
Vugrin, E. D.; McKenna, S. A.; White Vugrin, K.
2007-12-01
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude. Sandia is a multi program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000. This work was supported under the Sandia Laboratory Directed Research and Development program.
Multivariate longitudinal data analysis with mixed effects hidden Markov models.
Raffa, Jesse D; Dubin, Joel A
2015-09-01
Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. PMID:25761965
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.
Plume mapping via hidden Markov methods.
Farrell, J A; Pang, Shuo; Li, Wei
2003-01-01
This paper addresses the problem of mapping likely locations of a chemical source using an autonomous vehicle operating in a fluid flow. The paper reviews biological plume-tracing concepts, reviews previous strategies for vehicle-based plume tracing, and presents a new plume mapping approach based on hidden Markov methods (HMM). HMM provide efficient algorithms for predicting the likelihood of odor detection versus position, the likelihood of source location versus position, the most likely path taken by the odor to a given location, and the path between two points most likely to result in odor detection. All four are useful for solving the odor source localization problem using an autonomous vehicle. The vehicle is assumed to be capable of detecting above threshold chemical concentration and sensing the fluid flow velocity at the vehicle location. The fluid flow is assumed to vary with space and time, and to have a high Reynolds number (Re>10). PMID:18238238
Multiple alignment using hidden Markov models
Eddy, S.R.
1995-12-31
A simulated annealing method is described for training hidden Markov models and producing multiple sequence alignments from initially unaligned protein or DNA sequences. Simulated annealing in turn uses a dynamic programming algorithm for correctly sampling suboptimal multiple alignments according to their probability and a Boltzmann temperature factor. The quality of simulated annealing alignments is evaluated on structural alignments of ten different protein families, and compared to the performance of other HMM training methods and the ClustalW program. Simulated annealing is better able to find near-global optima in the multiple alignment probability landscape than the other tested HMM training methods. Neither ClustalW nor simulated annealing produce consistently better alignments compared to each other. Examination of the specific cases in which ClustalW outperforms simulated annealing, and vice versa, provides insight into the strengths and weaknesses of current hidden Maxkov model approaches.
Markov state models of biomolecular conformational dynamics
Chodera, John D.; Noé, Frank
2014-01-01
It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges. PMID:24836551
Growth and Dissolution of Macromolecular Markov Chains
NASA Astrophysics Data System (ADS)
Gaspard, Pierre
2016-07-01
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.
Behavior Detection using Confidence Intervals of Hidden Markov Models
Griffin, Christopher H
2009-01-01
Markov models are commonly used to analyze real-world problems. Their combination of discrete states and stochastic transitions is suited to applications with deterministic and stochastic components. Hidden Markov Models (HMMs) are a class of Markov model commonly used in pattern recognition. Currently, HMMs recognize patterns using a maximum likelihood approach. One major drawback with this approach is that data observations are mapped to HMMs without considering the number of data samples available. Another problem is that this approach is only useful for choosing between HMMs. It does not provide a criteria for determining whether or not a given HMM adequately matches the data stream. In this work, we recognize complex behaviors using HMMs and confidence intervals. The certainty of a data match increases with the number of data samples considered. Receiver Operating Characteristic curves are used to find the optimal threshold for either accepting or rejecting a HMM description. We present one example using a family of HMM's to show the utility of the proposed approach. A second example using models extracted from a database of consumer purchases provides additional evidence that this approach can perform better than existing techniques.
Fuzzy Markov random fields versus chains for multispectral image segmentation.
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. PMID:17063681
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.
Comparing quantum versus Markov random walk models of judgements measured by rating scales
Wang, Z.; Busemeyer, J. R.
2016-01-01
Quantum and Markov random walk models are proposed for describing how people evaluate stimuli using rating scales. To empirically test these competing models, we conducted an experiment in which participants judged the effectiveness of public health service announcements from either their own personal perspective or from the perspective of another person. The order of the self versus other judgements was manipulated, which produced significant sequential effects. The quantum and Markov models were fitted to the data using the same number of parameters, and the model comparison strongly supported the quantum over the Markov model. PMID:26621984
COCIS: Markov processes in single molecule fluorescence
Talaga, David S.
2009-01-01
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system. PMID:19543444
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.
Bayesian Markov models consistently outperform PWMs at predicting motifs in nucleotide sequences.
Siebert, Matthias; Söding, Johannes
2016-07-27
Position weight matrices (PWMs) are the standard model for DNA and RNA regulatory motifs. In PWMs nucleotide probabilities are independent of nucleotides at other positions. Models that account for dependencies need many parameters and are prone to overfitting. We have developed a Bayesian approach for motif discovery using Markov models in which conditional probabilities of order k - 1 act as priors for those of order k This Bayesian Markov model (BaMM) training automatically adapts model complexity to the amount of available data. We also derive an EM algorithm for de-novo discovery of enriched motifs. For transcription factor binding, BaMMs achieve significantly (P = 1/16) higher cross-validated partial AUC than PWMs in 97% of 446 ChIP-seq ENCODE datasets and improve performance by 36% on average. BaMMs also learn complex multipartite motifs, improving predictions of transcription start sites, polyadenylation sites, bacterial pause sites, and RNA binding sites by 26-101%. BaMMs never performed worse than PWMs. These robust improvements argue in favour of generally replacing PWMs by BaMMs. PMID:27288444
A New Approach for Constructing Highly Stable High Order CESE Schemes
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2010-01-01
A new approach is devised to construct high order CESE schemes which would avoid the common shortcomings of traditional high order schemes including: (a) susceptibility to computational instabilities; (b) computational inefficiency due to their local implicit nature (i.e., at each mesh points, need to solve a system of linear/nonlinear equations involving all the mesh variables associated with this mesh point); (c) use of large and elaborate stencils which complicates boundary treatments and also makes efficient parallel computing much harder; (d) difficulties in applications involving complex geometries; and (e) use of problem-specific techniques which are needed to overcome stability problems but often cause undesirable side effects. In fact it will be shown that, with the aid of a conceptual leap, one can build from a given 2nd-order CESE scheme its 4th-, 6th-, 8th-,... order versions which have the same stencil and same stability conditions of the 2nd-order scheme, and also retain all other advantages of the latter scheme. A sketch of multidimensional extensions will also be provided.
High-order fully general-relativistic hydrodynamics: new approaches and tests
NASA Astrophysics Data System (ADS)
Radice, David; Rezzolla, Luciano; Galeazzi, Filippo
2014-04-01
We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars (Radice et al 2014 Mon. Not. R. Astron. Soc. 437 L46-L50). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late-inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or more.
Markov constant and quantum instabilities
NASA Astrophysics Data System (ADS)
Pelantová, Edita; Starosta, Štěpán; Znojil, Miloslav
2016-04-01
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.
Adaptive relaxation for the steady-state analysis of Markov chains
NASA Technical Reports Server (NTRS)
Horton, Graham
1994-01-01
We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.
Approach Detect Sensor System by Second Order Derivative of Laser Irradiation Area
NASA Astrophysics Data System (ADS)
Hayashi, Tomohide; Yano, Yoshikazu; Tsuda, Norio; Yamada, Jun
In recent years, as a result of a large amount of greenhouse gas emission, atmosphere temperature at ground level gradually rises. Therefore the Kyoto Protocol was adopted to solve the matter in 1997. By the energy-saving law amended in 1999, it is advisable that an escalator is controlled to pause during no user. Now a photo-electric sensor is used to control escalator, but a pole to install the sensor is needed. Then, a new type of approach detection sensor using laser diode, CCD camera and CPLD, which can be built-in escalator, has been studied. This sensor can derive the irradiated area of laser beam by simple processing in which the laser beam is irradiated in only the odd field of the interlace video signal. By second order derivative of laser irradiated area, this sensor can detect only the approaching target but can not detect the target which crosses and stands in the sensing area.
A preference-ordered discrete-gaming approach to air-combat analysis
NASA Technical Reports Server (NTRS)
Kelley, H. J.; Lefton, L.
1978-01-01
An approach to one-on-one air-combat analysis is described which employs discrete gaming of a parameterized model featuring choice between several closed-loop control policies. A preference-ordering formulation due to Falco is applied to rational choice between outcomes: win, loss, mutual capture, purposeful disengagement, draw. Approximate optimization is provided by an active-cell scheme similar to Falco's obtained by a 'backing up' process similar to that of Kopp. The approach is designed primarily for short-duration duels between craft with large-envelope weaponry. Some illustrative computations are presented for an example modeled using constant-speed vehicles and very rough estimation of energy shifts.
The Core-Shell Approach to Formation of Ordered Nanoporous Materials
Chang, Jeong H.; Wang, Li Q.; Shin, Yongsoon; Jeong, Byeongmoon; Birnbaum, Jerome C.; Exarhos, Gregory J.
2002-03-04
This work describes a novel core-shell approach for the preparation of ordered nanoporous ceramic materials that involve a self-assembly process at the molecular level using MPEG-b-PDLLA bloack copolymers. This approach provides for rapid self-assembly and structural reorganization at room temperature. Selected MPEG-b-PDLLA block copolymers were synthesized with systematic variation of the chain lengths of the resident hydrophilic and hydrophobic blocks. This allows the micelle size to be systematically varied. Results from this work are used to understand the formation mechanism of nanoporous structures in which the pore size and wall thickness are closely dependent on the size of hydrophobic cores and hydrophilic shells of the block copolymer templates. The core-shell mechanism for nanoporous structure evolution is based on the size and contrasting micellar packing arrangements that are controlled by the copolymer.
Optimal Control of Markov Processes with Age-Dependent Transition Rates
Ghosh, Mrinal K. Saha, Subhamay
2012-10-15
We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2015-01-01
We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ODEs. We establish an important interconnection between the extended Prelle–Singer procedure and λ-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, λ-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.
Modeling two-vehicle crash severity by a bivariate generalized ordered probit approach.
Chiou, Yu-Chiun; Hwang, Cherng-Chwan; Chang, Chih-Chin; Fu, Chiang
2013-03-01
This study simultaneously models crash severity of both parties in two-vehicle accidents at signalized intersections in Taipei City, Taiwan, using a novel bivariate generalized ordered probit (BGOP) model. Estimation results show that the BGOP model performs better than the conventional bivariate ordered probit (BOP) model in terms of goodness-of-fit indices and prediction accuracy and provides a better approach to identify the factors contributing to different severity levels. According to estimated parameters in latent propensity functions and elasticity effects, several key risk factors are identified-driver type (age>65), vehicle type (motorcycle), violation type (alcohol use), intersection type (three-leg and multiple-leg), collision type (rear ended), and lighting conditions (night and night without illumination). Corresponding countermeasures for these risk factors are proposed. PMID:23246710
Reprint of "Modeling two-vehicle crash severity by a bivariate generalized ordered probit approach".
Chiou, Yu-Chiun; Hwang, Cherng-Chwan; Chang, Chih-Chin; Fu, Chiang
2013-12-01
This study simultaneously models crash severity of both parties in two-vehicle accidents at signalized intersections in Taipei City, Taiwan, using a novel bivariate generalized ordered probit (BGOP) model. Estimation results show that the BGOP model performs better than the conventional bivariate ordered probit (BOP) model in terms of goodness-of-fit indices and prediction accuracy and provides a better approach to identify the factors contributing to different severity levels. According to estimated parameters in latent propensity functions and elasticity effects, several key risk factors are identified-driver type (age>65), vehicle type (motorcycle), violation type (alcohol use), intersection type (three-leg and multiple-leg), collision type (rear ended), and lighting conditions (night and night without illumination). Corresponding countermeasures for these risk factors are proposed. PMID:23915470
A general approach to develop reduced order models for simulation of solid oxide fuel cell stacks
Pan, Wenxiao; Bao, Jie; Lo, Chaomei; Lai, Canhai; Agarwal, Khushbu; Koeppel, Brian J.; Khaleel, Mohammad A.
2013-06-15
A reduced order modeling approach based on response surface techniques was developed for solid oxide fuel cell stacks. This approach creates a numerical model that can quickly compute desired performance variables of interest for a stack based on its input parameter set. The approach carefully samples the multidimensional design space based on the input parameter ranges, evaluates a detailed stack model at each of the sampled points, and performs regression for selected performance variables of interest to determine the responsive surfaces. After error analysis to ensure that sufficient accuracy is established for the response surfaces, they are then implemented in a calculator module for system-level studies. The benefit of this modeling approach is that it is sufficiently fast for integration with system modeling software and simulation of fuel cell-based power systems while still providing high fidelity information about the internal distributions of key variables. This paper describes the sampling, regression, sensitivity, error, and principal component analyses to identify the applicable methods for simulating a planar fuel cell stack.
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
NASA Astrophysics Data System (ADS)
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.
Process-chain approach to high-order perturbation calculus for quantum lattice models
Eckardt, Andre
2009-05-15
A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3, and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].0.
A new approach to the higher order superintegrability of the Tremblay-Turbiner-Winternitz system
NASA Astrophysics Data System (ADS)
Rañada, Manuel F.
2012-11-01
The higher order superintegrability of systems separable in polar coordinates is studied using an approach that was previously applied for the study of the superintegrability of a generalized Smorodinsky-Winternitz system. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by M and N). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system and to the explicit expression of the constants of motion. A second family (related with the first one) of superintegrable systems is also studied.
An approach for generating the first order structure of multi-movable zoom lens
NASA Astrophysics Data System (ADS)
Song, Qiang; Huang, Hao; Lv, Xiangbo; Zhu, Jing; Huang, Huijie
2016-01-01
This work provides a method to obtain the first order structure of a zoom system based on particle swarm optimization (PSO) algorithm. The kinematic rule of a zoom system with fixed image plane is described by differential equations. PSO algorithm is introduced to solve the differential equations with considering both the merit functions and the boundary constraint. The smooth of the kinematic function of the zoom system is checked for considering the fabrication feasibility. Examples with two types of zoom system are presented for verifying the proposed method. This approach provides a powerful and practical tool for construction of a zoom structure.
Action approach to cosmological perturbations: the second-order metric in matter dominance
Boubekeur, Lotfi; Creminelli, Paolo; Vernizzi, Filippo; Norena, Jorge
2008-08-15
We study nonlinear cosmological perturbations during post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-({partial_derivative}{phi}){sup 2}]{sup (1+w)/2w}. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second-order metric during matter dominance in the comoving gauge directly as a function of the primordial inflationary perturbation {zeta}. Going to Poisson gauge, we recover the metric previously derived in the literature.
A second order residual based predictor-corrector approach for time dependent pollutant transport
NASA Astrophysics Data System (ADS)
Pavan, S.; Hervouet, J.-M.; Ricchiuto, M.; Ata, R.
2016-08-01
We present a second order residual distribution scheme for scalar transport problems in shallow water flows. The scheme, suitable for the unsteady cases, is obtained adapting to the shallow water context the explicit Runge-Kutta schemes for scalar equations [1]. The resulting scheme is decoupled from the hydrodynamics yet the continuity equation has to be considered in order to respect some important numerical properties at discrete level. Beyond the classical characteristics of the residual formulation presented in [1,2], we introduce the possibility to iterate the corrector step in order to improve the accuracy of the scheme. Another novelty is that the scheme is based on a precise monotonicity condition which guarantees the respect of the maximum principle. We thus end up with a scheme which is mass conservative, second order accurate and monotone. These properties are checked in the numerical tests, where the proposed approach is also compared to some finite volume schemes on unstructured grids. The results obtained show the interest in adopting the predictor-corrector scheme for pollutant transport applications, where conservation of the mass, monotonicity and accuracy are the most relevant concerns.
NASA Astrophysics Data System (ADS)
Maity, R.; Prasad, D.
2011-01-01
In this paper, Split Markov Process (SMP) is developed to assess one-step-ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process (MP) and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first-order Markov chain to simulate daily rainfall variation at a point through state/sub-state Transitional Probability Matrix (TPM). The state/sub-state TPM is based on the historical transitions from a particular state to a particular sub-state, which is the basic difference between SMP and general MP. In MP, the transition from a particular state to another state is investigated. However, in SMP, the daily rainfall magnitude is categorized into different states and change in magnitude from one temporal step to another is categorized into different sub-states for the probabilistic assessment of rainfall variation. The cumulative state/sub-state TPM is represented in a contour plot at different probability levels. The developed cumulative state/sub-state TPM is used to assess the possible range of rainfall in next time step, in a probabilistic sense. Application of SMP is investigated for daily rainfall at Khandwa station in the Nimar district of Madhya Pradesh, India. Eighty years of daily monsoon rainfall is used to develop the state/sub-state TPM and twenty years data is used to investigate its performance. It is observed that the predicted range of daily rainfall captures the actual observed rainfall with few exceptions. Overall, the assessed range, particularly the upper limit, provides a quantification possible extreme value in the next time step, which is very useful information to tackle the extreme events, such flooding, water logging etc.
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.
The sharp constant in Markov's inequality for the Laguerre weight
Sklyarov, Vyacheslav P
2009-06-30
We prove that the polynomial of degree n that deviates least from zero in the uniformly weighted metric with Laguerre weight is the extremal polynomial in Markov's inequality for the norm of the kth derivative. Moreover, the corresponding sharp constant does not exceed (8{sup k} n {exclamation_point} k {exclamation_point})/((n-k){exclamation_point} (2k){exclamation_point}). For the derivative of a fixed order this bound is asymptotically sharp as n{yields}{infinity}. Bibliography: 20 items.
Using Games to Teach Markov Chains
ERIC Educational Resources Information Center
Johnson, Roger W.
2003-01-01
Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…
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.
Generators of quantum Markov semigroups
NASA Astrophysics Data System (ADS)
Androulakis, George; Ziemke, Matthew
2015-08-01
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48, 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6, 211-216 (1955)], and Kraus [Ann. Phys. 64, 311-335 (1970)] imply that the generator of the semigroup has the form L ( A ) = ∑ n = 1 ∞ Vn ∗ A V n + G A + A G ∗ , where Vn and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus' result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains.
Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
Levi, Michele
2010-11-15
We use an effective field theory (EFT) approach to calculate the next-to-leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of nonstationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the nonrelativistic gravitational field parametrization, making the calculation more efficient with no need to rely on automated computations, and illustrating the coupling hierarchy of the different gravitational field components to the spin and mass sources. Finally, we show explicitly how to relate the EFT derived spin results to the canonical results obtained with the Arnowitt-Deser-Misner (ADM) Hamiltonian formalism. This is done using noncanonical transformations, required due to the implementation of covariant SSC, as well as canonical transformations at the level of the Hamiltonian, with no need to resort to the equations of motion or the Dirac brackets.
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Bungartz, H.J.
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
On the entropy of a hidden Markov process⋆
Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech
2008-01-01
We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order. PMID:19169438
Testing the Markov hypothesis in fluid flows
NASA Astrophysics Data System (ADS)
Meyer, Daniel W.; Saggini, Frédéric
2016-05-01
Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered.
Approach to the glass transition studied by higher order correlation functions
NASA Astrophysics Data System (ADS)
Lacevic, N.; Glotzer, S. C.
2003-08-01
We present a theoretical framework based on a higher order density correlation function, analogous to that used to investigate spin glasses, to describe dynamical heterogeneities in simulated glass-forming liquids. These higher order correlation functions are a four-point, time-dependent density correlation function g4(r,t) and a corresponding 'structure factor' S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times. g4(r,t) and S4(q,t) were extensively studied via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above in Franz et al (1999 Phil. Mag. B 79 1827), Donati et al (2002 J. Non-Cryst. Solids 307 215), Glotzer et al (2000 J. Chem. Phys. 112 509), Lacevic et al (2002 Phys. Rev. E 66 030101), Lacevic et al (2003 J. Chem. Phys. submitted) and Lacevic (2003 Dissertation The Johns Hopkins University). Here, we examine the contribution to g4(r,t), S4(q,t) and the corresponding dynamical correlation length, as well as the corresponding order parameter Q(t) and generalized susceptibility chi4(t), from localized particles. We show that the dynamical correlation length xi4SS(t) of localized particles has a maximum as a function of time t, and the value of the maximum of xi4SS(t) increases steadily in the temperature range approaching the mode coupling temperature from above.
Hidden Markov models for threat prediction fusion
NASA Astrophysics Data System (ADS)
Ross, Kenneth N.; Chaney, Ronald D.
2000-04-01
This work addresses the often neglected, but important problem of Level 3 fusion or threat refinement. This paper describes algorithms for threat prediction and test results from a prototype threat prediction fusion engine. The threat prediction fusion engine selectively models important aspects of the battlespace state using probability-based methods and information obtained from lower level fusion engines. Our approach uses hidden Markov models of a hierarchical threat state to find the most likely Course of Action (CoA) for the opposing forces. Decision tress use features derived from the CoA probabilities and other information to estimate the level of threat presented by the opposing forces. This approach provides the user with several measures associated with the level of threat, including: probability that the enemy is following a particular CoA, potential threat presented by the opposing forces, and likely time of the threat. The hierarchical approach used for modeling helps us efficiently represent the battlespace with a structure that permits scaling the models to larger scenarios without adding prohibitive computational costs or sacrificing model fidelity.
Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan
2013-05-13
In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations. PMID:23547230
Regeneration and Fixed-Width Analysis of Markov Chain Monte Carlo Algorithms
NASA Astrophysics Data System (ADS)
Latuszynski, Krzysztof
2009-07-01
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and sufficient conditions in terms of regeneration for central limit theorems for ergodic Markov chains and a regenerative proof of a CLT version for uniformly ergodic Markov chains with E_{π}f^2< infty. To obtain asymptotic confidence intervals for MCMC estimators, strongly consistent estimators of the asymptotic variance are essential. We relax assumptions required to obtain such estimators. Moreover, under a drift condition, nonasymptotic fixed-width results for MCMC estimators for a general state space setting (not necessarily compact) and not necessarily bounded target function f are obtained. The last chapter is devoted to the idea of adaptive Monte Carlo simulation and provides convergence results and law of large numbers for adaptive procedures under path-stability condition for transition kernels.
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy.
Abler, Daniel; Kanellopoulos, Vassiliki; Davies, Jim; Dosanjh, Manjit; Jena, Raj; Kirkby, Norman; Peach, Ken
2013-07-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of 'general Markov models', providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. PMID:23824126
Approach for LIDAR signals with multiple returns.
Yin, Wenye; He, Weiji; Gu, Guohua; Chen, Qian
2014-10-20
Time-correlated single photon counting (TCSPC) and burst illumination laser (BIL) data can be used for depth reconstruction of a target surface; the problem is how to analyze the response for the reconstruction. We propose a fast-approach STMCMC (Simulated Tempering Markov Chain Monte Carlo) for LIDAR signals with multiple return, in order to obtain a complete characterization of a 3D surface by the laser range system. STMCMC is used to explore the spaces by the preset distributions instead of the prior distributions. Added active intervention tempering makes the Markov chain mix better through the temporary expansion of the solutions. The added step keeps the operation under control and yet retains the Markov characteristic of the operation. The theoretical analysis and the demonstrations on the practical data show flexible operation, and the parameters can be estimated to a high degree of accuracy. PMID:25402782
NASA Technical Reports Server (NTRS)
Nese, Jon M.; Dutton, John A.
1993-01-01
The predictability of the weather and climatic states of a low-order moist general circulation model is quantified using a dynamic systems approach, and the effect of incorporating a simple oceanic circulation on predictability is evaluated. The predictability and the structure of the model attractors are compared using Liapunov exponents, local divergence rates, and the correlation and Liapunov dimensions. It was found that the activation of oceanic circulation increases the average error doubling time of the atmosphere and the coupled ocean-atmosphere system by 10 percent and decreases the variance of the largest local divergence rate by 20 percent. When an oceanic circulation develops, the average predictability of annually averaged states is improved by 25 percent and the variance of the largest local divergence rate decreases by 25 percent.
Photoassociation of a cold-atom-molecule pair. II. Second-order perturbation approach
Lepers, M.; Vexiau, R.; Bouloufa, N.; Dulieu, O.; Kokoouline, V.
2011-04-15
The electrostatic interaction between an excited atom and a diatomic ground-state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions competes with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 Bohr radii. Numerical results are given for the long-range interaction between Cs and Cs{sub 2}, showing that the photoassociation is probably efficient for any Cs{sub 2} rotational energy.
Multiple testing for neuroimaging via hidden Markov random field.
Shu, Hai; Nan, Bin; Koeppe, Robert
2015-09-01
Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative. PMID:26012881
Markov reliability models for digital flight control systems
NASA Technical Reports Server (NTRS)
Mcgough, John; Reibman, Andrew; Trivedi, Kishor
1989-01-01
The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.
General Approach to First-Order Error Prediction in Rigid Point Registration
Fitzpatrick, J. Michael
2015-01-01
A general approach to the first-order analysis of error in rigid point registration is presented that accommodates fiducial localization error (FLE) that may be inhomogeneous (varying from point to point) and anisotropic (varying with direction) and also accommodates arbitrary weighting that may also be inhomogeneous and anisotropic. Covariances are derived for target registration error (TRE) and for weighted fiducial registration error (FRE) in terms of covariances of FLE, culminating in a simple implementation that encompasses all combinations of weightings and anisotropy. Furthermore, it is shown that for ideal weighting, in which the weighting matrix for each fiducial equals the inverse of the square root of the cross covariance of its two-space FLE, fluctuations of FRE and TRE are mutually independent. These results are validated by comparison with previously published expressions and by simulation. Furthermore, simulations for randomly generated fiducial positions and FLEs are presented that show that correlation is negligible correlation coefficient < 0.1 in the exact case for both ideal and uniform weighting (i.e., no weighting), the latter of which is employed in commercial surgical guidance systems. From these results we conclude that for these weighting schemes, while valid expressions exist relating the covariance of FRE to the covariance of TRE, there are no measures of the goodness of fit of the fiducials for a given registration that give to first order any information about the fluctuation of TRE from its expected value and none that give useful information in the exact case. Therefore, as estimators of registration accuracy, such measures should be approached with extreme caution both by the purveyors of guidance systems and by the practitioners who use them. PMID:21075718
Investigation of Commuting Hamiltonian in Quantum Markov Network
NASA Astrophysics Data System (ADS)
Jouneghani, Farzad Ghafari; Babazadeh, Mohammad; Bayramzadeh, Rogayeh; Movla, Hossein
2014-08-01
Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.
NASA Astrophysics Data System (ADS)
Kroll, Herbert; Schlenz, Hartmut; Phillips, Michael W.
1994-12-01
The excess Gibbs free energy due to non-convergent ordering is described by a Landau expansion in which configurational and non-configurational entropy contributions are separated: 269_2004_Article_BF00203931_TeX2GIFE1.gif G^L = - hQ_t + tfrac{1}{2}a^* (T - T_c^* )Q_t^2 + tfrac{1}{n}e_n Q_t^n - TS_{conf \\cdot }^{ord} Neglecting higher order terms in Q t t, this expansion is formally equivalent to the reciprocal solution model for the distribution of Fe2+ and Mg over the non-equivalent M1 and M2 sites of orthopyroxenes: 269_2004_Article_BF00203931_TeX2GIFE2.gif begin{gathered} G^{ord} = - tfrac{1}{2}[Δ G_{exch}^0 - (L_{M1}^G - L_{M2}^G )X] + Q_t \\ {text{ + }}tfrac{1}{4}[Δ G_{rec}^0 - (L_{M2}^G - L_{M1}^G )] + Q_t^2 {text{ - }}TS_{{text{conf}}^ \\cdot }^{{text{ord}}} \\ The Q t term describes a temperature and composition-dependent thermodynamic field that prevents the crystal from attaining full disorder at a finite temperature. The X term models the dependence of the field on composition. It causes the isotherms in a Roozeboom diagram X{Fe/M2}vs. X{Fe/M1}to be asymmetric. The Q{t/2}term incorporates nearest-neighbour interactions. Higher order interactions are accounted for by the Q{t/n}term, which is not routinely foreseen in the reciprocal solution model. The critical temperature T{c/*}is interpreted as a ratio of enthalpy and entropy contributions to the free energy, ΔG{rec/0}, of a reciprocal reaction 269_2004_Article_BF00203931_TeX2GIFE3.gif T_c^* = {Δ H_{rec}^0 - (L_{M1}^H + L_{M2}^H )}/{Δ S_{rec^0 - (L_{M1}^S + L_{M2}^S )}}. The comparison of Landau and classical approaches is extended to convergent ordering models which are shown to be incorporated in expressions for non-convergent ordering.
Taheri, Shahrooz; Mat Saman, Muhamad Zameri; Wong, Kuan Yew
2013-01-01
One of the cost-intensive issues in managing warehouses is the order picking problem which deals with the retrieval of items from their storage locations in order to meet customer requests. Many solution approaches have been proposed in order to minimize traveling distance in the process of order picking. However, in practice, customer orders have to be completed by certain due dates in order to avoid tardiness which is neglected in most of the related scientific papers. Consequently, we proposed a novel solution approach in order to minimize tardiness which consists of four phases. First of all, weighted association rule mining has been used to calculate associations between orders with respect to their due date. Next, a batching model based on binary integer programming has been formulated to maximize the associations between orders within each batch. Subsequently, the order picking phase will come up which used a Genetic Algorithm integrated with the Traveling Salesman Problem in order to identify the most suitable travel path. Finally, the Genetic Algorithm has been applied for sequencing the constructed batches in order to minimize tardiness. Illustrative examples and comparisons are presented to demonstrate the proficiency and solution quality of the proposed approach. PMID:23864823
NASA Astrophysics Data System (ADS)
Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro
2012-03-01
The chemical zoning profile in metamorphic minerals is often used to deduce the pressure-temperature ( P- T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a new stochastic framework for estimating precise P- T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P- T path inversion. The most probable P- T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P- T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg-Fe-Ca garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed shape of the synthetic P- T path by eliminating appropriately the statistical compositional noises without operator's subjectivity and prior knowledge. It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse problems in petrology.
Entropy and long-range memory in random symbolic additive Markov chains
NASA Astrophysics Data System (ADS)
Melnik, S. S.; Usatenko, O. V.
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.
Entropy and long-range memory in random symbolic additive Markov chains.
Melnik, S S; Usatenko, O V
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory. PMID:27415245